THE UNIVERSITY OF ILLINOIS LIBRARY G'z:^.oa CG3c& CENTRAL CIRCULATION BOOKSTACKS The person charging this material is re- sponsible for its renewal or its return to the library from which it was borrowed on or before the Latest Date stamped below. You may be charged a minimum fee of $75.00 for each lost book. Thaff# mutilation, and underlining of books are reasons for disciplinory action ond moy result In dismissal from the University. TO RENEW CALL TELEPHONE CENTER, 333-8400 UNIVERSITY OF ILLINOIS LIBRARY AT URBANA-CHAMPAIGN ££021 099 When renewing by phone, write new due date below previous due date. L162 I THE UNIVERSITY OF ILLINOIS LIBRARY G'z:?.os CG^cS i 1 i V ■ ...n ^ ' t*, 3Bii£ ■Smeeviug Library Digitized by the Internet Archive in 2017 with funding from University of Illinois Urbana-Champaign Alternates https://archive.org/details/coalmetalminersp00unse_0 ' i--. r- ... li .'.aAL COAL^ METAL MINERS' POCKETBOOK OF PRINCIPLES, RUL'ES, FORMULAS, AND TABLES. SPECIALLY COMPILED AND PREPARED FOR THE CONVENIENT USE OF MINE OFFICIALS, MINING ENGINEERS, AND STUDENTS PREPAR- ING THEMSELVES FOR CERTIFICATES OF COMPETENCY AS MINE INSPECTORS OR MINE FOREMEN. EIGHTH 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.: INTERNATIONAL TEXTBOOK COMPANY, Copyright, 1890 , 1893 , 1900 , BY The Colliery Engineer CoMPi Copyright, 1902 , BY International Textbook Comp Entered at Stationers’ Hall, L( All Rights Reserved. PRINTED BY International Textbook Company, Scranton, Pa., U. S. A. 6ZZ.06 C&'icd Preface to Seventh Edition. The speedy exhaustion of the sixth edition of The Coal and Metal Miners^ Pocketbook, coupled with a steady and increas- ing demand for it, has made necessary this seventh edition. In it a few typographical errors which unavoidably occurred (as is the case in every book of this nature and size), have been corrected, all departments have been carefully revised, improved, and brought up to date, and considerable new matter has been added. Thus, the value of the work has been materially increased. The value of suggestions as to improve- ments in this edition made by users of the sixth edition is acknowledged with thanks, and we request that users of this new, or seventh, edition, will kindly call our attention to any errors or omissions they may discover, so that future editions may be kept fully abreast with the requirements of mining practice as such practice continues to advance. iii Preface to Sixth Edition. 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. 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 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. v VI 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 one 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 hack of volume. See also Glossary of Mining Terms, page 565.) WEIGHTS AND MEASURES. The Metric System.— 1. We IGHTS.— Troy, 1; Apothecaries’, 1; Avoirdupois, 2; Metric, 2. M EASU RES OF Le NOTH.— 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 \ Girths, 13; Board Measure, 13. Mathematios.— Ceneral Principles, 14; Signs and Abbreviations, 14. Arithmetic.— 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. M ENSU ration. Surfaces, 28; Solids, 33; Prismoidal Formula, 34. Plane Trigonometry.— 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. vii Vlll 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. Fr I CTi ON. —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 and Sheet-Metal Gauges, 122d. 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, 141; 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; Infiuence 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, 15-4; 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 Raised 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. IX 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. X TABLE OF CONTENTS. Opening a Min e.— 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, 260; Freezing Process, 260; Table of Well-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; Rock-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; I'lat 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, 335. 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 I^amps, 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. xl Workings, 360; Pressure as Affecting Explosive Conditions, 361; Rapid Succession of Shots in Close Workings, 361; Mine Explosions, 361; Recoil of an Explosion, 361; Exploring Workings After a Serious Explo- 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.— I^ouhle 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, 430; 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; Calum^'" TABLE OF CONTENTS. xii 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, ^ 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. = meter. 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.) = 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 = - kilogram. 3. The liter, or unit of liquid volume, is the volume of 1,000 cubic centi- meters of distilled water at 4° 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), hekto (100), kilo (1,000). The sub- multiples or divisions are obtained by prefixing the Latin words deci {^f), centi The abbreviations of these several units as mven 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. 2 WEIGHTS AND MEASURES. AVOIRDUPOIS WEIGHT. 27.34375 grains = 1 dram. 16 drams = 1 ounce 16 ounces = 1 pound 28 pounds = 1 quarter 4 quarters = 1 hundredweight 20 hundredweight = 1 ton 1 stone 1 quintal 1 “ short ton ” 1 “long ton” 1 ounce troy or apothecaries’ = 1.09714 1 pound troy or apothecaries’ = .82286 1 ounce avoirdupois = .911458 1 pound avoirdupois = 1.21528 = 437i grains. = 7,000 grains = 256 drams. = 448 ounces. = 112 pounds. = 2,240 pounds. = 14 pounds. = 100 pounds. = 2,000 pounds. = 2,240 pounds, avoirdupois ounces, avoirdupois pound, troy or apothecaries’ ounce, troy or apothecaries’ pounds. METRIC WEIGHT. 10 milligrams (mg.) 10 centigrams 10 decigrams 10 grams 10 decagrams 10 hectograms 10 kilograms 10 myriagrams 10 quintals = 1 centigram (eg.) = 1 decigram (dg.) = 1 gram (g.) = 1 decagram (Dg.) = 1 hectogram (Hg.) = 1 kilogram (Kg.) = 1 myriagram (Mg.) = 1 quintal (Q.) = 1 tonneau, millier, or tonne .15432 grain. 1.5432 grains. 15.432 grains. .0220461b. avoir. .22046 lb. avoir. , 2.2046 lb. avoir. 22.046 lb. avoir. 220.46 lb. avoir. 2,204 lb. 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 * = ll 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 ^ 12, or .58333 ft. To reduce fraxitions 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 TENTUS OF FOOT 1 2 ^ 4 i } f. , 7 , f. t 7 8 8 10 n 12 INCHES 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 7i 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. 0" 1" 2" 3" 4" 5" 6" 7" 8" 9" 10" 11" 0 0 .0833 .1667 .2500 .3333 .4167 .5000 .5833 .6667 .7500 .8333 .9167 .0026 .0859 .1693 .2526 .3359 .4193 .5026 .5859 .6693 .7526 .8359 .9193 .0052 .0885 .1719 .2552 .3386 .4219 .5052 .5885 .6719 .7552 .8385 .9219 .0078 .0911 .1745 .2578 .3411 .4245 .5078 .5911 .6745 .7578 .8411 .9245 h .0104 .0937 .1771 .2604 .3437 .4271 .5104 .5937 .6771 .7604 .8437 .9271 .0130 .0964 .1797 .2630 .3464 .4297 .5130 .5964 .6797 .7630 .8464 .9297 'h .0156 .0990 .1823 .2656 .3490 .4323 .5156 .5990 .6823 .7656 .8490 .9323 X .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 .0234 .1068 .1901 .2734 .3568 .4401 .5234 .6068 .6901 .7734 .8568 .9401 S .0260 .1094 .1927 .2760 .3594 .4427 .5260 .6094 .6927 .7760 .8594 .9427 .0286 .1120 .1953 .2786 .3620 .4453 .5286 .6120 .6953 .7786 .8620 .9453 1 .0312 .1146 .1979 .2812 .3646 .4479 .5312 .6146 .6979 .7812 .8646 .9479 .0339 .1172 .2005 .2839 .3672 .4505 .5339 .6172 .7005 .7839 .8672 .9505 X .0365 .1198 .2031 .2865 .3698 .4531 .5365 .6198 .7031 .7865 .8698 .9531 .0391 .1224 .2057 .2891 .3724 .4557 .5391 .6224 .7057 .7891 .8724 .9557 i .0417 .1250 .2083 .2917 .3750 .4583 .5417 .6250 .7083 .7917 .8750 .9583 .0443 .1276 .2109 .2943 .3776 .4609 .5443 .6276 .7109 .7943 .8776 .9609 .0469 .1302 .2135 .2969 .3802 .4635 .5469 .6302 .7135 .7969 .8802 .9635 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 .0547 .1380 .2214 .3047 .3880 .4714 .5547 .6380 .7214 .8047 .8880 .9714 a .0573 .1406 .2240 .3073 .3906 .4740 .5573 .6406 .7240 .8073 .8906 .9740 U .0599 .1432 .2266 .3099 .3932 .4766 .5599 .6432 .7266 .8099 .8932 .9766 i .0625 .1458 .2292 .3125 .3958 .4792 .5625 .6458 .7292 .8125 .8958 .9792 §1 .0651 .1484 .2318 .3151 .3984 .4818 .5651 .6484 .7318 .8151 .8984 .9818 H .0677 .1510 .2344 .3177 .4010 .4844 .5677 .6510 .7344 .8177 .9010 .9844 1 ? .0703 .1536 .2370 .3203 .4036 .4870 .5703 .6536 .7370 .8203 .9036 .9870 1 .0729 .1562 .2396 .3229 .4062 .4896 .5729 .6562 .7396 .8229 .9062 .9896 If .0755 .1589 .2422 .3255 .4089 .4922 .5755 .6589 .7422 .8255 .9089 .9922 H .0781 .1615 .2448 .3281 .4115 .4948 .5781 .6615 .7448 .8281 .9115 .9948 .0807 .1641 .2474 .3307 .4141 .4974 .5807 .6641 .7474 .8307 .9141 .9974 10 millimeters (mm.) 10 centimeters 10 decimeters 10 meters 10 decameters 10 hectometers 10 kilometers METRIC SYSTEM. = 1 centimeter (cm.) = 1 decimeter (dm.) = 1 meter (m.) = 1 decameter (Dm.) = 1 hectometer (Hm.) = 1 kilometer (Km.) = 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. 4 WEIGHTS AND MEASURES. SWEDISH. 12 inches = 1 foot = .97410 American foot. 6 feet = 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 = 9 sq. feet = 30i sq. yards = 40 perches = 4 roods = 640 acres = 1 square foot. 1 square yard = 1,296 sq. in. 1 perch = 272i sq. ft. 1 rood = 1,210 sq. yd. = 10,890 sq. ft. 1 acre = 160 perches = 4,840 sq. yd. = 43,560 sq. ft. 1 square mile. TABLE FOR REDUCING SQUARE FEET TO ACRES. Square Feet. Acres. Square Feet. Acres. Squarfe Feet. Acres. Square Feet. Acres. 100,000,000 90,000,000 2,295.684 2,066.116 900,000 20.661 9,000 .207 90 .0021 80,000,000 1,836.547 800,000 18.365 8,000 .184 80 .0018 70,000,000 1,606.979 700,000 16.070 7,000 .161 70 .0016 60,000,000 1,377.410 600,000 13.774 6,000 .138 60 .0014 50,000,000 1,147.842 500,000 11.478 5,000 .115 50 .0011 40,000,000 918.274 400,000 9.183 4,000 .092 40 .0009 30,000,000 688.705 300,000 6.887 3,000 .069 30 .0007 20,000,000 459.137 200,000 4.591 2,000 .046 20 .0005 10,000,000 229.568 100,000 2.296 1,000 .023 10 .0002 9,000,000 206.612 90,000 2.066 900 .021 9 .00021 8,000,000 183.655 80,000 1.836 800 .018 8 .00018 7,000,000 160.698 70,000 1.607 700 .016 7 .00016 6,000,000 137.741 60,000 1.377 600 .014 6 .00014 5,000,000 114.784 50,000 1.148 500 .011 5 .00011 4,000,000 91.827 40,000 .918 400 .009 4 .00009 3,000,000 68.870 30,000 .689 300 .007 3 .00007 2,000,000 45.914 20,000 .459 200 .005 2 .00005 1,000,000 22.957 10,000 .230 100 .0023 1 .00002 METRIC SYSTEM. 1 square millimeter ^sq. mm.) 1 square centimeter (sq. cm.) 1 square decimeter (sq. dm.) 1 square meter, or centare (m.2 or sq. m.) 1 square decameter, or are (sq. Dm.) 1 hectare (ha.) 1 square kilometer (sq. Km.) 1 square rayriameter (sq. Mm.) = .001550 sq. in. = .155003 sq. in. = 15.5003 sq. in. = 10.764101 sq. ft. = .024711 acre. = 2.47110 acres. = 247.110 acres. = 38.61090 sq. mi. MEASURES OF VOLUME. 5 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 lb.) 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 lb. in Kentucky, Illinois, and Missouri, 76 lb. in Pennsylvania, and 70 lb. in Indiana. METRIC SYSTEM. .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. = 28.876 cu. in. = 57.75 cu. in. 4 quarts = 1 gallon = 32 gills = 8 pints = 231 cu. in. 3U gallons == 1 barrel = 7,276i cu. in. = 4.21 cu. ft. 63 gallons = 1 hogshead. 2 hogsheads = 1 pipe. 2 pipes = 1 tun. A box 19f in. on each side contains 1 barrel. 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 537.^50 cu. in. 4 pecks = 1 bushel = 64 pints = 32 quarts = 8 gal. = 2,150.42 cu. in. 1 milliliter, or cu. centimeter (cc. or cm.^) = 1 centiliter (cl.) = 1 deciliter (dl. or dl.^) = 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.^) = 1 myrialiter, or decastere (Ml.) = LIQUID MEASURE (u. S.). 4 gills = 1 pint = 16 liquid oz. 2 pints = 1 quart = 8 gills 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, 18i 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. 6 WEIGHTS AND MEMmES. 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 4i' 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. Diam. in Inches. Diameter in Decimals of a Foot. Gallons of 231 Cu. In. (U. S. Stand- ard.) Weight of Water in Lb. in I Ft. of Length. JL 4 .0208 .0025 .02122 5 .4167 1.020 8.488 .0417 .0102 .08488 5i .4583 1.234 10.270 1 .0625 .0230 .19098 6 .5000 1.469 12.223 1 .0833 .0408 .33952 6i .5417 1.724 14.345 li .1042 .0638 .53050 7 .5833 1.999 16.636 U .1250 .0918 .76392 7i .6250 2.295 19.098 .1458 .1249 1.0398 8 .6667 2.611 21.729 2 .1667 .1632 1.3581 8i. .7083 2.948 24.530 2i .1875 .2066 1.7188 9 .7500 3.305 27.501 .2083 .2550 2.1220 9i .7917 3.682 30.641 21 .2292 .3085 2.5676 10 .8333 4.080 33.952 3 .2500 .3672 3.0557 m .8750 4.498 37.432 .2917 .4998 4.1591 11 .9167 4.937 41.082 4 .3333 .6528 5.4323 Hi .9583 5.396 44.901 4i .3750 .8263 6.8750 12 1.0000 5.875 48.891 Diameters in Feet. li 1.25 9.18 76.392 10 10.00 587.6 4,889.12 li 1.50 13.22 110.00 lOi 10.50 647.7 5,404.24 U 1.75 17.99 149.73 11 11.00 710.9 5,915.84 2 2.00 23.50 195.56 Hi 11.50 777.0 6,485.72 2i 2.25 29.74 247.51 12 846.1 7,040.00 2i 2.50 36.72 305.57 13 992.8 8,710.00 2f 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 3i 3.50 71.97 631.00 17 1,698.0 14,166.00 31 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 4i 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 5i 5.25 161.9 1,351.06 24 3,384.0 28,160.00 5i 5.50 177.7 1,478.96 25 3,672.0 30,557.00 5f 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 6i 6.25 229.5 1,915.18 28 4,606.0 40,384.00 6i 6.50 248.2 2,177.48 29 4,941.0 41,117.00 6i 6.75 267.7 2,233.96 30 5,288.0 44,002.00 7 7.00 287.9 2,524.00 31 5,646.0 46,9M.OO 7i 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 8i 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 9i 9.50 530.2 4,422.84 36 7,614.0 63,364.00 WEIGHTS AND MEASURES. 7 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. Arroba (dry) Cuba 1 25.3664 pounds. Arroba (dry) Venezuela 25.4024 pounds. Arroba (liquid) — Cuba and Venezuela 4.263 gallons. Barril Argentine Republic and Mexico 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)... Paraguay 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) Mexico 1.54728 bushels. Fanega (dry) Uruguay (double) 7.776 bushels. Fanega (dry) Uruguay (single) 3.888 bushels. Fanega (dry) Venezuela 1.599 bushels. Frasco Argentine Republic 2.5096 quarts. Frasco Mexico 2.5 quarts. League (land) Paraguay ^,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 : Venezuela 1.0161 pounds. Livre Guiana 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 Paraguay 100 pounds. 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 -f- 32.1869 + 8.04674 = 201.16864 kilometers. 8 WEIGHTS AND MEASURES, CUSTOMARY TO METRIC. Linear. Capacity. Inches to Millimeters. eet to Meters. Yards to Meters. Miles to Kilometers. luid Drams to Milliliters, or Cubic Centimeters. Fluid Ounces to Milliliters. Quarts to Liters. Gallons to Liters. 1 25.4 0.304801 0.914402 1.60935 1 3.70 29.57 0.94636 3.78543 2 50.8 0.609601 1.828804 3.21869 2 7.39 59.15 1.89272 7.57087 3 76.2 0.914402 2.743205 4.82804 3 11.09 88.72 2.83908 11.35630 4 101.6 1.219202 3.657607 6.43739 4 14.79 118.29 3.78543 15.14174 5 127.0 1.524003 4.572009 8.04674 5 18.48 147.87 4.73179 18.92717 6 152.4 1.828804 5.486411 9.65608 6 22.18 177.44 5.67815 22.71261 7 177.8 2.133604 6.400813 11.26543 7 25.88 207.02 6.62451 26.49804 8 203.2 2.438405 7.315215 12.87478 8 29.57 236.59 7.57087 30.28348 9 228.6 2.743205 8.229616 14.48412 9 33.27 266.16 8.51723 34.06891 Square. Weight. Square Inches to Square Centimeters. Square Feet to Square Decimeters. Square Yards to Square Meters. I Acres to Hectares. Grains to Milligrams. Avoirdupois Ounces to Grams. Avoirdupois Pounds to Kilograms. Troy Ounces to Grams. 1 6.452 9.290 0.836 0.4047 1 64.7989 28.3495 0.45359 31.10348 2 12.903 18.581 1.672 0.8094 2 129.5978 56.6991 0.90719 62.20696 3 19.355 27.871 2.508 1.2141 3 194.3968 85.0486 1.36078 93.31044 4 25.807 37.161 3.344 1.6187 4 259.1957 113.3981 1.81437 124.41392 5 32.258 46.452 4.181 2.0234 5 323.9946 141.7476 2.26796 155.51740 6 38.710 55.742 5.017 2.4281 6 388.7935 170.0972 2.72156 186.62088 7 45.161 65.032 5.853 2.8328 7 453.5924 198.4467 3.17515 217.72437 8 51.613 74.323 6.689 3.2375 8 518.3914 226.7962 3.62874 248.82785 9 58.065 83.613 7.525 3.6422 9 583.1903 255.1457 4.08233 279.93133 Cubic. 1 09 OJ ot d “.Th Miscellaneous. OJ W 'g.sS i-H p d o0.9 . 4-3 <1^ 0 . a>.9 09 'Sd . .00 d rP h-3 d 0 ^ ‘rO oS M d d ® o o d 0 1 Gunter’s chain = 1 sq. statute mile ^ 20.1168 meters. 259.000 hectares. 1 16.387 .02832 0.765 0.35239 1 fathom _ 1.829 meters. 2 32.774 .05663 1.529 0.70479 3 49.161 .08495 2.294 1.05718 1 nautical mile = 1,853.25 meters. 4 5 65.549 81.936 .11327 .14158 3.058 3.823 1.40957 1.76196 1 ft. --- .304801 meter 9.4,S40ir>8 log. 6 7 98.323 114.710 .16990 .19822 4.587 5.352 2.11436 2.46675 1 avoir, pound 453.5924277 gram. 8 131.097 .22654 6.116 2.81914 15, 432..3.5039 grains - 1 kilogram. 9 147.484 .25485 6.881 3.17154 CONVERSION TABLES. 9 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 80 meters = 87.48889 yards; and 6 meters = 6.561667 yards. Hence, 86 meters = 87.48889 + 6.561667 = 94.050557 yards. METRIC TO CUSTOMARY. Linear. Capacity. Meters to Inches. Meters to Feet. Meters to Yards. Kilometers to Miles. Milliliters, or Cubic Centi- liters to Fluid Drams. Centiliters to Fluid Ounces. Liters to Quarts. Decaliters to Gallons. Hectoliters to Bushels. 1 39.37 3.28083 1.093611 0.62137 1 0.27 0.338 1.0567 2.6417 2.8377 2 78.74 6.56167 2.187222 1.24274 2 0.54 0.676 2.1134 5.2834 5.6755 3 118.11 9.84250 3.280833 1.86411 3 0.81 1.014 3.1700 7.9251 8.5132 4 157.48 13.12333 4.374444 2.48548 4 1.08 1.353 4.2267 10.5668 11.3510 5 196.85 16.40417 5.468056 3.10685 5 1.35 1.691 5.2834 13.2085 14.1887 6 236.22 19.68500 6.561667 3.72822 6 1.62 2.029 6.3401 15.8502 17.0265 7 275.59 22.96583 7.655278 4.34959 7 1.89 2.367 7.3968 18.4919 19.8642 8 314.96 26.24667 8.748889 4.97096 8 2.16 2.705 8.4535 21.1336 22.7019 9 354.33 29.52750 9.842500 5.59233 9 2.43 3.043 9.5101 23.7753 25.5397 Square. Weight. Square Centi- meters to Square Inches. Square 1 Meters to Square Feet. Square Meters to Square Yards. Hectares to Acres. Milligrams to Grains. Kilograms to Grains. Hectograms to Ounces Avoir. 1 Kilograms to Pounds Avoir. 1 0.155 10.764 1.196 2.471 1 .01543 15,432.36 3.5274 2.20462 2 0.310 21.528 2.392 4.942 2 .03086 30,864.71 7.0548 4.40924 3 0.465 32.292 3.588 7.413 3 .04630 46,297.07 10.5822 6.61387 4 0.620 43.055 4.784 9.884 4 .06173 61,729.43 14.1096 8.81849 5 0.775 53.819 5.980 12.355 5 .07716 77,161.78 17.6370 11.02311 6 0.930 64.583 7.176 14.826 6 .09259 92,594.14 21.1644 13.22773 7 1.085 75.347 8.372 17.297 7 .10803 108,026.49 24.6918 15.43236 8 1.240 86.111 9.568 19.768 8 .12346 123,458.85 28.2192 17.63698 9 1.395 96.875 10.764 22.239 9 .13889 138,891.21 31.7466 19.84160 Cubic. Cubic Centi- meters to Cubic Inches. Cubic Deci- meters to Cubic Inches. Cubic Meters to Cubic Feet. Cubic Meters to Cubic Yards. 1 .0610 61.023 35.314 1.308 1 2 .1220 122.047 70.629 2.616 2 3 .1831 183.070 105.943 3.924 3 4 .2441 244.094 141.258 5.232 4 5 .3051 305.117 176.572 6.540 5 6 .3661 366.140 211.887 7.848 6 7 .4272 427.164 247.201 9.156 7 8 .4882 488.187 282.516 10.464 8 9 .5492 549.210 317.830 11.771 9 {Continue d). Quintals to Pounds Avoir. Milliers, or Tonnes to Pounds Avoir. Kilograms to Ounces Troy. 220.46 2,204.6 32.1507 440.92 4,409.2 64.3015 661.39 6,613.9 96.4522 881.85 8,818.5 128.6030 1,102.31 11,023.1 160.7537 1,322.77 13,227.7 192.9044 1,543.24 15,432.4 225.0552 1,763.70 17,637.0 257.2059 1,984.16 19.841.6 289.3567 10 WEIGHTS AND MEASURES, METRIC CONVERSION TABLE. {Arranged by C. W. Hunt, New York.) Millimeters X .03937 = in. Millimeters 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 1.6093 = miles. Kilometers X 3,280.7 = ft. Square millimeters X .0155 = sq. in. Square millimeters 645.1 = sq. in. Square centimeters X .155 = sq. in. Square centimeters 6.451 = sq. in. Square meters X 10.764 = sq. ft. Square kilometers X 247.1 = acres. Hectare X 2.471 = acres. Cubic centimeters ^ 16.383 = cu. in. Cubic centimeters ^ 3.69 = fluid drams (U. S. P.). Cubic centimeters ^ 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 -f- 3.78 = gal. (231 cu. in.). Liters 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 -t- 26.42 = gal. (231 cu. in.). Grams X 15.432 = gr. (Act Con- gress). Grams -j- 981 = dynes. Grams (water) 29.57 = fluid oz. Grams 28.35 = oz. avoir. Grams per cu. cent. 27.7 = lb. per cu. in. Joule X .7373 = ft.-lb. Kilograms X 2.2046 = lb. Kilograms X 35.3 = oz. avoir. Kilograms 1,102.3 = ton (2,000 lb.). Kilogr. per sq. cent. X 14.223 = lb. per sq. in. Kilogram-meters X 7.233 = ft.-lb. Kilo per meter X .672 = lb. per ft. Kilo per cu. meter X .026 = lb. per cu. ft. Kilo per cheval X 2.235 = lb. per H. P. Kilowatts X 1.34 = H. P. Watts ^ 746 = H. P. Watts -j- .7373 = ft.-lb. per sec. Calorie X 3.968 = B. T. U. Cheval vapeur X .9863 = H. P. (Centigrade X 1-8) + 32 = degree F. Franc X .193 = dollars. Gravity Paris = 980.94 centimeters per sec. MONEY. United States Currency. British Money. 10 mills = 1 cent. 10 cents = 1 dime. 10 dimes = 1 dollar. 10 dollars = 1 eagle. 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 Quarter eagle * Three-dollar piece Half eagle Eagle Double eagle i^l.OO 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 Half dollar Quarter dollar... Dime «1.00 1.00 .50 .25 .10 420.0 gr. 412.5 gr. 192.9 gr. 96.45 gr. 38.58 gr. “ 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 pute metal, 100 alloy; alloy of gold coin is copper or copper and silver, but in no case shall silver exceed ^ of total alloy. Alloy of silver coin is copper. Piece. Weight. Contents. 5-cent( nickel) 77.16 grains 75^ copper, 25/^ nickel. *3-cent 30 grains 75^ copper, 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 $1,000,000 $5,000 in 8-oz. duck bags Nearly 17 cu. ft. Silver dollars 1,000,000 1,000 in 8-oz. duck bags 250 cu. ft. Subsidiary silver 1,000,000 1,000 in 8-oz. duck bags 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.) 2.02771, or X .U9312 = English pence. Example.— 100 cents X .49312 = 49.312 pence = 4s. 1.312d. English pence X 2.02771 = cents {U. S.). Example.— lOOd. X 2.02771 = 202.771 cents = $2.0277. _ , Dollars ^ ^ 7 - Rule-— = pounds sterling. U.oboo Example.— = £20.548. £.548 X 240 = 131.5d. = 10s. 11.5d. 4.oboo Ru I e.— Pounds X U.8665 '= dollars (U.S.). Shillings X 2U.332-{- = cents {U.S.). VALUES OF FOREIGN OOINS, U. S. TREASURY DEPT., JAN. 1, 1899. Argentine, Argentine Re- public $ 4.824 Bolivar, Venezuela .193 Boliviano, Bolivia 439 Centen, Cuba 5.017 Colon, Costa Rica 465 Condor, Chile 7.300 Condor, U. S.of Colombia and Ecuador 9.647 Copeck, Russia 0075 Crown, Austria-Hungary 203 Crown, Denmark, Norway, and Sweden 268 Crown, Germany 1.06 Crown, Great Britain 1.13 Crown, Sicily 96 Crown, Spain (half pistole) 1.95 Dollar, Bolivia .96 t Dollar, British Honduras, British Possessions, N. A. (except Newfoundland), and Liberia'. 1.000 Dollar, Chile, Peru, and Ecuador 93 Dollar, Mexican (gold) 983 Dollar, Mexican ( silver) 477 Dollar, Newfoundland 1.014 Dollar, U. S. of Colombia .935 Doubloon, Central America $14.50 Doubloon, Chile 3.650 Doubloon, New Granada 15.34 Doubloon, Spain and Mexico 15.65 Drachma, Greece 193 Ducat, Austria, Bohemia, Hamburg, Hanover 2.28 Ducat, Denmark 1.11 Ducat, Sweden 2.20 Escudo, Chile 1.825 Florin, Austria-Hungary 1.929 Florin, Hanover (g-old) 1.66 Florin, Hanover (silver) 56 Florin, Holland, South Ger- many 38 Florin, Netherlands 402 Florin, Prussia 55 Florin, Silesia 48 Franc, Belgium, Bulgaria, France, Italy, Roumania, Switzerland 193 Gourde, Hayti 965 Groschen, Prussian Poland .024 Guinea, Great Britain 5.11 Gulden, Baden. 40 Imperial, Russia 7.92 Kran, Persia 081 Kreutzer, Bavaria .0067 t The British dollar has the same legal value as the Mexican dollar in Hongkong, the Straits Settlements, and Lahuan. 12 WEIGHTS AND MEASURES. VALUES OF FOREIGN coxus.— {Continued.) Lira, Italy $ .193 Mark, Finland 193 Mark, German Empire 238 Maximilian, Bavaria 3.30 Milreis, Brazil 546 Milreis, Portugal 1.080 Mohur, India 7.105 Napoleon, France 3.84 Peseta, Spain 193 Peso, Argentine Republic ... .965 Peso, Chile 365 Peso, U. S. of Colombia 439 Peso, Cuba 926 Peso, Guatemala, Honduras, Nicaragua, Salvador 365 Peso, Uruguay 1.034 Piaster, Egypt .049 Piaster, Turkey .044 Piastre, Spain 1.04 Pistole, Rome 3.37 Pistole, Spain 3.90 Pound, Egypt 4.943 Pound Sterling, Great Britain 4.8665 Ruble, Russia 515 Rupee, India $ .208 Shilling, Great Britain 243 Sol, Peru 439 Sou, France 01 Sovereign, Great Britain 4.8665 Sucre, Ecuador. .439 f Amoy .710 Canton .708 Chefoo 679 Chin Kiang 693 Fuehau 656 Haikwan (Cus- toms) 722 Tael, China ^ Hankow 664 Hongkong f Niuchwang 665 Ningpo 682 Shanghai 648 Swatow 655 Takau 714 ^Tientsin 688 Toman, Persia 3.409 Yen, Japan 498 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 pure. The carat is also a unit of weight for precious stones. Its value varies according to different authorities, but the international carat is 3.168 grains, or 206 milligrams. Diamond Weight (Nystrom). Carats. 1 = .25 = .015625 = .3125 = 15.5 = Grains. Parts. Grains, Troy. 4 = 64 = 3.2 1 ^ 16 _ ,8 .0625 = 1 = .05 12.5 = 20 = 1 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: 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: Multiply as before and divide by Uh. TIMBER AND BOARD MEASURE. v: Round Timber.— Table of i Girths. i Girths. Inches. Area in Feet. i Girths. Inches. Area in Feet. i Girths. Inches. Area in Feet. 6 .250 12i 1.04 19 2.50 6i- .272 m 1.08 19i 2.64 .294 12f 1.12 20 2.77 6^ .317 13 1.17 20i 2.91 7 .340 13i 1.21 21 3.06 7i .364 13i 1.26 21i 3.20 n .390 m 1.31 22 3.36 7^ .417 14 1.36 22i 3.51 8 .444 14i 1.41 23 3.67 .472 14i 1.46 23i 3.83 .501 m 1.51 24 4.00 8^ .531 15 1.56 24i 4.16 9 .562 15i 1.61 25 4.34 9i .594 15i 1.66 25i 4.51 H .626 15f 1.72 26 4.69 9f .659 16 1.77 26| 4.87 10 .694 16i 1.83 27 5.06 lOi .730 m 1.89 27i 5.25 m .766 m 1.94 28 5.44 10^ .803 17 2.00 28i 5.64 11 .840 I7i 2.09 29 5.84 Hi .878 17i 2.12 29h 6.04 Hi .918 17^ 2.18 30 6.25 IH .959 18 2.25 12 1.000 18i 2.37 Area corresponding to i 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 8i .688 i .042 4i .375 8i .708 1 .063 4i .396 8i .729 1 .083 5 .417 9 .750 li .104 5i .438 9i .771 li .125 5i .458 9i .792 li .146 5i .479 9i .813 2 .167 6 .500 10 .833 2i .188 6i .521 lOi .854 2i .208 6i .542 lOi .875 • 2i .229 6i .563 lOi .896 3 250 7 .583 11 .917 3i .271 7i .604 Hi .938 3i .292 7i .625 Hi .958 3i .313 7i .646 Hi .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. We 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 pTane 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. -f means plus, or addition. — means minus, or subtraction. X means multiplication. ± means plus or minus. T means minus or plus. means division. : means ratio. : : means proportion. 2 : 3 ; : 4 : 6 shows that ^ is to 3 as 4 is to 6. — means equality. =0= means equivalency, y means square root, f means cube root, etc. square root of 3. ^ 5 cube root of 5. 72 7 squared. 83 8 cubed. ^ = a/b, a-^b. 15 16 = 0 lb therefore. > greater than. < less than. □ square. □' square feet. □" square inches. O round. ( ) [ 1 I } » vincula, denoting that the numbers enclosed are to be taken together; as, (a + 5) c = 4 + 3 X 5 = 35. ° degrees, arc or thermometer. ' minutes or feet. " seconds or inches. 30° 40' 4" is 30 degrees AO minutes A seconds. 4' 6" is A feet 6 inches. ' " accents to distinguish letters, as a', a", a'". ai, 02, ai, Oc, read osMft 1, a sub 6, etc. a-, 03 o squared, a cubed. a\ = 1^^, o^ = 1/ o3. sin o = the sine of a. log = logarithm. l_ angle. L mght angle. _L perpendicular to. sin sine. cos cosine. ARITHMETIC. 15 MATHEMATICAL SIGNS AND ABBREVIATIONS— tan, or tang, tangent. sec secant. versin versed sine. cot cotangent. cosec cosecant. covers coversed sine. TT pi, ratio of circumference of circle to diameter 3.14159. g acceleration due to gravity = (32.16 ft. per sec.). R, r radius. W, w weight. H. P. horsepower. I. H. P. indicated horsepower. B. H. P. brake horsepower. A. W. G. American wire gauge (Brown & Sharpe). B. W. G. Birmingham wire gauge. r. p. m., or rev. per min., revolutions per minute. A decimal point is a period (.) pre- fixed to a number to show that the number is less than unity (1); thus, .2 = .35 = 5.75 = or 5j. 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 1 0,7 0 3,9 5 9 7. Ans. To Prove Subtraction.— Add the remainder to the lesser number; their sum should equal the larger number. To Prove M uiti pi i cation.— 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 6,1 9 6 4 21,946,232 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. 554,407f §. Ans. Proof.— Take 43 from 31,046,835, and divide the remainder, 31,046,792, by 554,407. 56. Ans. Ruie.— To square any number containing the fraction i, multiply the whole number by the next higher whole number, and add i. Example.— (8i)2 = 8 X 9 + i = 721. COMMON FRACTIONS. A fraction is a part of a whole, as 1, §, 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, 1 and | have common denominators; and again, 12 is a common de- nominator for I, 1, 1, and I, as they each are respectively equal to and To Add Common Fractions.— If of the same denominator, add together the numerators only. Thus ^ + + T6 — T%- 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 § + 1 + ^ ? § = iSa = U, and ^ = U- le + M M = U- Ans. To Multiply Common Fractions.— Multiply the numerators together for the numerator, and the denominators for the denominator. Thus, | X X § == TS* To Divide Common Fractions.-Invert the divisor, and multiply. Example.— Divide by |. X t 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. 5 X 3 + 2 = 17, or the numerator, and the fraction is therefore V-. 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 to a compound fraction. 9)64(7 6 3 Compound fraction = 7^. Ans. To Reduce Common Fractions to Decimal 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 je to a decimal fraction. 16 ) 9.00 0 0 (.56 25 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. ISi .015625 .265625 il .515625 49 67 .765625 TUf .03125 .28125 .53125 .78125 .046875 19 64 .296875 M .546875 67 .796875 .0625 16 .3125 9 T6 .5625 e .8125 .078125 u .328125 67 .578125 II .828125 3^ .09375 hh .34375 .59375 §1 .84375 .109375 .359375 if .609375 II .859375 5 .125 3 .375 5 s .625 1 .875 .140625 if .390625 u .640625 II .890625 .15625 .40625 ih .65625 if .90625 .171875 if .421875 .671875 II .921875 .1875 T6 .4375 .6875 1 5 T6 .9375 .203125 §1 .453125 .703125 H .953125 3^3 .21875 .46875 §§ .71875 u .96875 .234375 ii .484375 II .734375 II .984375 .25 .5 3 7 .75 1 l.OOOO DECIMALS. Decimal fractions have for their denominators 10 or a power of 10. but the denominator is usually omitted. Thus, .1 == .01 = yio; .001 — To’&o. etc. n A r To Add Decimals.— Place whole numbers under .00 /o whole numbers, tenths under tenths, hundredths <>3 under hundredths, etc., and add, placing the deci- 10 6 mal point in the sum directly under the i>()ints 17.9312 above. Thus, 1 9.6 3 1 7 DECIMALS. 17 To Subtract Decimals.— Arrange the figures as in addition, and proceed as in simple subtraction. Thus, 5.9 6 9 7 8 3.2 8 6 9 4 2.6 8 2 8 4 To Multiply Decimals.— Proceed as in simple multiplication, pointing off as many decimal places in the result as there are decimal places in both mul- tiplicand and multiplier. Thus, To Divide Decimals.- 4.6 7 5 3 1 .0 5 3 1402593 2337655 (5 decimal places.f (3 decimal places.) 0.247 79143 (8 decimal places.) . . -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 60 0 ( 1.441 2 Ans. 33 145 132 136 132 40 33 70 4 Example 2.— Divide .006 by 20. 20 ).0 0 60 (.0 0 03 Ans. 60 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, 5, 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 by b), or simply by placing the two letters together, as ab. We can indicate division as in common fractions, ^ 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: lb h’ When two or more letters are placed together, without anything between them, it is understood that the quantities represented by those letters should be multiplied together. If I represents 8 and b represents 4, then 4 and 8 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: lAb h • The square of the length multiplied by the cube of the breadth, thus: l^bK The square root of the length divided by the cube root of the breadth, thus: V I fT' The square root of the difference of the length and breadth divided by the height, thus: i/T^ h * 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 5 X 4 = 10 X 2. 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.— I f 6 men load 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) 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, 2. The product of all the terms in the extremes equals the product of all the terms in the means. Thus, in f4 : 12) . . f5 : 10) 17 : 14/ • • 16:18; 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 4 = 5 X 6 X 12 X 14 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 f4 : 12) . . r5: : 10) 17 : 14 ; • • 16: : 18/ we have 5 = (4 X 7 X 10 X 18) (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. 1 1 . 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 S24 in 7 days, how much can 14 men earn in 12 days ? The sum : $24 : : | ^2 • 7 } 5 the sum ^ ^ ^ 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, 5 ft. high? r 40 : 35 ) ^ 140 : 144 y : : I 6:5 j 12 : ( ) = 35 X 144 X 5 X 12 40 X 140 X 6 = 9. Ans. 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. 11. 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. HI. Divide this dividend, omitting the figure on the right, by double the 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 OPEKATION. 18 3r6T2' ^ 549 186 519325 9325 9 X 2 = 18. 18 into 64 goes 3 times, hence new divisor = 183. 93 X 2 = 186. 186 into 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 g? = f . 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. ^ S'7 4 9 r 9 q ^ fi-u EXAMPLE 2.— Find the square 8 7 4.2 2 5 ( 2 9.5 6+ root of .00874225. .0 0'8 7'4 2'2 5 (.0 9 3 5 81 18 31' 58 5r3322 2 9 2 5 5M«71 1 9 ^ 6 a 642 549 186 51 93 25 9325 4 3 08+ 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. Y. 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.— F ind the cube root of 12,812,904. OPERATION. 1 2,8 1 2,9 0 4 ( 2 3 4 Ans. 2 ‘^= 8 1st partial divisor, 3 X 202 = 1,2 0 0 4,812 3X20X3 = 180 32 9 4,1 6 7 1st complete divisor, 1,3 8 9 6 4 5,9 0 4 2d partial divisor, 3 X 2302 = 1 5 8,7 0 0 3 X 230 X 4 = 2,7 6 0 42 = 16 6 4 5,9 0 4 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 f . (See logarithms for shorter method.) PERCENTAGE. Percentage means by or on the hundred. Thus, 1^ = = .01, ^ = .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 -- .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 ^ 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 =/ -f (2 — l)d ==/ -|- d; the fourth term =/ H- (4 — l)d; and the nth term = f+{n-l)d. (1) From equation (1) we obtain f = I ±{n- l)d. (2) a = (4) 'll ' ' “ = -^ + 1- «=|C/' + 0. (6) GEOMETRICAL PROGRESSION. 21 Substituting the value of I from ( 1 ) , « = (6) Example 1.— A company contracts to put down a bore hole at one dollar ($1) 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 ? « = §;/= 100; and d = 2. Substitute these values in formula (6). s = f [2 X 100 + (8 — 1) 200] = i|6,400. Ans. Example 2.— If water fiowing 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 ? Dunng 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 = [2 X 10.12 + (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 ^3 50 02 Then, * + 1 = 675, the depth at which the rock will run dry, and s = [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 + 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, 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. (1) (4) » - ~ (2) / = s _ r (s - 1). (5) (3) ( 6 ) r — 1 Zr-/ ‘~s~l 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.; 4 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. Substituting in formula (1), 33,554,432 X 2 — 2-T ^ ^671,088.63^1. Ans, / = X (229) 33,554,432, and s [formula (3)] 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, 100= we have logarithm of 1 = 0. 101 = 10, we have logarithm of 10 = 1. 102 = 100, we have logarithm of 100 = 2. 10^ = 1,000, we have logarithm of 1,000 = 3. 104 = 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 1.83059, the characteristic of this logarithm is 1 and the mantissa is .83059. 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 2.51455. 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 .48001. 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, r.nd then along the top of the page for the fourth figure. Down the colamn 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.— W hat 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 1.83059. The logarithm of 6.77 is 0.83059. The logarithm of .677 isL83059. The logarithm of .0677 is 2.83059. The logarithm of .00677 is 3.83059. 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 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 “ 0 ” 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 = 1.83059 Log .677 = 1.83059 1.66118 1.66118 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 = 1.83059 Log .0677 = 2.83059 3.00000 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 = L83059 2 1.66118 1.66118 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 = 2.79588. 2.79688^2 = 1.39794. 1.39794 = 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.— ^^68^ ^ 2.1082282. Example 2.— 14.326847 2 ^ (14 + 4 = 18) + (4 + .3268472) ^^ + 4.3268472 ^ 2.4807608. Example 3.— i/Wl = M ; I + " = T.966U78 = .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 triang:le 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 ? 32 : 62 ; : 28.274 : 113.096 sq. in. Ans. PRACTICAL PROBLEMS IN GEOMETRICAL CONSTRUCTION. ^ To Bisect a Given Straight Line A 5. —From y A and B as centers, with a radius greater than I one-half of A B, describe arcs intersecting at E ^ j B and F. Draw E F. It will bisect A B. C will be the middle point, and EF will be perpendic- ! ular to A B. The points E and F will be equi- )|;F distant from A, B, or C. From a Given Point C, Without a Straight Line AB^ to Draw a Perpendicular to the Line.— From 0 as a center, with a radius sufficiently great, describe an arc cutting A ^ 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. € E A* 26 GEOMETRY. '>fD A^r C At a Given Point C in a Straight Line AB, 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 B, and draw the line D C. At a Point -4 on a Given Straight Line A B, to Make an Angle Equal to a Given Angle EFG. From jP as a center, with any radius F G, describe the arc E G. From J. as a center, with the same radius, describe the arc CB; then with a radius equal to the chord E G, describe an arc from £ as a center, cutting CB at Z), and draw A D To Bisect a Given Arc .4(75.— With the same radii and the extremities .4 5 as centers, describe arcs intersecting at D and E. The line DE bisects the arc at C, To Bisect an Angle A B (7.— With any radius and 5 as a center, describe an arc cutting the sides at A and C. With these points as centers, describe arcs of equal ^^dius intersecting at 5. The line 5 is the biseccor, and the LA B D = LB B C. ^ To Bisect an Open Angle {Method by L. L. Logan).— Let AB and CZ) be the sides of an open angle. With any point 0 as a cen- ter, describe a circle cutting the sides at e,/, g, and h, and with e and/, and g and h as centers and any radius, describe arcs intersecting at k and I, respectively. Draw Ok and 01 and mn. With p and q as cen- ters, and any radius, describe arcs intersect- ing at R and S. The line drawn through RSis the required bisector. Through a Given Point A, to Draw a Straight Line Parallel to a Given Straight Line (7 A— From .4 as a center, with a radius greater than the shortest distance from A to CB, describe an indefinite arc B E. From D as a center, with the same radius, describe the arc A F. Take B E equal to A F, and draw A B. -4E- \ 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 B O 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 C the center of the circle, draw the radius G 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 P; with P as a center, and a radius P (7, describe the cir- cumference intersecting the given circumference at A and B. From the intersections A and P, 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 0 ^ k L AO C. An acute angle included between a chord and a tangent is equal to one-half the central angle subtended by the chord. Thus, [_ AB G = \ L_ GOB. 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, AB = A G^ and [_ D AG = L BOG. To Divide a Straight Line Into Any Number of Equal Parts. — To divide the line AB into, say, 6 parts, draw the line A G from A, making any angle with A B; measure off 6 equal spaces on A C; draw 6 B, and from 1, S, 4, 5 on ^ C draw parallels to 6 B. These divide ^ P 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 G divisions proportional to the required divisions, and draw the parallel lines as explained above. 23 MENSVRATION. MENSURATION. MENSURATION OF SURFACES. PARALLELOGRAMS. A parallelogram is a four-sided figure whose opposite sides are parallel. V Square. Rectangle. Rhombus. Rhomboid. {Four equal sides {Four right angles {Four equal sides {Four oblique angles and and four right an- and opposite sides and oblique angles.) opposite sides equal.) gles.) equal.) T# 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 5 by the height B C. The areas of the rhombus and rhbmfed are found by multiplying the length A B by the height C D. 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. Ti 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. T« 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 Circie. Divide the diameter of the circle by 1.41421, or multiply it by .707107. TRIANGLES. Atriangieisa figure having three straight sides. Equilateral. Isosceles. Scalene. {Three equal {Two equal {Three un- sides.) sides.) equal sides.) T# 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 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 whose lengths are 30, 40, and 50 ft., then ^ 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, A B ^ 21 ft., B C = 17.25 ft., and A C = S2 ft. Draw BD per- pendicular io A C\ then, 32 : 21 + 17.25 = 21 — 17.25 : AD — DC; or, AD — DC = 4.48 But AD A DC = 32 Adding, Subtracting, 2AD = 36.48 A Z> = 18.24 2 D (7 = 27.52 DC = 13.76 cos A = = .86857, or A = 29° 42' 25.7". cos C = = .79768, ox C = 37° 5' 26.7". B = 180° — (A + C) = i80 — (29° 42' 25.7"+ 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 ABC, let A ^ = 19 ft., AC = 2? ft., and A = 36° 3' 29". Draw B D perpendicular to A a ^ D = 19 X sin A = 19 X .58861 = 11.18 ft. A D = 19 X cos A 19 X .80842 = 15.36 ft. D C = 2 d — 15.36 = 7.64 ft. Tan C = = 1.46335, or C = 55° 39' 10". .B = 180 — (A -f (7) = 180 7? D 11 18 - (36° 3' 29" + 55° 39' 10") = 88° 17' 21". BC = = 13.54 ft. sin (7 .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 the given angles, so is the square of the given side to twice the required area. Thus, sin C : sin AXsin B :: AB ^ : 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, ABj^_C^ X EF = 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 pcriygons. ooo 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. Octagon. 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 of SideS. Name of Polygon. Areas. Outer Radii. Angles Contained Between Two Sides. Angle at Center of Circle. 3 Equilateral triangle .4330 .5774 60° 120° 4 Square 1.0000 .7071 90° 90° 5 Pentagon 1.7205 .8507 108° 72° 6 Hexagon 2.5981 1.0000 120° 60° 7 Heptagon 3.6339 1.1524 128° 34' 17" + 51° 25' 43"— 8 Octagon 4.8284 1.3066 135° 45° 9 Nonagon 6.1818 1.4619 140° 40° 10 Decagon 7.6942 1.6180 144° 36° 11 Undecagon 9.3656 1.7747 J O 32° 43' 38" + 12 Dodecagon 11.1962 1.9319 150° 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-fburth 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 ^ 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. To Find the Area of an Elllpse.—Multiply one-half of the two axes and 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, h c the major, and a e half the minor axis of an ellipse. Draw the rectangle bfgc, and the diagonal line be; at a right angle to b e, draw linefh cut- ting J5 .Bat f. With radius ae, and from a as a center, draw the dotted arc ej, giving the pointy’ on the line B B. From k, which is central between b and j, draw the semicircle b mj, cutting A A ail. 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 ho, and from center h, draw the arc poq. 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 hpr and hqs, and also the lines p i t and qvw. From A as a center, draw that part of the ellipse lying between r and s with radius hr. From p as a center draw that part of the ellipse lying between r and t with the radius pr. From q, draw the ellipse from s to w. With radius i t, from i as a center, draw the ellipse from t to 5 with radius i t, and from 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 h, p, and q; these new centers correspond in position to h, p, q. A V 1 hy ' Rv" \ i R \ {k a / \ / 1 \ I \v| Straightedge Method.— On a straightedge, lay off ^.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. 33 MENSURATION OF SOLIDS. THE CUBE AND THE PARALLELOPI PED. To Find the Surface of a Cube.— Multiply the area of one side by 6. To Find the Surface of a Paralleiopiped.— Add together t.wice the area of the base, twice the area of the side, and twice the area of the end. To Find the Cubicai Contents of a Cube or Paralleiopiped.— 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- eters or circumferences of the two bases by the slant height. 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 Cyiindrical 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. Plane 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 0 C is the complement of B 0 C. The supplement of an arc is 180° minus the arc; AE is the supplement of the arc B D E, and the angle B 0 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. Thus, CE or OD 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, T is the tangent of A C. The cotangent of an arc is equal to the tangent of the compl-ement of the arc. Thus, B T' is the cotangent of^a 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, 0 T is the secant of A C. The cosecant of an arc is the secant of the complement of the arc. Thus, 0 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. DA is the versed sine of A C. The coversed sine is the versed sine of the complement of the arc. Thus, 5 jE is the CO versed 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°. tangent of 70° = tangent of 110°. cotangent of 70° = cotangent of 110°. secant of 70° = secant of 110°. cosecant of 70° == cosecant 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. l\xyz, the following relations hold: Functions of the sum and difference of two angles: sin {A A B) = sin A cos B + cos A sin B. cos {a B)= cos A cos ^ — sin ^ sin B. sin \A — B) — sin A cos B — cos A sin B. cos {A — B) ^ cos A cos jB + sin ^ 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 B AC. 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 Bis 300 ft. and the angle BAC== 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 2.400934 or log of 251.73+ ft. Hence, BC= 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 ^ 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 = 300, ^ ^ 90 °^ (7 = 60°, and the side B C — 200 ft. Then, sin A: B Gw sin 0 : A B, or .5 : 200 : : .866025 : ( ), or 346.41 ft. By logarithms: Log 200 = Log sin 60° = Log sin 30° = 2.301030 9.937531 12.238561 ^ 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 By and take the angles formed by the lines B AC 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 AB = 500 ft., we have the angle C= 180° — (60° + 50°) = 70°. Then, sin 70° : A .B : : sin A : B C, and sin 70° : AB w sin B . AC', or, .939693 : 500 : : .866025 B C, or 460.8+, .766044 : A C, or 407.6+. and .939693 : 500 By logarithms: Log 500= 2.698970 Logsin60°= 9.937531 12.636501 Log sin 70°= 9.972986 2.663515= log of 460.8+. Log500= 2.698970 Log sin 50°= 9.884254 12.583224 Logsin70°= 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 C A 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 ; tan ^ , A + B _ 180° - 60° ^ 2 ' “ 2 Then, , or 60°. Then, 1,100 : 100 : : tan 60° : tan 7^- A. 2 * 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 or 8° hT. Then, and (S) 60° + 8° 57' = 68° 57', or angle B, 60° — 8° 57' = 51° 03', or angle A. Note.— T he 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 DC on a line from the foot of the object, and, at the point D, measure the angles of elevation EDA and ED B 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 to be 1,200 ft. long, the angle A, 25°, and the angle D B C, 40°, we have the following: As the angle DB C is 40°, the angle ABC= 90° — 40°, or 50°. Then, having the side B C, and the angle D B C = 40°, and the angle B D C = 90°, we find the side CD by the same method as in Case 1. Second Method.— li it is not convenient to measure a horizontal base line toward the object, measure any line AD, Fig. (6a), and also measure the horizontal angles BAD, A BD, and the angle of elevation D B C. Then, by means of the two triangles ABD 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 DC, we have the angle D; 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 DAC, and DAB, and, at the point B, take the angles CB A and CBD. Assume the length of A D = 400 ft. Angle DAC = 56° 30'. Angle DAB = 42° 24'. Angle CD A = 44° 36'. Angle CDD = 68°50'. 88 SVnVEYING, In the triangle ABD, we have AB = 40^ ft., the angle DAB = 42^24', the angle ABB = (44° 36' + 68° 50') = 113° 26', and the angle AD B = 180° — (42° 24' + 113° 26') = 24° 10'. Then, according to Case 1, lind the side D B. We then have three angles and two sides of the triangle J. D .B. We find the third side ADhy Case 1. Then in the triangle AB C, 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 ADC, we have the sides A D and A C, and the angle D A C, and we then find the side CDhy 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 bri \g the bubbles into the center by the pressure of the hand on different partt 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 tJie 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 half way 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 MAGNETIC VARIATION. 39 circle; if any error is there manifested, the correction must be made in the 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 1900. 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. The annual change in declination is given in minutes; a + 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 timej 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 tra nsit 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 h 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 k, 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. m-- te' 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 verniei, 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 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 20i° on the limb of the transit, and the line marked 10 should coincide with a line on the limb, the reading would be 20° 40'. In case the 12th line from zero 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 0° each way to 90°, and thence to 0° on the opposite side of the circle, the other set is marked from 0° to 360° to the right, as a clock face. The inside set has the N, S, E, and W points marked, the 0° 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 of the line of collimation. 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 tne 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 half way 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- Q - 2 > scope; that is, turn it over on f its axis until it points in the " jIqq' opposite direction, and set a *UO point at about the same dis- tance, which will be at D, 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. Having 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 B, 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 S in on the ground, which will come at C. The distance R (7 is ouble 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 nearlv 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 he 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,!!. 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 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 v/ith 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 i 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.” When 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 ^ound, 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-ffishioned plummet, so that the majority of the best engineers have gone bac ^ 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 0° 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. Bearings. Distances. 1-2 N 35° E 270.0 At 1 -f 37 ft. crossed small stream 3 ft. wide. At 1 -f- 116 ft. = first side of road. At 1 -h 131 ft. = second side of road. At 1 -f 137 ft. = blazed and painted pine tree, 3 ft. left, marked for a “go by.” TRANSIT SUE VEYTNG. 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 -f 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 + 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 + 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 0 with backsight at B and foresight at C, we shall find that there are two angles made by the line C 0 with the line BOA, namely the included angle B 0 (7, 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 SVRVEYING. 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 maybe 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”— that is, not loose rock, even if a large boulder— at such a distance from the works as to be beyond the influence of moving machinery, and a line of sight is taken to sonue 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 vertictd plane with the north star 17 minutes before the latter 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 Elongation. — 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. The cross-wires are made to bisect the star; they are JPolaris \ I \i \tt9erver 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, arid 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. A line 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, furnished 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 90° 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. A 48 TRANSIT S UR VE YINO. 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 not 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 ei^hemeris 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 callehe 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 2,401i in., or 200 ft. 1^ in., which is the radius of the curve. The formula is thus stated, A ^2 + ^ 2)2 ~2BD~ - Or, applied to the above example. 1002 4- q = 2,40U in. - 200 ft. U in. 2X3 To Find the Radius of a Circular Railroad Curve, the Straight Portions of a Road Being Given.— If Q I and P D, Fig. 3, are the straight portions that are to be connected, the radius of the curve I D may be found as follows: Produce Q I and P D until they meet and form the angle T. Bisect the angle Q TP by the line TC. From the point on either line from which the curve is to be^n, in this instance making the point I 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 D, draw a line from C, perpendicular to TP. The line CD will also be a radius of the circle of which I D 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, K R, 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 AP, PP is perpendicular to Q A and KR. 80 SURVEYING. To find the radii OB, C Q, Fig. 3 (c), to connect two straight lines of rail- road, A B, DE, the rOad has to pass from the point B, through the point C, and to touch the straight road E F 2 it any point D. Join B and C, make the angle B CO = 0 B C, which is supposed to he given, equal ^{P—TB C. Draw B 0 perpendicular to AB, then OB = CO, and is the radius of the arc B C. With 0 B SiS radius, describe the arc B C; draw CF perpendicular to CQ, and produce B E to meet it in F; make D F = CF, and draw D Q perpen- dicular to E F, to meet C Q in Q. Then CQ = QD, and the radii 0 B and QD 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 B, 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 f 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 g f. 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 hk 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 f g 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 f 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 work, 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, th6 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 Akthuk 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 distances from 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 wuth 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 h 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 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 h B, in Fig. l{b), 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: d _ a 'p ~ 1' d = ^ a, (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 .vires; I = distance of stadia wires apart. If p remained the same for all lengths of sight, then ^ 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): Therefore, — + i i approximately, , ^ ''d , and _ = _ _ 1 . ^ ^ ^ d a From (1), Whence, P I f »= T « + /• (S) 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 -^ = i is only approximately true, and p a j 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 f form, and also in that the expression corresponding to ~ is a constant, and that the amount to be added remains, practically, /. The constant corre- sponding to -y may be called lc\, 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 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 readings 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. I The instrument * This is demonstrated later on. t ft is dependent on I, 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' -f- /. t 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, and a fuller description is contained in “ Annales des Mines,” Vol. XVI, fourth series. 84 SURVEYim. 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, ft 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 (&), A B = a = reading on rod; me = d ^ inclined distance = c + GF = c + k, CH\ MP = D = horizontal distance = d cos w; FP = Q = vertical distance = D tan n\ n = vertical angle; AG B = 2m. It is first required to express d in terms of a, n, and m. From the proportionality existing between the sides of a triangle and the sines of the opposite angles, AF __ GF ~ sin [90° + (w — m)] ’ or, and or, or AF = GFsinm cos {n — m)* BF _ sin m GF ~ sin [90° — (7t -f m)] ’ 1 B F = G F sin m A F B F = G F sin m AF F BF = a, and GF = cos {n -{-my r 1 + ] Lcos(w — m) cos(7i-[-m) CR ^ CH cos m 2 tan m ~~ 2 sin m' By substituting and reducing to a common denominator, CR cos m [cos (ti + m) + cos (n — m)] 2 cos (?^ -J-m) cos(n — m) Reducing this according to trigonometrical formulas. ^ cos2 n cos2 m — sin^ n sin2 m CR = a T , cos n cos2 m as d = M F = c -{■ k. CR. , , - cos2 n cos2 m — sin^ n sin- m d = c -{■ ka 5 . cos n cos2 m The horizontal distance, D — d cos n. J) = c cos n -{- k a cos^ n~ka sin^ n tan^ m. The third member of this equation may safely be neglected, as it is very small even for long distances and large angles of 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 The vertical distance Q is easily obtained from the relation: Q — i)tanw. Q = c sinn -{- ak cosn Sinn; • . 7 sin27i or, Q = c sin w 4- a A: — - — . (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 ak 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: Distances. Feet. Spaces Intercepted on the Rod. 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. Specbt in an article on Topographical Surveying in “Van Nostrand’s Engineering Magazine,” February, 1880, though enlarged and corrected. 86 SUEVEVING. 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 + .17 600 498.67 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 onlj' .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 A: + 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.! 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 thh 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 k 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 he held vertical, and the stadia wires be equidistant from the center wire. They are as follows: D = c cos n ak cos^ n; Q D tan n = c sin n + ak sin2w^ 2 ’ 1 ) = horizontal distance; Q = difference of level; c = distance from center of instrument to center of object glass, plus focal length of object glass; k = focal length of object glass divided by distance of stadia wires apart; a = reading on stadia rod; n = vertical angle; ak = 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 ak cos2 n and sm2yi qyqyy 2 minutes, when ak = 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', ak = 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^n when ak = 100; therefore, when ak = 570, a k cos2 n = 98.80 X 5.70 = 563.16. To this must be added c cos ti, 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) + .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. 88 STADIA MEASUREMENTS. o o Diff. Elev. l>l>I>t^t>t^I>I>t^I>l>l>I>t^l>I>-l^OOQOOOCOCOGOQOODQOOOOOOOCOOO i-IrHTHrHr-lTHrHT-lT-lT-H^T-lr-l^rHrHrHT-lTHrHrHrHrHrHrHT-lT-lT-li-HrHTH '-i Hor. Dist. 96.98 96.96 96.94 96.92 96.90 96.88 96.86 96.84 96.82 96.80 96.78 96.76 96.74 96.72 96.70 96.68 96.66 96.64 96.62 96.60 96.57 96.55 96.53 96.51 96.49 96.47 96.45 96.42 96.40 96.38 96.36 2 s. Difr. Elev. 15.45 15.51 15.56 15.62 15.67 15.73 15.78 15.84 15.89 15.95 16.00 16.06 16.11 16.17 16.22 16.28 16.33 16.39 16.44 16.50 16.55 16.61 16.66 16.72 16.77 16.83 16.88 16.94 16.99 17.05 17.10 CO '-i Hor. Dist. S §0 .*s i 13.78 gSg8SS?5SS8!§SSSSE2gS8S5 383^ i lO.ZO 15.34 15.40 15.45 S Hor. Dist. S o Diff. Elev. 12.10 T2.15 iilli XZi.UU 12.60 12.66 12.72 12.77 12.83 12.88 12.94 13.00 13.05 13.11 13.17 13.22 13.28 13.33 13.39 13.45 Id.OJL 13.‘73 13.78 S S Hor. Dist. iiSiiSliiSiiiiiiliiiliii ^SS8 gggg TtH I-'; S Diff. Elev. 10.40 10.45 10.51 10.57 10.62 10.68 10.74 10.79 10.85 10.91 10.96 11.02 11.08 11.13 11.19 11.25 11.30 11.36 11.42 11.47 11.53 11.59 iX.OX 11.87 11.93 11.98 12.04 12.10 S Hor. Dist. 98.91 mm 98.88 98.87 98.86 98.85 98.83 98.82 98.61 98.60 98.58 98.57 98.56 98.54 98.53 98.51 s 0 Diff. Elev. 8.68 8.74 8.80 8.85 8.91 8.97 9.03 9.08 9.14 9.20 9.25 9.31 9.37 9.43 9.48 9.54 9.60 9.65 9.71 9.77 9.83 9.88 9.94 10.00 10.05 10.11 10.17 10.22 10.28 10.34 10.40 o lO Hor. Dist. 2 ' o Diff. Elev. «Di>t>i>t^i^i^i>i>i>i>i>i>-'t-‘i>i>x>i>-‘i>oidQ6odo6cx5c6odo6odo6o6o6 s S O j 1 Hor. Dist. gggggsggsggsgsggsgsggggsggsgsgs 8 a o CO Diff. Elev. u:j lO lO lO »o lO lO lO lO id id id lO lO o CO «:> 'sd cd cd CO cd cd cd o CO IU5 CO ;d ;d s o Hor. Dist. 99.73 99.72 99.71 99.71 99.70 99.69 99.69 99.68 99.68 99.67 99.66 99.66 99.65 99.64 99.63 99.63 99.62 99.62 99.61 99.60 99.59 99.59 99.58 99.57 99.56 99.56 99.55 99.54 99.53 99.52 99.51 8 r-; 2 Diff. Elev. § S S Hor. Dist. §8SSS5SgSSSSS8S8S§3SS8gSSSSf:E:gges:SE2f; gggggggggggsggggggsggsssgsggggg 8 2 Diff. Elev. 2S222ii33§i3liii§S5issii5iiasis § § Hor. Dist. ggggggggggggggggggg-gggggggggggg 8 rH- 2 o o ta > S w O OT Wq O S S 88SSSg888SS8SgggggggggggggggSSS i§i§ii§ii^§i*8g8gSgg8gg88ggggg I 2 V) c = 1.00 1 c = 1.25 1 STADIA MEASUREMENTS. 89 o Diflf. Elev. 32.14 32.18 32.23 32.27 32.32 32.36 32.41 32.45 32.49 32.54 32.58 32.63 32.67 32.72 32.76 32.80 32.85 32.89 32.93 32.98 33.02 33.07 33.11 33.15 ill O CO CO CO O CO CO CO lO CO Hor. Dist. 88.30 88.26 88.23 »».ll 88.08 88.04 88 00 o 19° 1 Diff. Elev. 30.78 30.83 30.87 30.92 30.97 31.01 31.06 OJ-.J-U •31.15 iiii gss gsg g885 i 31.65 31.69 31.74 31.78 31.83 31.87 31.92 31.96 32.01 32.05 32.09 32.14 lO CO CO Hor, Dist. 89.40 89.36 89.33 89.29 89.26 89.22 89.18 89.15 89.11 89.08 89.04 89.00 88.96 88.93 ill 88.71 88.67 88.64 88.60 88.56 88.53 88.49 88.45 88.41 88.38 88.34 88.30 H 18° 1 Diflf. Elev. 29.39 29.44 29.48 29.53 29.58 29.62 29.67 29.72 29.76 29.8 L 29.86 29.90 29.95 30.00 30.04 30.09 30.14 30.19 30.23 30.28 30.32 30.37 30.41 30.46 au.oi 30.55 30.60 30.65 30.69 30.74 30.78 CO Hor. Dist. iO(MQOu: 8888 vyj.oo 90.31 90.28 90.24 90.21 90.18 90.14 90.11 90.07 90.04 90.00 89.97 89.93 89.90 89.86 89.83 89.79 89.76 89.72 89.69 89.65 89.61 89.58 89.54 89.51 89.47 89.44 89.40 rH lO 05 1 1.19; o Diflf. Elev. 27.96 28.01 28.06 z,o.ou 28.34 28.39 28.44 28.49 28.54 28.58 28.63 28.68 28.73 28.77 28.82 28.87' 28.92 28.96 29.01 29.06 29.11 29.15 29.20 29.25 29.30 29.34 29.39 CO o CO S' Hor. Dist. 91.45 91.42 91.39 91.35 91.32 91.29 91.26 91.22 91.19 91.16 91.12 91.09 91.06 91.02 90.99 90 96 Sggggggggggg 90.52 90.48 90.45 lO leri J 16° 1 Diflf. Elev. sags 26.69 26.74 26.79 26.84 26.89 26.94 26.99 j Hor. Dist. 92.40 92.37 92.34 92.31 92.28 92.25 92.22 92.15 92.12 92.09 92.06 92.03 92.00 91.97 91.93 91.90 91.87 91.84 91.81 91.77 91.74 91.71 91.68 91.65 91.61 91.58 91.55 91.52 91.48 91.45 r 1 1 Diflf, Elev. 25.00 25.05 25.10 25.15 25,20 25.30 25.35 25.40 25.45 25.50 25.55 25.60 25.65 25.70 25.75 ggggggsss sag? sag? Z,U.O-J 26.40 26.45 26.50 Hor. Dist. 93.30 93.27 93.24 92.80 92.77 92.74 92.71 92.68 92.65 92.62 92.59 92.56 92.53 92.49 92.46 92.43 92.40 (M CO 05 S ol-I Diflf. Elev. 23.47 23.52 23.58 23.63 23.68 23.73 23.78 23.83 23,88 23.93 23.99 24.04 24.09 24.14 24.19 24.24 24.29 24.34 24.39 24.44 24.49 24.55 24.60 24.65 24.70 24.75 24.80 24.85 24.90 24.95 25.00 05 s Hor. Dist. 94.15 94.12 94.09 94.07 94.04 94.01 93.98 93.90 93.87 93.84 93.81 93.79 93.76 93.73 93.70 93.67 93.65 93.62 93.59 93.56 93.53 93.50 93.45 93.42 93.39 93.36 93.33 93.30 CO 05 1 1.211 13° Diflf. Elev. (Nr-(NOOCO( OSClOOr-li sasiss! S83? gj g| si gj gj S gj ?l 85 ?5 S sags ^0.0^ 23.37 23.42 23.47 I> 1-H Hor. Dist. 94.94 94.91 94.89 94.86 94.84 94.81 94.79 94.76 94.73 94.71 94.68 94.66 94.63 94.60 94.58 94.55 94.52 94.50 94.47 94.44 94.42 94.39 94.36 94.34 94.31 94.28 94.26 94.23 94.20 94.17 94.15 CO I> 05 2 12° 1 Diflf. Elev. 20.34 20.39 20.44 20.55 20.60 20.66 20.71 20.76 nSS Zi.DU 21.66 21.71 21.76 21.81 21.87 21.92 CO 05 2 o rH Diflf. Elev. 18.73 18.78 18.84 ±o.ov 18.95 19.00 19.05 19.11 19.16 19.21 19.27 19.32 19.38 19.43 19.48 19.54 19.59 19.64 19.70 19.75 19.80 19.86 19.91 19.96 20.02 20.07 20.12 20.23 1 20.28 20.34 lO s Hor. Dist. 96.36 96.34 96.32 96.29 96.27 96.25 96.23 96.21 96.18 96.16 96.14 96.12 96.09 96.07 96.05 96.03 96.00 95.98 95.96 95.93 95.91 95.89 95.86 95.84 95.79 95.77 95.75 95.72 95.70 95.68 CO 11 V = 1.00 1 a II V 90 STADIA MEASUREMENTS. % CO Diff. Pllev. 43.30 43.33 43.36 43.39 43.42 43.45 43.47 43.50 43.53 43.56 43.59 43.62 43.65 43.67 43.70 43.73 43.76 43.79 43.82 43.84 43.87 43.90 43.93 43.95 43.98 44.01 44.04 44.07 44.09 44.12 44.15 s Hor. Dist. 2 0 01 C ^ J ( load is raised (in ft. )j ^ 33.000 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 lb. The total load equals car + contents + rope = 2,000 + 2,000 + 1,500 = 5,500 lb. The vertical height through which the load is hoisted equals 1.000 X sin 30° = 1,000 X .5 - 500 ft. 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 = WX pitch, or P : W : : p : 2 n r. 2 TT r p ' 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 lb. applied at the end of a wrench 14 in. long, using a screw with 5 threads per inch ? WX^ = 40 X 28 X 3.1416. W = 17,593 lb. The wedge usually consists of two inclined planes placed back to back. (Fig. 6.) In theory, the same formula applies to the weage as to tne inclined plane. Case 2. Fig. 6. P : W w thickness of wedge ; length of wedge. 94 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 IF, 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-haff 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 = ^ W. v' — 2 V. Combinations of Pulleys.— (1) In Fig. 9, we have the IF sustained by three cords, each of which is stretched by a tension equal to the P, hence, 1 lb. of power will balance 3 lb. of weight. (2) In Fig. 10, a power of 1 lb. will in the Fig. 7. Fig. 9. Fig. 10. Fig. 11. S 4 21 » Fig. 12. same manner sustain a IF of 4 lb., and must descend 4 in. to raise the IF 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 a*? great as the load on the free end as there are parts of the rope support- ing ttw 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 IF is 16; hence, IF = 16 P. If n = number of pulleys, p = \Y = 2" P. Differential Pulley.— Fig. 13. IF = V-y 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 comm.on point of application, draw the diagonal of the parallelogram; this diagonal will he 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 of 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 lb. standing on another block, and it takes 35 lb. pressure to slide it, the coefficient of friction = or .35. Table of Coefficients of Fkiction. 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 .14 .082 Wrought iron on brass .17 .103 Cast iron on cast iron .15 .100 Cast iron on brass .15 .103 S*teel 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. 9G 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 coeflicients of Motion 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 Bell metal .07 .049 Wrought iron Bell metal .07 • .05 Wrought iron Cast iron .07 .05 Cast iron Cast iron .07 .05 Cast iron Lignum vitse .10 Wrought iron Lignum vitae .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 -f 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 XPXE; .0112 X P X P; H = .000000556 X P X P X P; .000000339 X P X P X P; 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 coal. 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 41f in. gauge, 3^ 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 on 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 ft. per min., the cars being attached to the moving rope by a chain, a ring at the end of which was slipj)ed 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 if for slow start and motion to 12^ for the rapid motion and twenty-car trips. Summary of Friction Tests on Susquehanna Coal Co.’s Mine Cars, April, 1889. 98 ELEMENTS OF MECHANICS. No. of Tests. •papBoi . 1-1 OXCO ^ O00l>l> 1276 [286 •i!^draa COCOTt^t^COCOCCO i-ICOiOtH tH 0X0^ O lO lO rH 1 Old-Style Wheels. | Loaded. | •iqSx9jii JO oSEjaaojaj 1 Level. OCOOC^ OlO 00 lO CO CO coos CO hc} 5 c4 CO iH r-H 1 Grade. 1 3.94 2.00 2.79 i> Cars pulled from side. J 1 Curve. oooo I> CO CO rJH CO rH 1 -H 1 Total number of tests •noi'joTjj oj 9na uox JOd OOJO^i OAIJOTJJX lOi-noOTf os--^ C» O U01> i001 l>iO C^J lO O CO 1-11:^ CO CO »0 lO OX lO O CO I-Il'' CO CO ox (M 1-1 I-H 1,950 1,800 425 O 05 CO CO O rH Tf ox TJH GC rH I-H UBO JO jq3i9A\. 8,500 7,885 7,885 7,885 9,000 9,000 7,885 7,885 7,885 OOOO OOOO lO t-^^o^o oefod 05”of Ph a w •jqSia^ JO oSBjuaoaad COCCOXOiOOOSOX TfODiOCOOO(NCXi-l Tf? CO cx’ ox’ ox’ CX TlH 00 ox O 00 o o o o o 05 1 -H OO OO CO o o •^’ CO ox ox’ CO lO lO OO O CO CO lO OOOXtJH lO ox Tl? •noijoud oj arid ’uox J9d aojo^ 8ATJ0TEJX OCDCOrtHOXt^COO OCOuOCOCOTlHCig tel® “m O 00 ox ox lO CO CO 1—1 CO CO CO GO I-H I-H t-H 1—1 1—1 125 62 50 100 •nopoiJd oj ana jad aojod aAijoEJj, M|e« OCOrt^OXOXt^COO OGOiOCOCO^tiOSCO i-l CO lO »C O ox UO CO CO O CO CO CO 00 rH rH rH 1 -H I— ( 125 62 50 100 •iCjiATSjf) oj ana aoaoa aAijonjj, lO tO tto OO 00 ox o ^ rfi CO 05 o Tf ^ OX OX •JBO jad aojo^ aAijoBJjj oco-^oxoTt^coo OGOiococoTjiaico rH CO O O lO O CO lO CO lO I-H ox Tf 00 I-H O lO lO rH rH rH CO CO 125 62 50 100 •JBO JO jqSiaji oooooooo OXt-IiHi-IOXOXOXOX ox’' ox” of of of of ox” ox” ooo oooo Tf Tf Tf Tf TTH rH rH rH OX OX OX OX of of of of of of of 2,240 2,240 2,240 2,240 C5 ^ o 0.2, o o B Bto ■ o3 o3 jii oT CO oT o OJ ‘ o o o .li! '♦-I Q O O frH t-i -i ^00^0 (H O) d 5f ^ ""IIIIb-s illllIBB coajfldddcoaj OOOOOOOO bX)tX)b£)tyDfcJCfcyc6ctiX) o3^c3^c3o3cda3 oooooooo o o o CO I— I rH o o o o (N oa ic «o .s ""S§IS . rd ^ .d O o" o ^ • dn d< pH pH Ph«h-i «d . . . . +J O O^H CO CO (N rH CO CO CC 00 2.20 2.36 1.63 1.93 05 CO CO CO lO CO 8§?SS (M rH tH iH OCOCOOO 005CO lO d I— 1 t— t iH lOOOO d CO CO CO oToococo OO 00 CO 00 CO 1> TjJ CO Tf lO d d iH r-l r-5 aj5-|2®l2„i4. d lOI> CO CO lO CO CO CO S’doS’t^ COCOTtiCOCO CO CO Tfi CO CO UO lO lO lO iC I—t I— 1 T-H rH T—* ddd"(dd ddcoco dcoco 3.73 1.58 1.85 1.69 SoOT^ W O d lO ^ CO iH rH -H CO CO 05 d 05 05 Tfl I— 1 CO CO d d 2,000 1,825 400 350 1 8,160 8,160 [8,160 1 8,160 4.06 1.56 1.12 «e-g 0»0i0 O5C0d O0QOt>- 05COd 502 502 73 ooo s^s 2,415 2,415 2,415 JO og'BjuaoJoj; •uopoij^j oj on’a uox jad aoaojj aAijoBix •aoijOTJjj oj ana jad aojo^d aAijonax •^fjiAnjf) oj ana aoio^i aAijoBJx •j'BQ jad aoJOjj aAjiOTSJx •a«0 JO jqSia^ •jqSia^Vi JO aS'Bjuaoja^ •aotjouj 01 an'a *aox jad aojo^i aAiioBJx •UOIlOtJ^J 01 ana •I'BO jad aojo^j aAjio'BJx •^fljA'BJf) 01 ana aojoj^ aAiioisjX •JBO Jad Oojo^i aAjio'BJx •JBo JO jqSioji - ^ 'N CO .0.0X1 O 0) o 0 0 0 0 O oil o o t-i O^Oh o> . . O-tJ^ . -M o o • d O O •*j -tj o ® ^ lO tH fH S-> -M ^ ^ 0 “ o o o ^loii M o) q q q 0) 0) 0) o» 0) 5c bo be be be o3 ^ o3 q ^ ;h ;h M M ;-i O) 0) 0> 0) 0) ^> > > > U f-i 03 o3 O O esa 'a o o Onft O) . . o o -O o q q “ o o o tq 43 "q llli 0) o> o> O) be be be be q c3 ^ c3 fH M ^4 f-l 0) 0) o> 0) > > > > be CO 1 ^ CO oT'O q q 0 <<-1 Vh Oh ffiSg - -R, tn M c3 c3 .. ■Sto ^ SS-* O) 02 0) O) o o o o >>> 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 feedwater 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 conditions, 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 lb. of water per hour; the other plant had a simple engine, taking 30 lb. 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 lb. 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- ])lishing 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 lubricants, leaving it to the purchaser himself to determine as to the intrinsic worth of the lubncante offered to him. In making his selection he would 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 most careful study, and who would most probably have the benefit of a wide experience in the applica- tion as well as the manufacture of lubricants. Some buyers have, to then ultimate regret, ^opted, 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. _ . i x, • x- 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 ri^nt 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 mme 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, becai^e 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 co'st 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, ^ ^ 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 acts as a reservoir for the oil, the oil passing from this reservoir through small holes onto a felt washer, which it must saturate, and by which it is applied to the axles. Such w^heels require a limpid oil, as a heavy, sluggish oil w’ould not so readily saturate the felt w asher referred to. A tight cap is adjusted to the end of the axle, to prevent waste of oil. These wheels will run quite a length of time without reoiling after the reservoir is once filled. Of course, it costs something to equip mine cars with these patent axles, but w e are convinced that such an outlay w^ould 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 RSTOn). Low temperatures, as in rock drills) driven iy compressed air | Light mineral lubricating oils. Very great pressures, slow speed { ‘lubS^®’ Heavy pressures, with slow speed | ''' HeaiT pressures and high speed { ^Sral' 0 "!^” Light pressures and high speed e-oft^e Lard oil, tallow^ oil, heavy mineral oils, and the heavier vegetable oils. Steam cylinders -j Heavy mineral oils, lard, tallow. (Clarified sperm, neat’s foot, x>or- Watches and other delicate mechanism. ^ poise, olive, and light mineral ( lubricating oils. For mixture with mineral oils, sperm is best; lard is much used; olive and cottonseed are good. Ordinary machinery.. STRENGTH AND WEIGHT OF MATERIALS 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 betw^een the supports, and multiply the quotient by the constant given in the table on the next page. Take safe w orking 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 betw’een 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 w orking load of a yellow-pine collar 8 in. square, 12 ft. between legs. 8 ^ 8 ^ Breaking load = — — X 500 = 21,333 lb. for seasoned, and 10,666 lb. for green timber. Safe w’orking load = 7,111 lb. for seasoned, and 3,556 lb. for green timber. Example 2.— Find the quiescent breaking load, and the safe w'orking load of a hemlock collar 10 in. diameter, 7 ft. betw een legs. Breaking load — ^ x 236 = 33,714 lb. for seasoned timber, and =* 16,857 lb. for green timber. OQ 714 11 9*^ Safe w’orking load = — -- — = 11,238 lb. for seasoned, and — or — — = 5,619 lb. 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. IRON AND STEEL BEAMS. 103 Example.— A rectangular collar 10 in. deep supports 15,000 lb. What will it support if its depth is increased to 12 in.? 10-' : 122 : : 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? _ _ if 6 : if 12 : : 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 lb. What will be the diameter of another beam the same length, to support a load of 19,440 lb.? if 32,160 : ^19,440 : : 11 ; 9. Ans. Example 2.— A beam 8 in. in diameter will support a load of 10,240 lb. What load will a beam the same length and 7 in. in diameter support ? 8^ : : : 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 vitae 650 383 Ash, black 300 177 Larch 400 236 Balsam, Canada 350 206 Maple 550 324 Beech, white 450 265 Oak, red or black ... 550 324 Beech, red 550 324 Oak, white 600 353 Birch, black 450 265 Oak, live 600 353 Birch, yellow 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? 83 ( 13 1:2::^: or 1 : 2 : : 2 X 83 : ( )3, or if r : if 2 : : 8if 2 : ( ) = 12.7. Ans. IRON 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 Safe Loads Uniformly Distributed for Standard and Special I Beams. {Tons of 2,000 Pounds.) 104 STRENGTH OF MATERIALS, •(jqSiaAi ui osBOioui •qi'iCiOAa joj ppv I O 05 OO tOiOLOiO 1 tH o o o o o oooo COt^OOCOGOOCO' Ul OSROJOUI •qi'XjOAa JOJ ppy r-l00lOC0 05 lO CO I>CO (MCarHrHrHr-lTHTHi-l OOOOOOOO 1> OO lO lO 00 CO iq CO C CO CO " 1-1 1-1 tH i-l rH »-l 1-1 iH i-( O O O O O lO CO rtt ' ^ CO CO o4 (o4(No oi o < 0acOTtlCOTHO5O5r •p0^ UT s:;jod(Jns uaaAvpg oour^^stq; lO CO 00 I •^qSpA\ UT osBajouj •qT;'toAa joj ppy 05 05 iH 25 ^ S 22 05 Qo CO 05 CO CO 05 1> CO O lO CO O 1> iC CO I— I o 00 l> iO CO CO iO lO l 6 lO ^^^^^c6c6c6c6c6 •;qSpA\ UT ospajoui •qq; AjOAq joj ppy jO05|>C0i0Tt 1> CO CO cdidiOiOiOiOTjH-TjJT^rjH qqSpAV ut osBajouj •qq XjOAq joj ppy 05 erfectly 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 .013 .015 .017 .020 .0225 .025 .030 .035 to .050 FLUMES. 145 As it is quite diflQcult to obtain the value of c by Kutter’s formula, the fol- lowing three approximate formulas for v are given: For canals with earthen banks, If the ditch is lined with dry stonework, /100,000r2s ^ ~ \ 9 r + 35 ‘ ;ioo,ooor^ If the ditch is lined with rubble masonry, v 1100,000 r2s \ 7.3r + 6 ’ To find the quantity Q of water fiowing through any channel in a given time, multiply the velocity by the area, or Q = av. 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 an^ 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' 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 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. 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. 116 HYDRAVLICS. Fig. 12 shows a timber flume in which no joints are cut, the bottoms of the posts being kept in place by stringers spixed 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 diagonarbraces. 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 i" 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. 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 deflnite 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: 1 100,000 r2 S \ 6.6 r + 0.46’ 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 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 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 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. FLOWTHROUGH 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 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 ah 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 b, the water would have no tendency to escape, but, on the contrary, air would probably enter, and the pipe flow only partially full from b 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 TJLICS. 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 = Y.S. gallons per minute; D = 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 = \/Wh = V = i.onV^- For diameter in inches, Q = Pipes between 3 and 8 in. in diameter, rough inside surface, q 0.89 = 0.89 D'^VWfi) V = 1.13i/dA. Large pipes, smooth inside surface, q = = 1.4 ir-\/'Dh] V = 1.78i/;M. Small pipes, smooth inside surface, q = = 1.25 D^\/Dh\ V = l.e/DA 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 done the results are liable to be disappointing, since 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 H D = .538 5 LX 'A/ H Hawksley’s Formula: G = number of gallons delivered per hour; L = length of pipe in yards; H = head of water in ffiet; 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 r s — 11 ^ r s. In cylindrical pipes, v multiplied by 47 . 124^2 gives the discharge per minute in cubic feet, or v multiplied by 293.7286 d2 gives the discharge per minute in gallons, d being the diameter of the pipe in feet. COMPARISOy OF FORMULAS, 149 COMPARISON OF FORMULAS. R = mean hydraulic depth in feet *= area wet perimeter circular section of pipe; J£ S = sine of slope = j- ; 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 1 / RS— .08; or, v = 99.88i/i2 5— .154. Eytelwein, V = 50-^1 1 dH L + 50 d' Eytelwein, V = 108/i2S- .13. Hawksley, V = 48^ 1 dH L + 54 d' Neville, V = 140i/RS-llfRS. Darcy, V = C|/ R S] for value of C, see following Table. = - for 4 Diameter of pipe (inches) k 1 2 3 4 5 6 1 7 i 8 Value oi C. 65 80 93 99 102 103 105 106 107 Diameter of pipe (inches) 9 10 12 14 16 18 20 22 24 Value of C 108 109 109.5 110 110.5 110.7 111 111.5 111.5 Maximum value of C for very large pipes, 113.3. Kutter, where V = Cy RS, 181 + .00281 (7 = .00281 \ ~) Weisbach, h L r 2 }/’ 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. Darcy, d V^12d' Siphons.— When any part of the pipe line rises above the source of supply, such a line is called a siphon. If this rise is greater than the height of tlie water barometer (34 ft. at sea level), water will not flow through the siphon. The flow through the siphon will oe 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 ULICS. B S g 5 s I I imMmmmmmmmimmm r^-rH'-r^-cic^'-C^'c^’-COCOCOiO^^^^ imrnimmmMmmMmmi " issiigg SSHSSS5SgEJg|S3||g|a||["'“'_ awsiEw^isiigimiffliilif -djilrl "co cb ib'o. I- CN ^ ^ CO ^ rH o'i> cn'co ar T-l r-( r-l I-H I-H tH rH co':ot^Tj'!^(MT-ii:bi^ cainovoo>coinocJOto>nrHm^cD -®--saa3ssssssi:«sss^|S|S|gs| O0>t-.tDC0rtt>Tl-t0>o'iS<5‘l:-^00(M<»r4«S!^5 M^(N 3S35!S3S!S2;Sa3aS?S"SgSiilI S S 3 SSSSSSS^??^^^^ 9 mm» 9 » T-'OCOCD00 0 04rt.oV^-(NrHOiOCOO^O^OO . ■rHrHr-5T--loic4oiC4c4Tl?iOOcbl>Qb05a5 0;^'» il-sis rHrHr-l,-l(M04(M04(MTfii0OC01>Q005a5O^C0;;H^ga;rHC0^ «??'«««33S53Sgi«Sia!!!!l .s .s .s .s .s .s .s .s .g .g .g .g .g .g .g .g .g .g .g .g .g .g .g .S .g .g .g .S rlOICOTriO'Ol-XOitrHOlCOrfiCy^l^OOasrH'MCOTf^tOOl-OOaiO The quantities above are American gallons per minute. For cubic feet, divide by 7.5. 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 Pel ton Water Wheel Co. Inside Diameter of Pipe. Inches. Velocity. Ft. per Sec. 1. 2 3 4 5 6 Loss of. Head. Ft. Cu. Ft. per Min. Loss of Head. Ft. Cu. Ft. per Min. Loss of Head. Ft. Cu. Ft. per Min. Loss of Head. Ft. Cu. Ft. per Min. Loss of Head. Ft. Cu. Ft. per Min. Loss of Head. Ft. Cu. Ft. per Min. 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 1.093 7.07 .819 12.5 .650 19.6 .547 28.2 2.6 3.78 .86 1.891 3.40 1.260 7.65 .945 13.6 .757 21.3 .631 30.6 2.8 4.32 .92 2.160 3.66 1.440 8.24 1.080 14.6 .864 22.9 .720 32.9 3.0 4.89 .99 2.440 3.92 1.620 8.83 1.220 15.7 .978 24.5 .815 35.3 3.2 5.47 1.06 2.730 4.18 1.820 9.42 1.370 16.7 1.098 26.2 .915 37.7 3.4 6.09 1.12 3.050 4.45 2.040 10.00 1.520 17.8 1.220 27.8 1.021 40.0 3.6 6.76 1.19 3.380 4.71 2.260 10.60 1.690 18.8 1..350 29.4 1.131 42.4 3.8 7.48 1.26 3.740 4.97 2.490 11.20 1.870 19.9 1.490 31.0 1.250 44.7 4.0 8.20 1.32 4.100 5.23 2.730 11.80 2.050 20.9 1.640 32.7 1.370 47.1 4.2 8.97 1.39 4.490 5.49 2.980 12.30 2.240 22.0 1.790 34.3 1.490 49.5 4.4 9.77 1.45 4.890 5.76 3.250 12.90 2.4.30 23.0 1.950 36.0 1.620 51.8 4.6 10.60 1.52 5.300 6.02 3.530 13.50 2.640 24.0 2.110 37.6 1.760 54.1 4.8 11.45 1.58 5.720 6.28 3.810 14.10 2.850 25.1 2.270 39.2 1.900 . 56.5 5.0 12.33 1.65 6.170 6.54 4.110 14.70 3.080 26.2 2.460 40.9 2.050 58.9 5.2 13.24 1.72 6.620 6.80 4.410 15.30 3.310 27.2 2.650 42.5 2.210 61.2 5.4 14.20 1.78 7.100 7.06 4.730 15.90 3.550 28.2 2.840 44.2 2.370 63.6 5.6 15.16 1.85 7.580 7.32 5.060 16.50 3.790 29.3 3.030 45.8 2.530 65.9 5.8 16.17 1.91 8.090 7.58 5.400 17.10 4.040 30.3 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. 7 8 9 10 11 12 -2 p, > d ^ fl" s ir £.3 .S s 1, o d a «H C3 Jh ij s w pH » ft tJ a> PC o S PP o S. PP o S, 2.0 .338 32.0 .296 41.9 .264 53.0 .237 65.4 .216 79.2 .198 a 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 .81 6 166,0 .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 1.02g 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 L183 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" j 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 £-1 "n u. Ft. r Min. Ft. Min. o Ft. Min. o Ft. Min. < 4 - ^ o a o o’ o O o "g p u o 'g p ^ i S H ij « O. n O K ^ e, w Q « P* K o « o< 1-3 V w O. 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.€ .290 144 .270 167 .252 191 .236 218 .210 275 .189 340 2.S .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 3.3 .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 4.8 .815 254 .757 295 .707 339 .662 385 .588 488 .529 602 4.1 .881 265 .818 308 .763 353 .715 402 .636 509 .572 628 6.0 .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 1.083 359 1.011 412 .949 469 .843 594 .758 733 5.3 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 24 26 28 30 36 w § o QB • - a o o © -J o k , £ o o ■ k >' a J- 1-9 4) te s •- o s , Los Head s , Los Head Los Head p ki OS . Los Head 9 t - O g, Losi Head og, 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.« .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 8.0 .222 475 .204 565 .188 663 .174 770 .163 883 .135 1,273 8.8 .249 507 .229 603 .211 708 .195 821 .182 942 .152 1,357 S.i .278 538 .255 641 .235 752 .218 872 .204 1,001 .169 1.442 8.t .808 570 .283 678 .261 796 .242 923 .226 1,060 .188 1,527 8.8 .840 601 .312 716 .288 840 .267 974 .249 1,119 .207 1,612 4.0 .378 633 .342 754 .315 885 .293 1,026 .273 1,178 .228 1,697 4.2 .408 665 .374 791 .345 929 .320 1,077 .299 1,237 .249 1,782 4.4 .444 697 .407 829 .375 973 .348 1,129 .325 1,296 .271 1,866 4.8 .482 728 .441 867 .407 1,017 .378 1,180 .353 1,.355 .294 1,951 4.8 .521 760 .476 905 .440 1,062 .409 1,231 .381 1,414 .318 2,036 5.0 .581 792 .513 942 .474 1,106 .440 1,28^ .411 1,472 .342 2,121 5.2 .602 823 .552 980 .510 1.150 .473 1,334 .441 1,531 .368 2,206 5.4 .645 855 .591 1,018 .546 1,194 .507 1,385 .473 1,590 .394 2,291 5.8 .690 887 .632 1,055 .583 1,239 .542 1,437 .506 1,649 .421 2,376 5.1 .735 918 .674 1,093 .622 1,283 .578 1,488 .540 1 ,708 .4.50 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 the same results as the foregoing table and will be found useful in many instances: F = +5F— 2), where = 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 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. Fig. 17. A = angle of bend or knee with forward line of direction; V = velocity of water in feet per second; R = radius of center line of bend; r = radius of bore of pipe (or i diameter); K = coefficient for angles of knees; L = coefficient for curvature of bends; H = head of water in feet necessary to over- come the friction of the bends, or knees. H = .0155 V^K. The value of K is as follows for different angles: = 1 20° 40° 60° 80° 90° 100° 120° K = 1 .046 .139 .364 .74 .98 1.26 1.86 For bends, 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 .131 .138 .158 .206 .294 .44 .66 .98 ! 1.4 2.0 In rectangular L .124 .135 j.l8 .25 .4 .64 1.01 1.55 2.3 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. 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 conflne 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 lo^s. 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 bv building up the lo^s 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 drv 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. la DAMS. 155 either case, some structure should be constructed above the outlet so as to ])revent 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. 10 ft.). Water is allowed to discharge through this during flood time, blit 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 2" 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 upder 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 HYDRAULICS. 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 ^ven 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 10^ 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. Debri« Dims.— 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 debris 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 natUT-e, 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 win§- 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. Misonry Dims. — 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 WQH = gross power in foot-pounds per minute, WQH ^ — = the horsepower. and 33,000 Substituting the value for Tf' we have - = .00189 Q H, as the horsepower of a fall. ooj 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 Feltons, etc. 4. By a combination of the above. The Horsepower of a Running Stream.— The gross horsepower, as seen above, is in which Q is the quantity in cubic feet per minute actually impinging on the float or bucket, and H the theoretical head added to the velocity of the stream, or 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 == = .139, and Q = 2X 10 X3X 60 = 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 or 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 168 HYDRAULICS. proportioned, it is possible to realize from to 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 unwatering 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 TJMP MA C MINER Y. 159 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 pump will start from any point, and can never be stalled for lack of steam, due to the position of the valves. Ordinarily, duplex pumps are to be pre- ferred for mine work. The packing for the water piston of a pump maybe either inside ov 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- Fig. 19. 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 ^reat 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- without flywheels or cranks. Fig. 20. mately constant, and direct-acting pumps, 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 hulk of the water from the bottom of the shaft, large pumping engines 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 veij 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 lb. 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 lb. of steam per horsepower per hour. Compound-condensing pumps, such as are commonly used as station pumps, consume from 40 to 70 lb. of steam per horsepower per hour. Triple-expansion, condensing, high-class pumping engines consume from 24 to 26 lb. per horsepower per hour. 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: (r = U. S. gallons per minute; d' = diameter of suction pipe in inches; d"= diameter of discharge pipe in inches; ‘*'= 4 . 95 ^ 1 ; <*"= 4 - 95 ^ 1 ;. v' = velocity of water in feet per minute in the suction pipe = from .50?/' to .75?/'; r" = velocity of water in feet per minute in the discharge pipe. A : D P : P ■■ E : RATIO OF STEAM AND WATER CYLINDERS IN A DIRECT-ACTING PUMP. area of steam cylinder; H = head of water ^ 2.309 p; diameter of steam cylinder; steam pressure in pounds per square inch; pressure per square inch, corresponding to the head H „ work done in pump cylinder efficiency of pump = — ^ ' work done in steam cylinder a — area of pump cylinder; d = diameter of pump cylinder; .433 H\ ap EP' EAI\ d --= t) P\l \ P ap ^ II II P ’ E~A* P = E A P^ a ’ 11= 2.309 FP X — a CAPACITY AND HORSEPOWER OF PVMPS, 161 If ^ = 75/., then H = 1.732 P X E 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 he 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 Then, Q ~ cubic feet of water per minute; G = U. S. gallons per minute; O' = 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* U = height of lift in feet; H. P. = horsepower. d2 ^ = 4 * Q=4 NdH = .0004545 Wd2/. 231 IN 144 ’ 12 .0034 iV^d2 1 Qf = .204 Nd^ I The diameter of piston required for a given capacity per minute will be d = = 17.15^'^, ord = 13.54^| = 4.95^f. 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. „ p _ _QP _ QRX 1 44: X .433 ^ QH ^ 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 p mrp MA CHINEE 1 : etc., and hence -we 'vvill call the total amount of water to be handled 40 gal per minute. The formula for the diameter ^f piston is Assuming that v = 100 ft. per^nute, we have d = 4.95]/ A = 4.95 X .63 = 3.13. In practice, a 3^" 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: G XP _ 30 X .433 X 125 1,714.5 1,714.5 = .95, or practically 1 H. P. In order to cover leakage through valves, friction, etc., an addition of at least should be made to a very small pump like this, and so we would count on U H. P. Depth of Suction.— Theoretically, a perfect pump will raise w^ater 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 buoket 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 lb. per horsepower per hour; for medium-sized electric pumps, about 30 lb. of steam per hour, and larger sizes from 20 to 80 lb. per horsepower per hour. It will be seen from these figures that for PUMV 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. 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 h(')isting engine would otherwise be idle. Wlu n* 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 lOfo, which is 25^ 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 substituted for the ordinary mine skips. These bailing buckets ran on the inclined skip road, and unwatered 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 about I 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. Fig. 21. Fig. 22. 160 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 lb. 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 2^ 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 lb. 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 of Combustibles. Air Re- quired. Temperature of Combustion. Theoretical Value. Highest Attainable Value Un- der Boiler. Kind of Combustible. Pounds per Pound of Combustible. With Theoretical Supply of Air. With 1^ Times Theoret- ical Supply of Air. With Twice Theoret- ical Supply of Air. With Three Times The- oretical Supply of Air. Pounds of Water Raised 1° per Pound of Combustible. | Lb. of Water Evapora- ted From and at 212°, with 1 Lb. Combustible. With Chimney Draft. With Blast, Theoretical Supply of Air at 60°, Gas 320°. Hvdrogen 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 "I ( 'arbon -j Coke > 12.13 4,580 3,215 2,440 1,650 14,500 15.00 13.30 14.14 (Anthracite.... j ('oal, 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 14,600 3,330 2,540 1,720 15,080 15.60 14.01 14.76 Coal, Lignite 9.30 3,210 2,490 1,670 11,745 12.15 10.78 11.46 Peat, Kiln dried 7.6814,470 3,140 2,420 1,660 9,660 10.00 8.92 9.42 Peat, Air dried, 25^ water 5.76 4,000 2,820 2,240 1,550 7,000 7.25 6.41 6.78 Wood, Kiln dried 6.00 4,080 2,910 2,260 1,530 7,245 7.50 6.64 7.02 Wood,Airdried,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, w'hen 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. Hickory (shell bark) Hickory (red heart) White oak Red oak Sjn-uce New .Tersey pine Weight. Wood. Weight. 4,469 Beech 3,126 3,705 Hard maple 2,878 3,821 Southern pine 3,375 3, -254 Virginia pine 2,680 2,325 Yellow pine 1,904 2,137 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, 2| to 2i lb. dry wood, 2|- to 3 lb. dried tan bark, 2f to 3 lb. cotton stalks, 3i 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 2i times the same weight of coal, or about 30,000 cu. ft. are equal to a ton of coal. Shck, 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 §ood coal = 7i eu. 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. Coal. Moisture. Volatile Matter. Fixed Carbon. Ash. 1 Sulphur. Heating Value per Lb. Coal, B. T. U. Volatile Matter Per Cent. of Combustible. Fixed Carbon. Per Cent, of Combustible. Heating Value per Lb. Combustible. Theoretical Evaporation From and at 212° per Lb. Combustible. 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 Clearfield 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. . . Youghiogheny, Pa. . 1.26 30.12 59.61 8.23 .78 14,050 34.03 65.97 15,300 15.84 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. Upper Freeport Seam, Pa. 1.81 35.33 53.70 7.18 1.98 13,200 40.27 59.73 14,500 15.01 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 . . Hocking Valley, Ohio . 4.80 34.60 56.30 4.30 13,010 38.20 61.80 14,300 14.80 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(?) 14.91 Scott Co., Tenn. . . 1.26 35.76 53.14 8.02 1.80 13,700 34.17 65.83 15,100(?) 15.63 Jefferson Co., Ala. . . 1.55 34.44 59.77 2.62 1.42 13,770 37.63 62.37 14,400(?) 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 Lignite and Lignitic Coals. 6.44 37.57 47.94 8.05 12,230 43.94 56.06 14,300(?) 14.80 Iowa 8.45 37.09 35.60 18.86 8,720 51.03 48.97 12,000(?) 12.42 Wyoming 8.19 38.72 41.83 11.26 10,390 48.07 51.93 12,900(?) 13.35 Utah 9.29 41.97 44.37 3.20 1.18 11,030 48.60 51.40 12,600(?) 13.04 Oregon lignite . . . 15.25 42.98 33.32 7.11 1.66 8,540 54.95 45.05 11,000(7) 11.39 A British thermal unit (B. T. U.) is the quantity of heat required to raise the temperature of 1 lb. of water 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 lb. of water 1° C. 1 French calorie = 3.968 British thermal units. 1 B. T. U. = .252 calorie. 1 lb. 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: )• in which C. //, and 0 are, respectively, the percentages of carbon, hydrogen, and oxygen. Heating value per lb. = 146 (7 -f ( CLASSIFICATION OF COALS. 169 Heat in pound calorie = 8,080 C -f 34,462 yH ~ or = 8,080 C + 34,462 f ) + 2,250 S. Heat in B. T. U. = 14,650 C — 62,100 (^H - in which C, 0, H, and S represent the weights of carbon, oxygen, hydro- gen, and sulphur in 1 lb. of the substance. i)- Composition of Fuels. {Mechanical Draft, B. F. Sturtevant Co.) Description. Carbon. Hydro- gen. Oxy- gen. Nitro- gen. Sul- phur. Ash: Anthracite. France 90.9 1.47 1.53 1.00 .80 4.3 Wales 91.7 3.78 1.30 1.00 .72 1.5 Rhode Island 85.0 3.71 2.39 1.00 .90 7.0 Pennsylvania 78.6 2.50 1.70 .80 .40 14.8 Semibituminous. Maryland 80.0 5.00 2.70 1.10 1.20 8.3 Wales 88.3 4.70 .60 1.40 1.80 3.2 Bituminous. Pennsylvania 75.5 4.93 12.35 1.12 1.10 5.0 Indiana 69.7 5.10 19.17 1.23 1.30 3.5 Illinois 61.4 4.87 35.42 1.41 1.20 5.7 Virginia 57.0 4.96 26.44 1.70 1.50 8.4 Alabama 53.2 4.81 32.37 1.62 1.30 6.7 Kentucky 49.1 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 66.9 5.32 8.76 1.02 2.20 15.8 Lancashire gas coal 80.1 5.50 8.10 2.10 1.50 2.7 Boghead cannel 63.1 8.90 7.00 .20 1.00 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. Pennsvlvania (crude) 84.9 13.70 1.40 Caucasian (light) 86.3 13.60 .10 Caucasian (heavy) 86.6 12.30 1.10 Refuse 87.1 11.70 1.20 CLASSIFICATION, COM POSITION, AN D PROPERTI ES 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 fiame and no smoke, but gives a great heat. Contains very little volatile combustible matter. Color, deep black, shining; sometimes iridescent. Fracture, conchoidal. 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 fiame, 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 semi viscid 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 of Coal. * {Coze Bros. <& 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 55.52 36.02 Free-burning stove 56.33 35.50 Lehigh broken 56.85 35.18 Free-burning nut — 56.88 35.16 Lehigh egg 57.74 34.63 Pittsburg 46.48 43.03 Lehigh stove 58.15 34.39 Illinois 47.22 42.35 Lehigh nut 58.26 34.32 Connellsville coke 26.30 76.04 Lehigh pea 53.18 37.60 Hocking 49.30 40.56 Lehigh buckwheat... 54.04 37.01 Indiana block 43.85 45.61 Lehigh dust 57.25 34.93 Erie 48.07 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 fiame. 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 fiame 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 0to7 Semianthracite 7 to 10 7.5 to 12 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 lb. 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 flame, 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 lb. of weight to be handled and 20 lb. 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 SI. 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 which 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 lb. 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 lb. 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 eonditions 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, firebox 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 the 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 20fc nor more than 30/c 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 20fc 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 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 i of a generous share, say 37^c 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 in. and through 4i in. square mesh. Egg, over 2 in. and through 2^ in. square mesh. Stove, over If in. and through 2 in. square mesh. Chestnut, over f in. and through If in. square mesh. Pea, over fin. and through f in. square mesh. Buckwheat, over f in. and through f in. square mesh. No. 2 Buckwheat, or Bird’s-eye, over f in. and through in. square mesh. The sizes of bituminous coal are Lump, Nut, and Slack. All coal that passes over bars If in. apart is called Lump. All coal that passes through bars If in. apart and over bars f in. apart is called Nut All coal that passes through bars f 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. W. F. Hillebrand, C. B. Dudley, and W. A. Noyes: Sampling. — At least 5 lb. 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 face. 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 general sample, samples of such portions of the vein as may display these differences. Moisture.— Dry 1 g. 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 a 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 li 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 10^6 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. In 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 i 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 .3 g., the third .5 g., 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 62.50 Ash 10 11.11 Total 100 100.00 100.00 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 lb. 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. Per Cent. 10 20.0 20 22.1 30 23.7 40 25.0 50 26.1 60 2’;.0 80 28.6 Lb. Per Cent. 100 29.8 125 31.1 150 32.2 200 33.9 250 35.3 300 36.5 170 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.^; 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 2,2.2‘fo. 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 hack 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 cylinjirical 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 expansiod 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 | in. The safe working pressure was about 60 lb. 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 lb. 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 lb. of water per hour from, a feedwater temperature of 100° F. into steam at 70 lb. gauge pressure, which is considered equivalent to 34.5 units of evaporation; that is, to 34.5 lb. of water evaporated from a feedwater temperature of 212° F. into steam at the same temperature. Example.— A boiler evaporates per hour 1,980 lb. of water from a feed temperature of 100° into steam at 70 lb. gauge pressure. What is the horsepower of the boiler? Since, under the given conditions, an evaporation of 30 lb. is equivalent to 1 horsepower, the number of horsepower is 1,980 -h 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 = 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. case 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. Type of Boiler. ^ Heating Surface Ratio = . » Horsepower .r. .. Heating Surface Grate Area Plain cylindrical 6 to 10 12 to 15 Flue 8 to 12 20 to 25 Return - tubular 14 to 18 25 to 35 Vertical 15 to 20 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 | 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 f = 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^ 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 32 X .7854 X 2 = 1,159.26. Total heating surface in square feet = 18,096 + 111,290.4 + 3,769.92 — 1,159.26 , — ■ — = 916.64 sq. ft. Ans. 144 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; lb. water evaporated per sq. ft. of heating surface per hour .... 2 3 3.5 4 4.5 5 6 7 8 Total water evapora- ted by 120 sq. ft. heating surface per hour, lb 240.00 360.00 420.00 480.00 540.00 600.00 720.00 840.00 960.00 Horsepower; 34.5 lb. per nour = 1 H. P. . 6.96 10.43 12.17 13.91 15.65 17.39 20.87 24.35 27.83 Pounds water evapo- rated per lb. com- bustible 10.88 11.30 11.36 11.29 11.20 11.05 10.48 9.48 8.22 Pounds combustible burned per hour ... 22.10 31.90 37.00 42.50 48.20 54.30 68.70 1 88.60 116.80 Pounds combustible per hour per sq.ft, of grate 1.85 2.65 3.08 3.55 4.02 4.52 5.72 7.38 1 9.73 Pounds combustible per hour per horse- power 3.17 3.05 3.04 3.06 3.08 3.12 3.30 3.64 j 4.16 1 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 lb. than when it is 3-5 lb. DANGER OF EXPLOSION. 179 The figures in the preceding table that represent the economy of fuel, viz., ‘ Pounds water evaporated per lb. 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 tiring and with every other condition most favorable. Unfavorable conditions, such as poor tiring, 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 boiler are: 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 tinallv 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, while 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 nsually 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 lire 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 lb. of water in 10 hours, or 390 tons per month; in comparatively pure water there would be 88 lb. of solid matter in that quantity, and in many kinds of spring water as much as 2,000 lb. 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 sv'diment 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; I in., 38^; and \ in., 60fc. 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 S750 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 of 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 feedwater. 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. Addition of barium chloride, etc. Carbonate of soda in large amounts. Priming. 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 lb. 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 lb., 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. Outside Diameter of Pipe, Without Felt. 1 Thickness of Covering. In 2 In. Diameter. 4 In. Diameter. 6 In. Diameter. ' 8 In. Diameter. 12 In. Diameter. Loss in Units per Foot Run per Hour. Ratio of Loss. Feet in Length per H. P. Lost. Loss in Units per Foot Run per Hour. 1 Ratio of Loss. Feet in Length per H. P. Lost. J 1 SS in Units per Foot Run per Hour. o o .2 Feet in Length per H. P. Lost. Loss in Units per Foot Run per Hour. Ratio of Loss. 1 Feet in Length per I 1 H. P. Lost. Loss in Units per Foot Run per Hour. Ratio of Loss. Feet in Length per 1 H. P. Lost. 1 0 219.0 1.00 132 390.8 1.00 75 624.1 1.000 46 729.8 1.000 40 1,077.4 1.000 26 1 4 100.7 .46 288 180.9 .46 160 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 .06 1,238 33.7 .054 860 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 op 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 fianged 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 i 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, 34i lb. 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 heat 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, fioats, or water alarms, but try the gauge-cocks. If they do not agree with water gauge, learn the cause and 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 yV' 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 outfiow 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 weakeh 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. 16ths. 34 In. Lb. 36 In. Lb. 38 In. Lb. 40 In. Lb. 42 In. Lb. 44 In. Lb. 46 In. Lb. 5 169.9 160.4 152.0 144.4 137.5 131.2 125.5 4i 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 31 113.2 106.9 101.3 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: . . . , cubic feet per hour gross feedwater Area in square inches = . ■ 8001 / pressure in atmospheres Delivery in Gallons per Hour with a Pressure Diameter of per Square Inch of Throat. Decimals 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 Mercury. Tempera- ture. Degrees F. Pressure. Inches of Mercury. Tempera- ture. Degrees F. Pressure. Inches of Mercury. Tempera- ture. 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 1.70 2.00 2.60 3.50 4.00 4.50 5.00 6.00 7.00 8.00 Per lb. combustible, maximum of other boilers, Centennial tests 11.90 12.00 12.10 12.05 12.00 11.85 11.70 11.50 10.85 9.80 8.50 Subtract extra radia- tion loss for cylin- der boilers 1.32 1.12 .87 .75 .64 .56 .50 .45 .37 .32 .28 Probable maximum per lb. combus- tible, cylinder boilers 10.58 10.88 11.23 11.30 11.36 11.29 11.20 11.05 10.48 9.48 8.22 Scheme for Boiler Test. 1 Number of test 2 Made by 3 Type of boiler 4 Date of test -5 Duration of test Hr. Dimensions and Proportions. 6 Number of boilers tested 7 Diameter, boiler In. 8 Length, boiler Ft. In. 9 Width, grate Ft. In. 10 Length, grate Ft. In. 11 Number of tubes No. 12 Diameter of tubes In. 13 Length of tubes Ft. In. 14 Total water heating surface Sq. Ft. 15 Total steam heating surface Sq. Ft. 16 Grate surface per boiler Sq. Ft. 17 Per cent, air space in grate 18 Ratio water heating to grate surface 19 Area of stack Sq. Ft. 20 Height stack above dead plates Ft. 21 Ratio stack area to grate surface Average Pressures. 22 Atmosphere by barometer In. 23 Steam pressure by gauge - Lb. CHIMNEYS. 189 Scheme for Boiler {Continued), 24 25 26 27 '28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 Force chimney draft, inches water Force blast in ash pit, inches water Average Temperatures. Of external air Of hreroom Of steam Of feedwater before heater Of feedwater after heater Of stack gases Fuel. Kind of coal Total coal consumed Moisture in coal Total dry coal consumed Total ash and refuse Per cent, ash and refuse in dry coal Total combustible consumed Calorimetric Tests. Per cent, moisture in steam Degrees superheat in steam Water. Total water pumped into boiler Water evaporated corrected for quality of steam Equiv. water evap. to dry steam from and at 212° Equiv. water evap. to dry steam from and at 212° per hour Economic Evaporation. Water evap. per lb. dry coal actual pressures and temp Equiv. water evap. lb. dry coal from and at 212° Equiv. water evap. lb. combustible from and at 212° Rate of Combustion. Dry coal burned per hr. per sq. ft. grate surface Combustible burned per hr. per sq. ft. grate surface Dry coal per hour per H. P. developed Rate of Evaporation. Water evap. from and ) Per sq. ft. grate surface at 212° per hour /Per sq. ft. heating surface Commercial Horsepower. Basis 20 lb. water from 100° feed to 70 lb. steam per hour.... Horsepower builders rating Heating surface to one horsepower developed Per cent, total horsepower due to feed heater. In. In. OF OF OF OF OF OF Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. Lb. H. P. H. P. Sq. Ft. fo CHIMNEYS. Chimneys have two important duties to perform, the first being to carry otF the waste furnace ^ases, 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 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, when 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 tlie quotient will be the height of the chimney in feet. Let A = area of chimney; H == horsepower of boiler; h = height of chimney. ( — \ 3.33 4 -2/^/ Then, 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 ? h = ( ^ — t=Y= \3.33 X 7 — 2l/ 7 / \3.33 X 7 — (2 X 2.65) J 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 flreroom, 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-drajt 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, of 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 Avas 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 33,000; 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: I. H. P. = 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 lb. 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, PXJiV^_ 40XlfX (10- X .7854) X 500 _ 59 5 g p 1. H. P. 33^000 33,000 Approximate Determination of M. E. P.— To approximately determine the M. E. P. of an engine, when the point of apparent cut-otf 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: Rule.— Add 14.7 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 — & constant (see following table); M. E. P. = mean effective pressure. Then, M. E. P. = .9[A:(p + 14.7) - 17]. Table. Cut-Off. Constant. Cut-Off. Constant. Cut-Off. Constant. .566 f .771 2 .917 .603 .4 .789 .7 .926 .659 h .847 .937 .3 .708 .6 .895 .8 .944 .743 6 s .904 7 s .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 f cut-off, and 92 lb. gauge pressure in the boiler, the M. E. P. is, by the formula just given, .9 [.917(92 -P 14.7) — 17] = 72.6 lb. 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 lb. gauge. 80 + 14.7 = 94.7. The constant for i 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 lb. per sq. in. Then, PLAN_ 56.89 X if X (.7854 X 92) X 240 X 2 “ "Wor “ “ "^poo “ 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 of loss by radiation. If a glass gauge tube is too long, take a triangular file and wet it with turpentine; 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 ineh or so apart, and then try to bend the glass, using your thumbs as fulcrums, and it will break at the mark, Avhich 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 o'ften 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 2^ 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 lb. 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 1? 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 then 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 oif 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, | 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 31, 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: (а) 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. (б) 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 Anally 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), (&), (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 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 the 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 lb. In using 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 60/c. *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 lb. 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 F = P' F' = a constant; in which F 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, hy a constant pro- portional part of the volume that it occupied at the freezing point; or, F' = V {1 P a t°), in which a equals 5^3 for centigrade degrees, or 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 F = P' F' is true. 2, Adidbatically, when the temperature is allowed to rise without check during the compression. Since the pressure rises faster than the volume diminishes, the equation P' / F P F = P' F' no longer holds, and we have = ( pv ) » 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. * iuoy 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 horsenower developed by the steam end of the compressor, as shown bv 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 lb. 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. 92 X 3.14 = 254.3 sq. in. = piston area. X 380 = 668.8 cu. ft. = volume dis- placed per minute by the piston; deducting lO/o for loss gives 602 cu. ft. At sea level at 15 80 lb. 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. 0 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 properly applied. But the question of heat loss is not the only consideration. Low first cost and simplicity of construction are often more advantageous than a close approximation to isothermal compression. Latterly, the wet system 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 1" 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 I)’ Arcy. As adopted for compressed-air transmission, it takes the form: = c^^ — P 2 ) Wil in which D = volume of compressed air in cubic feet per minute discharged at final pressure; c = coetficient varying with diameter of pipe, as determined by experiment; d = diameter of pipe in inches (the actual diameters of If" and ly' 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; wi = 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: 10,000 D^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; o = coefficient, depending on the size of pipe. TRANSMISSION OF AIR IN RIPFS. 197 Values of a for nominal diameters of wrought-iron pipe: 1" 350 3" 730 8" 1.125 U" 500 3F' 787 10" 1.200 U" - 662 4" .840 12" 1.260 2" 565 5" 934 2i" 650 6" 1.000 The values of a fur 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 ib. 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 Ebervale, Pa., two 31" 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 cost 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 li" 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 li in., are butt-welded, while all from li 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 hot often necessary underground, as the temperature is usually nearly constant, except in shafts, or where there may be considerable variations of temperature between su mm er 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 M to 10^. This can all be saved. The third loss or series of losses arises in tne 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/c. It is clear that if the air were conveyed through a pipe, and the length of the pipe and the veloeity of flow were such that 2.9 lb. pressure was lost in friction, then its efficiency, instead of being 94.85f 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 lOO/ei 14.7 lb. IK, and 88.2 lb. only a trifle over ^ of \veen a and &, 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 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 fiowing 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 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 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 swit(!li 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 ab is known as an alternation. An alternation is, therefore, half a cycle. The number of cycles passed through per second is known as XhQ 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 Fig. 23. frequency of 60 is very 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: _ number of poles , , rev. per min. Frequency = 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 / = X = 60 cycles per second. - Alternators may be divided into the two following classes: (a) Single- phase alternators; (6) 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 , 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, bul they are gradually being replaced by multiphase machines, because the single-phase machines are not well suited for the operation of alternating- current motors. (5) 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 I', the other circuit connects to rings 2 and 2\ 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 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; (5) Induction motors. (rt) 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. AL TERN A TING- C UR RENT MO TORS. 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 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 MO TOES, lines of force. The speed drops slightly from no load to fhll 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- Fig. 28. vide the armature with a winding simih the terminals to collecting rings, so that armature circuit. tacts whatever. Such motors can therefore operate with absolutely no 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 required, it is customary to pro- • to that of the field and bring out resistance may be inserted in the 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, 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 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: Fig. 29. Fig. 30. Secondary E. M. F. = primary E. M. F. X secondary turns^ primary turns ' BATTERIES. 229 j -r^ nr T-. primary E. M. F. or, secondary E. M. F. = - — ^ — - — 7 . primary turn s secondary turns The ratio primary turns . , • IS known as the 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 transforma- 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 1000 v-~* p lonnnnnnnnnr Fig. 33. -‘joo r — • Fig. 31, ■1000 V- p' WifffirBTnrmNi rminnn s' -100 V- 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 LeclancM 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 Pig 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 w'here the insulation is good and where there is no leakage causing the cell to give 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 delivery 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 (&) 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 in parallel across the battery wires, as in Fig. 37 at a and 6, 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 eacn 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 AA ® fl Ut ¥ 'sa bcOi SI ,2 •S''? pH oT 'd a «a >1 03 o ^i OS o ^ ^0-2 ’S rd .2 O C3 -'O 3i C o) d o'd W ^ «rrt ' d 0^ d i1S^|2 IS'Ssofi d od3 JSrd a ag'dS'go Ph O M d dd3 •d ^ S ^ I (jj VO^ a ft to .s « ^ s O) ^ .2d ^1 O) d r^ M 'dd Oft ^ gs o « O ^ -M O 'S fH rrt tn 53 ^ O d w 'd p>»'d ^ ^ ^ o o .jH ♦ 5 Opd d^ ^ 2 9 d p, S d'd'S'd-d.d^ d god.^g^o-go O CO CQ o o o o d G d o o o .22 O.G 020 go o 2 oo ftrrt 9 d-d 2| -gd di G o S:3 .a.2-a pq-M G o^H : : rt d 2 ^ d S 03 'ag-2ftg^9 ?0 CCridO OOVh M.G O o od ^ w J ^ 2 pS M OjH -M O rt +S M O P.S ^ ftts g g d ft-rHp3 ft-drd S 03 o ^ fto ^ fto bo O O Ph 2^.0^ ^ ft;-( M f-{ O 03 o3 c3 QOO O P fto S §i too rH OO CC O O ^a-^a a ° g as-i o3 W.G o3 o ■^ft p — — •Grp o G 'dGl o“ ^ 2 o ft ftft fto o o >^o .2 •I 9< ;p : : ^ • . bX) dj p §g§9”'2a o o o o o G G G G N N N N G G G G N N N CSJ N >A d= _: ►■d'^:o o^'di^g'S : O i S i?-d c3 I'drrtgOGSgo G f I ^BfJJifs4l% Q Q Cb A A O A d Ph Ph 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. ring a bell from one of a ' Fig. 40. Fig. 41. Fig. 42. 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. Ihe keys k' are of the double-contact type, making connections normally between bell h or b' and line wire L. When one key, as k, is depressed, a current from B flows along the wire through the upper contact of k' to bell h' 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, b to the bell and battery. This current releases a pivoted arm which, on falling, completes the circuit betw'een 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 tw^o or three Leclanche cells is placed at 'B in any convenient location. The size of wire used throughout may be No. 18 annuncia- tor wure. 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 etc. for each g lace. The upper portion of the annunciator oard 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 BELL WIRING. 233 position, the closing of the circuit by the push button in any room, such as No. 4, rings the office bell and releases No. 4 drop, the path of the current in Fig. 43. this case being from push 4 to a-c-d-e-f-g-B-h-h back to the push button. On the return sig- nal being made by pressing the button at the lower part of the annunciator board, the office-bell circuit is broken at d, and a new circuit formed through k as follows: From the battery B to g-m-r-n-o-a-c-k-p to battery, the room bell being in this circuit. A gen- eral fire-alarm may be added to this system, consisting of an automatic clockwork appa- ratus for closing all the room-bell circuits at once, or as many at a time as a battery can ring. When this system is installed, the bat- tery wire should be either No. 14 or No. 16. Four or five Leclanche cells are usually re- quired in this case. It will be seen that the connections are so arranged that the room bell will ring when the push in that room is pressed. If this be not desired, a double-contact push may be substituted, so that the room-bell circuit is broken at the same time that the circuit is made through the annunciator. This double push should be so connected that the circuit is nmmally complete through the bell, the leading wire being connected to the tongue, and the battery wire being connected to the second contact point, which is normally out of circuit. Telephones are also used for signaling and communicating purposes. It has been found that a first-class long-distance bridging tele- phone is the best type to use. Bridging tele- phones are so called because they are bridged or connected in parallel across the line, and are not connected in series. If one telephone should get out of order, the others are not likely to be disabled. Fig. 43 shows a com- plete bell annunciator and telephone outfit, lac. LJEVKI. 8JfD. LEVEL aBD. LEVEL '1 234 ELECTRIC SIGNALING. Hoisting Engine House, 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 Fig. 44. 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 between 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. The conductors a and 6, leading from the battery run parallel to each other along the roadside, and about 6 in. apart. A short iron rod, placed across the wires a, h, 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 r.o/tev Fig. 48. V/OO' \200 [^< 300 * ^ 00 * in' Fig. 48. White lights indicate a clear track and dark- ness an occupied section. A single-center hinge, double- — handle switeh 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, 4i 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 perfeet 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 If lb., and should have a piek on one end and a square-faced ham- mer on the other, the handle bein^ 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, suflicient 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 lb. 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 lb. 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, ana 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 SigillariaQ, 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 riot 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 defined 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 accomjmnied 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 and flat portions of the mountain i:)arks 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 OEE 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 bave 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 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 oh 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 mst 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 caseSj 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. 4-Lb. Sample. Grains. Fineness, 780. Value per Oz., S16.12. Fineness, 830. Value per Oz., $17.15. Fineness, 875. Value per Oz., $18.08. Fineness, 920. Value per Oz., $19.01. 5.0 $83.97 $89.36 $94.20 $99.05 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 .6 10.07 10.73 11.30 11.88 .5 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 lb. 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 61b. 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 1" 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 If" iron bar, fitted with ordinary 1" 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, w^ater, 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 the character of the strata penetrated than is the case with the diamond drill. In the case of highly inclined beds of varying hardness, the holes frequently run out of line and be- come so crooked that the tools w'edge. and drilling has to be suspended. For drilling through moderately hard formations, usually encountered in searching for gas or w'ater, such as sandstones, limestones, slates, etc., the accompanying costs, from the American Well 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. Cost of Well-Drilling. Size of Well. Inches. Cost per Foot. 6 $1.50 8 2.25 10 3.00 12 5.00 15 8.00 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 in. to lx% 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 PROSPECTim. 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 ':he 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, l)Ockets, 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 S5 or more per foot to sink, while the cost of drilling in firm rock varies from 10.50 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 $1.15 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 $0.7703, which was divided as follows: Carbons $0.34 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 r 400i days setter at $3.00 $1,200.75 1 Cost. per Ft. ToU.^r.J 372 days runner at 2.25 837.00 ! m aaq Labor j 230i days runner at 2.00 460.50 f ^^,506.10 $0,669 [ 4i days laborer at 1.75 7.85 J 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 1,414 ft. 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 Payroll 4,000.03 0.502 Total cost f7,045,25 $0,834 246 PROSPECTING. Records of Cost per Foot in Diamond Drilling. A B C D E F G H I J K L M N 0 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 .5:18: .295 .621 .384 ; .549 .516 .495 .519 .595 .644 .722 .636 Repairs .... .1:^9 .110 .294 .171 1 .135 .144 .103 .185 .154 .165 .040 .087 .138 .126 .116 Supplies . . . .034 .065 .039 .074 .023 .032 .011 .039 .048 .097 .020 .092 .076 .097 .088 Carbon .... .263 .658 .859 .860 .843 1.587 .934 1 .684 .684 .733 .227 • .209 .553 .239 1 .330 Supt .239 .322 .628 .040 .063 .192 .140 .305 1 .259 .172 .347 .220 .106 .196 .199 Total . . . 1.849 3.024 5.348 2.852 1 1.940 4.407 2.692 1 1 3.696 3.007 3.285 2.293 2.732 2.582 2.374 ^2.604 1 A 5 holes, 1,066 ft. T Sandstone and marble. B 1 hole, 1,293 ft. Black slate and jasper. J C 3 holes, 478 ft. Jasper, very hard. K D 5 holes, 780 ft. Jasper, hard. L E 1 hole, 216 ft. Iron slates. M F 1 hole, 174 ft. Jasper and slate. N G 2 holes, 267 ft. Jasper and slate. 0 H 3 holes, 410 ft. Jasper. Average cost of total work of drilling 21 holes. Total of 4,684 ft. 2 holes, 634 ft. Iron slates. 2 holes, 360 ft. Schist and jasper. 6 holes, 1,350 ft. Iron slates. 2 holes, 611 ft. Schist, jasper, and quartzite. 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 0 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 324.2 ft. of rather hard, tough diorite rock: Labor $341.25 Diamonds 74.30 Coal 17.50 Total $433.05 Cost per foot 1.34 (86.6 ft. of this was drilled with a If" bit, and 237.6 ft. was drilled with a li" bit.) Drilling 150.7 ft. of very hard syenite rock: Labor $158.00 Diamonds 298.60 Coal 10.50 Total $467.19 Cost per foot 3.10 (Size of drill U in.) DRILLING OR BORE HOLES. 247 The following was the cost of drilling 286.1 ft. of soft schist rock: Labor S190.00 Diamonds 87.75 Coal 11.50 Total $289.25 Cost per foot 1.01 (Size of drill, If in.) 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 $2,070.00 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 -^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. The Buttes 1,621.2 196.0 1,817.2 Queen Creek 857.8 55.6 413.4 Riverside 729.8 40.2 770.0 Dikes 80.0 0.0 80.0 San Carlos 143.2 30.4 173.6 Total 2,932.0 322.2 3,254.2 248 PROSPECTING. Magnetic Prospecting.—Bodiesof 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 dipping 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 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 F, and the line X Y 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 F, 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 vertical lines to the right and left of it for the indi- 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 6 being consider- ably less, and the dip at a being less than that at h. 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. Fig. 3. Fig. 4. 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 sign 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 Geological 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 yV 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 note^ 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, J5, and (7, 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. 7. strike A f. The distance Ch, equal to Cd, is laid off at right angles to Cg, when the angle Cgh 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 x y 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 EG, 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-section 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' must be projected to the points a, h, c, a', and b', 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 not 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 i proportionate number of shovelfuls for the sample, as every third or fourtn 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 phospecting. 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. The 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 work. 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 i)oint, 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 sloping 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. Situation AND Sur- roundings. { 1. Name. | 2. Distance ■ 1. Location, if on surveyed land. 2. Nearest town or village. 3. Mineral district. . 4. County, state, or territory. and direction from one or more points. REPORTS ON MINERAL LANDS. 253 DIAGRAM FOR REPORTING ON MINERAL LAN DS— (C'onfowwed). { 1. Hills or mountains. 2. Character of surface, vegetation, and timber, 3. Streams and water supply. 4. Elevations. 3. Geology. ' 1. Rocks. 2. Axes. 3. Faults. 1. Struc- ture. 4. Dikes. ^ 5. Horses. 2. Geological period. 3. (a) Coal / 1. Number, beds. ( 2. Thickness. or 1. Veins. (6) Ore bodies. 2. B e d s or lenses. ( 1. Stratified. < 2. Crystalline, f 3. Igneous. Anticlines or synclines. ' 1. Number. 2. Strike. 3. Dip. , 4. Throw. ' 1. Number. 2. Strike. - 3. Dip. 4. Filling. _ 5. Throw. ' 1. Number and size. ^ 2. Location. 3. Material. Uniformity. ^ u?emenr’ Number. urement. Character. Strike. Dip. Width. Vein filling. Ore chutes. Walls. Throw of walls. Number. Walls. Strike. Dip. Length. Height. Maximum width. Average width. 4. (a) Quality of coal, specimens, appearance in mine, in cars, benches. or (5) Ore. 1. Color, external, powder. 2. Luster. 3. Clearness from clay or sand, shale. 4. Sulphur. 5. Resin. 6. Firmness, size of lumps, air slaking. 7. Cleavage or fiber. 8. Coking. 9. Color of ashes. 10. Use: Gas, steam, domestic, forge, metallurgy. 11. Analyses or assays. 1. Shipping. 2. Concentrating. 3. Metals or minerals. 4. Gangue. 5. Impurities. 6. Assays or analyses. 254 PROSPECTING. 4. Mining. 1. History. DIAGRAM FOR REPORTING ON MINERAL LAN DS— ( 1. Dates of opening, abandoning, reopening, number of mines and names, 2. Ownership. 3. Superintendence. 1. Shaft, slope, or tunnel, r 1. Total depth. 2. Extent of J 2. Depth below water level, workings, j 3. Number of levels. t 4. Extent of levels. 3. Water pumps, size, and kind, water cars, number and size, natural drainage. 4. Ventilation, natural, furnace, fan (for- cing or drawing out), sufficient or insuf- ficient. 5. Lighting, system used. 6. Powder, kind and grade used. 7. Explosive or noxious gases. 8. Coal-cutting machines and power drills. 9. (a) Mode of working, holding under, shearing, blasting, or wedging. tid sloping. 2. Mine. (6) Mode of working. 1. Underhand 2. Overhead sloping.' 3. Filling. 4. Caving. 5. Rooming with or with- out timber. 6. Square sets. 10. Rooms, or slopes, pillars, dimensions, and general plan. 11. Timbering, timber trees. 12. Roof, or hanging wall, strong or weak, air slakes or not. 13. Floor, or foot- wall, hard or soft, creeps or not. 14. Roads, rails, and cars. ' 1. Men. 15. System of under- ground tram- ming. 16. System of hoisting. 2. Mules. 3. Electricity. 4. Compressed air. 5. Wire rope. 6. Chain. 7. Locomotive. Cage. Skip. Cars. L '• -L 5. Maps and Drawings. 1. Of the whole region. 2. Of the underground workings. I I. Cross. 2. Longitudinal. (1. General. 3. Columnar. < 2. Coal bed or other de- [ posit. 4. Buildings, works, or machinery. ' 1. Scale. 2. North line, magnetic variations. 3. Date. 4. Maker. 5. Can buy, take, borrow, or have copied. 5. Explanation. 6. Concentra- tion. 1 1 Hand picking. Cobbing and picking. Magnetic. 4. Mechanical, jg Diy REPORTS ON MINERAL LANDS. 255 Coke Ovens. 6. Operations. DIAGRAM FOR REPORTING ON MINERAL LfKHDS-^{Vontinued). 1. History, ownership, etc. 2. Number. 3. Character of ovens. 4. Dimensions. 5. Construction, materials, etc. ' 1. Charge, quantity, etc. 2. Working. , 3. Discharging, quenching. 7. Repairs. 8. Quality of product. (Assays, if any.) ^ 9. Disposition of by products. " ^ In heaps. In stalls. In kilns. 4. By mechanical calciners. 5. Number and dimensions of roasters. 1. Base bullion. I. Metallur- gical Works AND Treat- ment OF Ore. 1. Roasted. jn oi \ 3. 2. Smelted. 9. Disposition OF Product. 1. Shipped. , 2. Shipment. 10. Statistics. ' 1. In shaft fur- nace to 2. In reverber- atory furnace to 3. In retorts to 1. As mined to 2. As concen- trates or coke. 3. Metal or matte to 1. Distance. 2. Roads. 3. Railroads. 4. Navigation, f 1. Capacity. 2. Matte. 3. Metal. 4. Number and dimen- sions of furnaces. 1. Metal. 2. Matte. 3. Number and dimen- sions of furnaces. 1. Metallic zinc. 2. Mercury. 3. Number and size of retorts. 1. Smelter. 2. Concentrator. 3. Sampling works. 4. Jobber at 1. Smelter or furnace. 2. Sampling works. 3. Jobber at 1. Refinery. 2. Smelter. t 3. Jobber at 1. Production. 2. Labor. I 2. Actual Daily, weekly, or month- ly, in tons. 2. Yearly in tons. [S. Average. 1. Whole number of workers. 2. Number of workers in each class. 3. Number of horses or mules. 3. Prices. 1. Timber. 2. Tools. 3. Fuel. 4. Oil. 5. Powder. C 1. Day, different classes. 6. Labor. ^ 2. Contract or piece, yard or ( ton. 7. Carriage. 8. Local sales of product. f 1. Machinery. 2. Buildings. 9. Value of plant. ^ 3. Roads, tracks, etc. 4. Rolling stock. . 1,5. Supplies. 256 PROSPECTING. DIAGRAM FOR REPORTING ON MINERAL LAN DS— ( 11. Surface Plant. 1. Power plant. 2. Shops. Powder houses. 14. Water. 1. Boilers. 2. Waterwheels. 3. Air compressors. 4. Steam and gas engines. 5. Electric plants. 1. Power for. 2. No. of forges. 3. Steam hammers. 4. Other tools. 1. Power for. 2. Saws. 3. Lathes. 4. Other machines. 5. Benches and vises. 1. Power. 2. Lathes. 3. Planers. 4. Shapers. 5. Drill presses. 6. Other tools. 7. Benches and vises. 1. Smith’s shop. 2. Carpenter shop. 3. Machine OflSces. t shop. Dry or change houses. Storehouses. Boarding and dwelling houses. Stables. Shaft houses. Tipples. Pockets or ore bins. Company store. Timber yard and plant for preparing timber. " 1 Citv or eoTo- f 1' Quality of water. me??ial J 2- Sufficient or in- merciai sufficient. 3. Pressure. 1. Quality of water. 2. Suflacient or in- sufficient. 2. Company 3. Gravity system, service. f 1. Direct, 4. Pump- ing sys- tem. 2. Reser- voir or stand pipe. 15. Lighting. 1. Character. 2. Origin. 16. Hoisting or wind- ing plant. 17 . Surface trans- portation. 1. Gas. 2. Electric. 1. Commercial plant. ^ 2. Company plant. 3. Sufficient or insufficient. 1. Steam engines. 2. Compressed-air engines. 3. Oil or gasoline engines. I 4. Electric motors, t 5. Water motors. ' 1. Gauge. 2p Total length. 3. Size of cars. 4. No. of cars. 5. Power used. 6. No. of motors. 1. Character and surface of. 2. Length. 3. No. of wagons and teams. 1. Size and capac- ity of. 2. No. of w agons for, 1. Railroad. 2. Wagon roads. 3. Traction engines. OPENING A MINE. 257 Diagram for reporting on mineral lands— (C bwfo’nwed) 12. Miscellaneous. . Gross. 13. Conclu- sions. 1. Yearly income, last year, or for any year. | ^ 2. Average cost per lb., or ton of material. " 1. Quality of ore or product. 2. Amount of ore or ( 1. Gross, material in sight. ( 2. Net. , 3. Value of material in sight. 2. Value of plant and works. ' 1. Continue present system. 3. Merits of property. 1. Deposits of value. 4. Advice. 1. Mining. 2. Disposition of product. 5. Local considerations. 1 2. Change system to - I 1. Ship as mined. I 2. Concentrate, or coke and j ship. [ 3. Smelt and ship. 1. Troubles. 2. Labor. 3. Supplies. 4. Climate. 5. Shipment facilities. ^ 6. Markets. OPENING A MINE. The location of the surface plant and the mine opening depend on the formation of the deposit primarily, and secondarily on the facilities for transporting the product to market. It is impossible for one not on the ground, and unfamiliar with natural or railroad transportation facilities in the neighborhood, to give an idea as regards the second consideration. In regard to the first consideration, the following observations will be found of value: When the seam or vein outcrops within the limits of the property and is flat, a water-level drift is the best method of opening it. If it has any con- siderable inclination, it should be opened by a slope, or by a tunnel driven across the intervening measures. Where the deposit has an inclination of but from of 1° to li°, the water-level drift is generally used, and the main- haulage entry is opened at the lowest accessible point on the outcrop, which insures free drainage and a favorable grade for haulage. When the outcrop dips into the hill, the drift is usually commenced a few feet below the out- crop terrace, and driven on a slight upgrade until the normal dip is reached. When the inward dip is too strong, the better plan is to sink a shaft in the center of the basin, provided the depth is not too great and the amount of water to be pumped is comparatively small. If the inward dip to the center of the basin does not exceed a total of 25 ft. difference in level, a drift may be used and drainage be effected by a siphon. Water-level drifts are only profitable where the inclined seam is exposed in ravines or gorges eroded across the strike of the measure, or where the vein can be reached by a short tunnel from the surface to the seam across the measures. This is often the case when the seam dips with the hill, but when the dip is against the hill, the tunnel is generally a long one. While the expense of operating a mine opened by a long tunnel is less than one opened by a slope or shaft, owing to cheaper drainage and haulage, when the coal above water level is exhausted the tunnel is almost worthless. When the seam is inclined and is accessible at no point along its outcrop low enough to furnish sufficient lift or breast length, it should be opened by a slope or shaft. Or, if the seam is flat and does not crop on the tract, a shaft is the only method of working it, unless it lies so near the surface that it can be stripped. Where a seam has a dip of 20° or more, and is brought close to the surface by an anticlinal axis or “saddle,” a “rock slope,” or, in other words, a tunnel dipping the same as the seam may be started from the surface, and, when the seam is reached, may be continued to the desired depth in the 258 OPENING A MINE. seam. In sinking slopes for coal mines, it is customary to sink an airway alongside of and parallel with the slope, with a pillar of about 10 yd. between. The slope for coal mines is usually sunk so that there is a “lift” of from 100 to lie yd., and then gangways are turned off on each side. The term “ lift ” in siiis connection means the length on pitch that breasts or rooms, driven at right angles to the gangway, can be driven in good coal. Subse- quent hfts are usually from 80 to 100 yd. long. . Op 3ning Up a Gold Mine.— The following description of the method of open- ing up a gold mine, by Mr. S. A. Joseph! (“ Mines and Minerals,” February, 1900), will also apply in general for the opening of any inclined narrow ore deposit: The equipment for the top of shaft for the preliminary work con- sists of three pieces of timber, either sawed or rough hewn, 12 to 16 ft. long, 8 to 10 in. in diameter, arranged as a tripod; they should be strongly bolted together, a pulley hung from the center, through this a rope passed with a bucket fastened to the end entering the shaft, and a horse hitched to the other end. This equipment is called a whip, and is sufficient for the first 100 ft. in depth. In locating the shaft, care should be exercised in placing it where there is ample dump, or ground for waste or valueless vein matter. Should the character of the surface not admit of sufficient ground for this purpose, have collar (or top) of shaft elevated 10 or 12 ft., and throw waste around the outside of same until filled up solid. The timbers should be square sets, made of rough or square timbers, preferably the latter, 8 in. X 8 in.; divide the shaft into two compartments 4 ft. X 4 ft. each, one for the bucketway, the other for the ladderway. Where air is bad, board up the ladderway to* aid the circulation. The sets should be not less than 4 ft. and not over 6 ft. apart, in the clear. Sink on the dip of the vein, and keep a careful record of the location, width, and value of ore body, until the depth of 100 ft. is attained; here place station sets 8 ft. high, start levels each side of shaft, and, if there is water in the shaft, a sump 16 ft. to 30 ft. deep should be sunk. The sump should be built in the same manner as the shaft, so that it will serve as a continuation of same when greater depth is wanted. Levels should be run on both sides of the shaft sufficiently long to deter- mine length of the ore chute, and also to determine the existence of other ore chutes in the vein. This development work should be an indicator of the strength, value, and permanence of the property; it is now ready for another examination by competent authorities, to determine the above conditions. Should their verdict be favorable, continue the shaft to the depth of an additional 100 ft.; if water is found in but small quantities, this can best be done by replacing the whip with a whim; this runs by the same horsepower, costing in the neighborhood of 8100. It is well adapted to put the shaft down 250 ft. When the shaft is down 200 ft., start levels as at the 100-ft. depth, provide sump, and drift both ways upon the vein, proving up ore bodies as before. Thus far the cost has been slight. The shaft, including timbers, supplies, and contingent expenses, should not cost over 820 a foot, a total of 84.000; the drifts 86 a foot, say 200 ft. each way from shaft on both levels, a total of 800 ft. or 84,800; total, 88,800, less amount received from mineral extracted in sinking and drifting, which is usually small. Now it is to be decided what further amount the owners are willing to expend, and how extensively they desire the mine opened up before the actual extraction of ore is to commence. We will put the depth of shaft at 500 ft., the drifts the full length of the claim, usually 1,500 ft. For this purpose, a shaft house should be built, say 40 ft. X 60 ft., with ore house, say, 40 ft. X 40 ft. The equipment should be a 40 H. P. engine and a 60 H. P. boiler (if a large flow of water is encountered, an additional boiler and pump must be provided), the shaft continued to the above stated depth, and levels extended at each 100 ft. It will also be advisable to make upraises at the farthest point practical from the. shaft, on each side, connecting each level with the other, and extending to the surface. These upraises should be made in ore. and are valuable both for ventilation and escape for men, in case of accident to or near the shaft. They should be furnished with ladders. The machinery, shaft house, and skip, with which all incline shafts should be equipped, will cost about 84,500. The additional 300 ft. of shaft, including contingent expenses of engineers, fuel, etc. will cost 840 a foot, or 812,000; the drifts, 86 a foot. The upraises, being on ore, should pay for the labor. It is prudent to estimate the cost of thoroughly opening up a gold mine to SHAFTS, 259 be between S40,000 and 850,000, which fact probably originated the remark that “it takes a gold mine to make a gold mine.” This is practically true, and no one should attempt to engage in the mining business, as a business, without both money and a willingness to use it. More failures can be attributed to insufficient capital for development than to any cause save mismanagement. SHAFTS. Shafts and tunnels may be, first, temporary, or those that are simply driven for exploration purposes, and are not to be used for any great length of time; second, permanent, or those that are driven for a specific purpose and usually have a definite predetermined capacity. Form of Shaft.— In the United States, shafts are usually square or rectangu- lar in form. This is largely due to the fact that timber is used in lining such shafts. In Europe, round or oval shafts are frequently employed with a lining of brick, iron, or masonry. Compartments.— The number of compartments in a shaft and their arrange- ment depends largely on the use to which the shaft is to be put; also on the number of shafts at the property, and the depth of the shaft. Where the material to be removed is comparatively near the surface, it is usually cheaper to sink a number of 2- or 3-compartment shafts than it is to tram all the ore to one large shaft; while, in the case of very deep mines, large 4- or 6-compartment shafts are sunk, and the underground haulage extends over a greater area. When the shafts are lined with timber, a stronger con- struction can be obtained by placing the compartments side by side, as shown in Fig. 1, than by placing them in the solid block, as shown in Fig. 2. When a body of material compara- tively near the surface is being re- moved through a number of shafts, 2-compartment shafts are frequently employed, both compartments being used for hoisting, and separate shafts being provided for the pump column and ladderways. This re- duces both the size of the shaft and the timbering necessary, and also Fig. 1. Fig. 2. does away with the special danger from fire that always exists when there is a ladderway in the shaft, for it is always difficult to fight fire in these special compartments. Shaft Sinking. — As a general thing, the loose material or wash above bed rock is not thick enough to cause any serious trouble, and ordinary cribbing of heavy timber or a masonry curbing is sufficient. But when the surface is very thick or loose, and runs like quicksand, considerable difficulty is experienced. The general method of overcoming this difficulty in the past was to at once divide the shaft into the required number of compartments by heavy timbers alternating or placed “skin to skin,” which had the effect of-bracing the cribbing against the lateral pressure of the loose material. This method is effectual where the wash will remain solid or stand long enough to allow the timbering and cribbing to be put in. But when the surface is thick, loose, or watery, or of quicksand, some one of the following special methods of sinking must be adopted: “ Forepoling.” “Metal linings.” (Forced down without the use of compressed air.) “Pneumatic”method. (Limited to about 100 ft. in depth. ) ^ “ Poetsch ” process. (Freezing j method. ) Rock (hard or soft, but very wet) | “ Kind-Chaudron ” method. Rock (hard or soft, but not very wet) — I * Continuous, ”or “Long-Hole,” ’ ( method. Size of Shafts. — Shafts vary greatly in size, depending on the number of^ compartments desired and the size of the compartments. For coal mines, they are generally from 10 to 12 ft. wide inside of timbers, and each Quicksand . 260 OPENING A MINE. compartment is from 6 to 7 ft. wide inside the guides. This would make the outside dimensions of a double-compartment shaft about 13 to 15 ft. wide, 17 to 18 ft. long, and a triple-compartment shaft from 24 to 25 ft. long. Shafts at metal mines are generally smaller than those at coal mines, but the prac- tice in different localities varies so that it is impossible to give general dimensions that would be of value. The table on opposite page gives the dimensions of a few well-known shafts in different localities. Fore poling.— When the ground is so bad that it will not stand for several days between excavation and the completion of the lining, it becomes necessary to carry the timber to the bottom of the work. This may be accomplished by using square-set shaft timbering and driving laths, or forepoling behind the timber so as to keep the soft material from running into the opening. The advantages of forepoling are that, if the shaft is being lined with square sets, it can be commenced at any point, and, if the ground is not too bad, the work can be continued by this means until solid material is encountered. When the ground is particularly bad, it may become necessary to use breast boards, which are simply boards braced against the bottom of the shaft so as to keep the material from rising into the opening, only one board at a time being removed while the material behind it is excavated. In particularly bad ground, where breast boards have to be used, the progress made is very slow. After the shaft has been put down by fore- poling, it is sometimes very difficult to repair or replace the lining. When the forepoling method is employed in quicksand, there is considerable risk of losing the shaft altogether, owing to sudden rushes or “boils” of the material that throw the timbering out of line and fill up the shaft. Metal Linings Forced Down.— Metal linings forced down without the use of compressed air are rarely resorted to, though in some cases they have been quite successful. If the formation contains but few boulders, it is some- times possible to force the lining down by flushing out the material from the in- side with jets of water. At other times, men enter the shaft and excavate the ma- terial as the work progresses. The pneumatic method of shaft sinking was developed from the system in use for put- ting down foundations for bridge piers. At the bottom of the shaft there is a small chamber called a caisson, in which a suffi- cient air pressure is maintained to exclude the water at all times. The shaft lining is built on above this chamber, and grad- ually forced down into the soil. Men enter the chamber and excavate the mate- rial from under the caisson as it descends. By this method the sinking commences at once and is continued without interrup- tion until the lining is completed to bed rock, to which the lining is joined, as shown in Fig. 3. An air compressor, which is subsequently used, is the only auxiliary machine necessary, while in the freezing process an ice machine is required. It is best to use electric lights in the caisson; hence, it may be necessary to install a small dynamo if the company does not have an electric-light system in operation. In the pneumatic system, the bottom of the shaft is always exposed to view, and the workmen* know when they reach a solid founda- tion; while, in the freezing process, it is sometimes difficult to tell to what depths the pipes should be sunk so as to reach below any fissures or seams in the bed rock. In the pneumatic process, the fine material is aspirated out of the caisson by the air pressure. The pneumatic process is limited to a depth of about 100 ft., as it is impossible for men to work under a greater air pressure than that which corresponds to about 100 ft. of hydrostatic pressure. By the freezing process, pipes are sunk in the ground about the area to be frozen, as a rule, not more than 3 or 4 ft. apart. The lower ends of the pipes Fig. 3. OP Well-Known Shafts. SHAFT SINKING, 261 a 0) P4 u • a *03 5:** S2 ^ Tt< (M 9 w X ^ -V .o'® o.®* i: 5? E? BS^|x|| I 9 . o a pioQ o q be tu}43 «q -rt o^ s.a.as lO lO ^ i> l> iO n< t> O X X x Xx X XXXXX X XX x x| o o c^ «bcb^cbo « «boo ^ oX Ib Ibib -raoQio-oM lO lO ^ TticO CO COCOiOCOCO «0 coco CO C<1C0 CO COiH Material Mined. Anthracite Anthracite Anthracite Bituminous Bituminous Gold, Silver, Copper, Lead Silver Copper Copper Copper Copper Iron Iron Iron f Silver iGold Gold Zinc Zinc be (D P4 ^r _ rd q.a ^ , . 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PILLAR DRAWING. 289 Compressive Strength of Anthracite.— Attention has recently been called by Mr. William 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 reason 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 and fioor, and the character of the coal. Figs. 5 and 6 show the common methods. In Fig. b, 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 Tests of Compressive Strength of Sawed Pieces of Anthracite Coal. 290 METHODS OF WORKING. Remarks. Checker coal from Exeter. Checker coal M. W. coal pile. Checker coal bottom of Clear Spring colliery. Clear Spring Pittston vein glassy coal. Clear Spring Marcey checker coal. Clear Spring Marcey checker coal. Clear Spring Marcey checker coal. Clear Spring Marcey. Very good test. Checker coal. Clear Spring Marcey. Knot in block. Not fair test. Clear Spring reddish glassy coal. Clear Spring reddish. Not fair average test. Crushing Weight. Tons. Deduced. Per Cu. In. I>T-lCl>05C. c^. C-. lO 05 rH GO lO Tfl tH j j ,_| Average Weight Sustained. Crush- ing. Tons. I>iQlOOlOlOI>OOOCCOOII>»OCOw Break- ing. Tons. 28(?) 17 ?) 30 (?) 28(?) 30 20 22 38 32 22 30 Dimensions of Test Piece. ’53 W -.la r-l(M(MiCCDCO(MrHi-HCOC'^'«f«^-^l>u0 Length. nlwoH- -I* H«-'le<-‘l«-'lo«-ila-Ic» TftCOiOCDOOTfTfrtlTtt^iO •^isax JO J8quin>^ iHC00 05O^ 1 rH tH 1 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 manway open to the heading be- low as a means of retreat. The pillar between A and B is very similarly worked. To remove that between B and C, 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: Urst, 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 cond^itions 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 ofl* 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 | 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 Ihe lace of a breast in a few minutes time. The buggy runs upon 20-lb. T rails spiked with 2U' X I" spikes upon 2" X 4" 892 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., und 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 the basin, and the lowest gangways or levels first driven to the property ■imits, 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. , T^®.P!l'3r-and-5tall 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 (if. 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 Fig. 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 beading The «average thickness of cover at tlie I.eith 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 fireclay 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 55^ (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. 11. CLEARFIELD METHOD. 295 coal iiself 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 on 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 2" X 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 6^ ft. and the pitch is 3° to 4°. The coal is hard and firm, 296 METHODS OF WOBKINQ, 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).—T\iQ 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), floor of this bed of coal, being composed of shale and fireclay, ofteu 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 some parts of New River, and also in the Flat Top field. Alabama Methods (J. E. Strong).— Fig. 12 shows the common methods used in working the Alabama coals. The seams now working vary from 2 to 6 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. 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 It. 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 pitch greater than 20°; where the pitch is greater, chutes are worked and the rooms are driven straight up the pitch (Fig. 12, R). 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 workiim is from 100 to 600 ft. Air-courses usually have an area of 30 ft., and sumcient.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, i in.; coal, 10 in.; fireclay; slate. The top bench is bony and frequently left in place to prevent disintegration of the roof by the air. Above this coal is from 8 to 10 ft. of “rashiiigs,” 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 3^ 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-pillaT method as used in Indiana. The entries are generally 6 ft. high, 8 ft. broad, IOWA METHOD. 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, which 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 Centerville, 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. Mdhwav Fig. 16. A cross-cut is then made connecting them, apd 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 .— 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 .— 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 lioor 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. These 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 N9 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 mil 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 worMng faces, and a safe and effectual means of securing all the coal in the seam is thus attained. Fig. 17 shows another system 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 B 0 » 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 manways go through the entry pillars to the air-course and thence along the ribs each side of the room, one manway 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 manways 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 Fig. 19. the air-course until the hanging wall is reached, manways, called hack 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 S S, coal being drawn out at the bottom as required. Section D, Fig. 18, shows a method of robbing a pillar. In doing this, the manways are moved back into the pillar each side 10 ft. or so, by mining on the lower bench as before, and holes are drilled into the roof with long drills, which bring down as much of the overhanging part as can be reached.— (“Mines and Minerals,” Vol. 17, page 377.) MODIFICATIONS OF LONGWALL METHOD. Fig. 19 shows a good arrangement of the main and temporary haulage- ways in a flat seam. The chief object in any plan of longwall workings is to have the permanent roadways the arteries of the system, providing the most direct route from all sections of the mine to the shaft. The temporary LONG WALL METHOD. 303 roads or working places are only maintained for a distance of 60 to 100 yd., until cut oif by subroads branching at regular intervals from the main roads. In the figure, full heavy lines indicate the permanent haulageways, except only the main intake airway (12 ft. wide), running west from the downcast shaft D, and the main return air-course (12 ft. wide) leading from the face on the east side to the man- way around the upcast U, which is the hoisting shaft. The full light lines indicate the diag- onal subroads, driven to cut off* the working S laces, shown by the otted lines. The stables are located as shown in the shaft pillar, between the two shafts, where they will not contami- nate the air going into the mine, but will receive air fresh from the down- cast and discharge it at once into the upcast cur- rent. This position also affbrds ready access from either shaft in case of accident, and for the handling of feed and refuse. The pumps may be located in any con- venient position at the foot of the upcast. The shaft bottoms are driven 14 ft. wide nearly through the shaft pillar, and are rj / /r > iTT- Fig. 21 continued 10 ft. wide north and south through the gob. The width of all other roads and subroads is made 8 ft. The extra width of the straight road through the hoisting shaft is to provide for the future need, when the size of the workings will demand that the mine be ventilated in four sections or splits; and these two roads will then each form the return of two sections. This will be accomplished by over- casting the main road forming the shaft bottom, and carrying half the cur- rent by this means to the east face, where it is again divided. The same thing is done on the west side. The divided currents, after traversing the faces of their own respective sections, unite and return to the hoisting shaft by the main haulage road. When the roof is very solid, the gob roads turn off* the entries at 45°. and 304 METHODS OF WORKING, may be a considerable distance apart, so that the tracks can be turned in along the working face and the mine cars loaded at the face. When the roof is tender, making it impossible to maintain sufficient room for the mine cars to pass along the face, gob roads are turned off near together, and the mine cars run to the road heads, to which ix)ints the coal is shoveled or hauled in buckets. When the working face has reached such a distance from the bottom of the shaft that it becomes impossible to work rapidly enough to avoid the destructive weighting action of the roof, the mining must be divided into panels or sections, the working face of each of which can be advanced at the proper rate. Figs. 20 and 21 show a plan and section, respectively, of two methods largely used in Europe for working thick pitching, contiguous seams of hard, long-grained coal. From the foot of the shafts, levels are driven on the strike, and jig roads turned off these in the top seam at right angles up the pitch. The working faces are advanced in the same horizontal plane, the lower one being always ahead. The coal from the two lower seams is run through horizontal passages to the upper seam, where it is lo vvered to the levels below by means of jigs or g:ravity planes. The slates between the seams and the refuse obtained in mining are used to fill in as the faces advance. This gobbing must be done quite thoroughly, in order to prevent excessive settling of the roof and consequent crushing of the coal at the faces. Where spontaneous combustion is liable to occur, it is not advisable to use this method, but rather that shown in the lower portion of the figures. Slopes, or inclined planes, are driven down the pitch from the levels to the basin, or, if possible, to the boundary line, where the working faces are formed by driving levels to the right and left of the ends of the slopes. The working faces are here also kept in a horizontal plane with the lower one farthest up the pitch. The coal from the two upper seams is taken through tunnels or flats to the slopes in the lower seam, and hoisted to the shaft bottom. Here all the inclined planes or other passages are in the solid coal, and the worked-out places are left behind. A very small amount of coal is left in the mine when worked from the basin upwards, and the eftects of squeezes are not felt to any great extent, as the weight of the roof is thrown on the gob. Where there is not sufficient refuse material to fill in with, it is taken into the mine from the surface, or from another adjacent mine having an extra amount of stowing material. It is not necessary that the slopes be sunk to the boundary line, in which case the main-slope pillars should be large and left in so that the dip workings, as they are called, can be continued downwards when desired. In this way,, the first cost of opening up is greatly reduced. The ventila- tion of these workings is quite simple, the intake being split at the ends of the main entries, or slopes, and the air forced along the different working faces to the right and left, and thence to the upcast by way of the main-return airways. If at all possible, it is advisable to provide an outlet near the faces of the rise workings that are advancing upwards, because the lighter gases cannot be forced down-hill with satisfaction unless an excessive velocity of the air-current be maintained. These systems are well adapted to deep or shallow mines, and to give maximum outputs for minimum development, provided the work is carried on quickly and steadily. Overhand-Stoping Method.— Where several thick and heavily pitching . seams, in which considerable firedamp is given off and the roof falls freely, are to be worked, a shaft is sometimes sunk in the adjacent strata, and at certain distances horizontal tunnels are driven to the coal seams. From these tunnels, levels or haulage roads are driven in each seam to the right and left, provided the seams are not so close together as to make it more profitable to use rock chutes or tunnels, through which the coal is run from one seam into the other. At certain intervals, depending on the length of the lifts horizontally, pairs of headings, usually called dips, are driven up the pitch until they intersect the levels and tunnels above. Headings are turned off these dips to the right and left, parallel to the main levels or haulage roads, and when they meet or have reached their limit horizontally they are holed, or cut through, by cross-cuts driven on the pitch. The working faces thus formed are then carried back, as shown in Fig. 22. Skips are taken off the face and the roof allowed to cave in after each operation and fill up the gob behind. The order of working is such that the top faces are worked in advance of the lower ones. The cars, which are taken to the working faces, are handled in the dips by balance carriages, or back balances, as they are termed in some localities. The ANTHRACITE MINING. 305 barney, or balance, runs on a narrow track in the middle of the track for the carriage on which the car is placed. The barney will raise the carriage with the empty car on it, and the carriage and loaded car will hoist the barney. These gravity planes are only made one-half the length of the dips, or about 150 ft., in order that greater safety may be secured and shorter ropes used. One is placed in the lower half of one of the pairs of dip headings, and another in the upper half of the other, thus necessitating that the cars be changed from one gravity plane to the other midway along the dips. This is done by taking the car off one carriage and pushing it through a break- through or cross-cut to the other. Fig. 22 shows the method of working these lifts in some parts of England and Belgium where the seams are gaseous, and some of them quite thick. The face is stepped more or less deeply, depend- ing on the pitch, in order to protect each miner from the falling coal of his neighbor. The men rtiach the higher portion of the working face through timbered manways. The coal is generally run down chutes to the cars below, but in some places it is run to the end of the gangway below by means of inclined chutes, or spouts, laid on the gob. The essential feature for the successful operation of this system is the close and careful stowing of the gob between walls. In Belgium, cord wood and brush wood are very largely used for gobbing material or stowing between the regular timbers. All the coal, except very thin vertical pillars, is taken out. Where there is Fig. 22. much firedamp, the miners simply nick the coal and leave it stand over night, during which time the gas either forces it off the solid or so loosens it that the miner can easily take it off with a pick. (See also Highly Inclined Mineral Deposits.) METHODS OF MINING ANTHRACITE. A perfectly flat seam of anthracite is seldom found in America, and even where a portion of the seam may be found lying comparatively flat, such sudden changes in dip must be expected that a system adapted to working on a pitch is almost universally used. A breast may start on a low pitch and the pitch may increase gradually until it becomes vertical, or the reverse may be the case. The cleat is usually lacking in anthracite, and the direc- tion of driving the breasts is determined largely by the pitch and by haulage considerations. For pitches up to 30°, the methods shown in Figs. 1,7, 8, 9, 10, 12, and 13 are, in general, applicable, with certain changes due to local considerations. There is considerable difference in the methods of opening rooms in anthra- cite and bituminous mines, owing to variations in the characteristics of the coals and to the fact that anthracite will slide on chutes of less inclination than bituminous coal. Where the pitch does not exceed 4°, the rooms are turned off at right angles to the gangway. In moderately thick coal seams, pitching between 4° and 18°, the rooms are generally driven across the pitch, forming room breasts, thus securing a grade that permits the haulage of the cars to the face. 306 METHODS OF WORKING. There are two methods of mining thick coal in breasts when nearly flat. (1) The breasts are opened out and driven to the limit in the lower bench of coal, and the top benches are blown down afterwards, beginning at the face and working back. (2) When the roof is good and there is no danger of its falling and closing up the workings, the upper benches may be worked in the opposite direction, beginning at the gangway and driving towards the limit of the lift, or the working of the upper bench may follow up that of the lower bench. When the seam is less than 12 ft., the top is supported by props; in thicker seams, the expense is so great for propping that but little attempt is made to support the roof. In the thicker anthracite seams (notably the Mammoth), the coal in the breasts is so worked as to make an arch of the upper benches of coal, which acts as a temporary support for the roof, the coal in the arch being extracted when the pillars are robbed. When the inclination of anthracite seams is less than 30°, the breasts may be opened with one chute in the center, which ends in a platform projecting into the gangway, off which the coal can be readily loaded into the mine car. When this method is employed, the refuse is thrown to either side of the chute. If the pillars are to be robbed by skipping or slabbing one rib only, it is well to keep most of the refuse on one side. Sometimes, when the top is good, and the breasts are driven wide, two chutes are used, but the cost of making the second chute is considerable and is therefore not advisable unless necessitated by the method of ventilation employed. Col. Brown’s Method.— Fig. 23 shows a panel system devised by Col. D. P. Brown, of Lost Creek, Pa., which gives good results in thick seams pitching from 15° to 45°, where the top is brittle, the coal free, and the mine gaseous. Rooms or breasts are turned off the gangway in pairs, at intervals of about Fig. 23. 60 yd. The breasts are about 8 yd. wide, and the pillar between about 5 yd. wide, which is drawn back as soon as the breasts reach the airway near the level above. In the middle of each large pillar between the several pairs ot breasts, chutes about 4 yd. wide are driven from the gangway up to the airway above. These are provided with a traveling way on one side, giving the miners free access to the workings. Small headings are driven in the bottom bench of coal, at right angles to these chutes, and about 10 or 20 yd. apart. These headings are continued on either side of the chutes until they intersect the breasts. When the chute and headings are finished, the work of getting the coal in the panel is begun by going to the end of the upper- most heading and widening it out on the rise side until the airway above is reached and a working face oblique to the heading is formed. This face is then drawn back to the chute in the middle of the panel. After the work- ing face in the uppermost section has been drawn back some 10 or 12 yd., work in the next section below is begun, and so on down to the gangway, working the various sections in the descending order. Both sides of the pillar are worked similarly and at the same time toward the chute. Small cars, or buggies, are used to convey the coal from the working faces along the headings to the chute, where it is run down to the gangway below and loaded into the regular mine cars. This system affords a great degree of safety to the workmen, because whenever any signs of a fall of roof or coal occur, the men can reach the heading in a very few seconds and be perfectly safe. A great deal of narrow work must be done before any great anthhacite mining. 307 quantity of coal can be produced. The breasts are driven in pairs and at intervals, to get a fair quantity of coal while the narrow work is being done, and they are not an essential part of the system. It is claimed that the facility and cheapness with which the coal can be mined, handled, and cleaned in the mine more than counterbalance the extra expense for the narrow work. Battery Working.— Fig. 24 shows a method of opening a breast by two chutes c, c, when there is a great amount of refuse, or when a great amount of gas is given off. The chutes are extended up along the rib to within a few feet of the working face, either by planking carried on upright posts, or by building a jugular manway, as shown in the sections (a) and (5), Fig. 25. These chutes, built of jugulars or inclined props and faced by 2" plank, are made as nearly air-tight as possible, to carry the air from the heading a to the working face. Fig. 24 shows a breast on a pitch too steep to enable the miner to keep up to the face. In seams of less than 35°, the platform / shown near the face of the breast is unnecessary, and in seams thicker than 12 ft. it cannot be built; hence, this method of working is applica- ble (1) to beds pitching more than 35°, and (2) to thin seams. The coal is separated from the refuse on the platform /, and is run down the manway chutes and loaded into the cars from a platform projecting into the gang- way g. The refuse is thrown in the middle of the breast behind the platform. A cer- tain amount of coal is kept on the plat- form to deaden the blow from the falling coal. The chutes are timbered when the character of the coal requires it. This plan can also be employed in thick seams having a heavy dip, if there is enough refuse to fill the center of the breast so that the miner can work without the platform. Fig. 25 (a) is a section through p, p when jugulars a, a are used to form the manways b, b along the sides of the breast; and (6) is a section through the 308 METHODS OF WORKING, same line when upright posts a, a are used to support the plank in forming the manways h, h. The refuse in these cases only partially fills the gob! In working very thick seams on heavy dips, where there is not enough refuse to fill the middle of the breast, the miner has nothing to stand on, the platform being impracticable; therefore, it is necessary to leave the loose coal in the breast. Loose coal occupies from 50 ^ to 90 ^ more space than coal in the solid. This surplus is drawn out through a central chute. If the roof ANTHRACITE MINING, 309 is ix)or, the movement of the coal will not in this way cause it to fall and mix with the coal; and if the floor is soft, the jugulars, which are stepped into the floor, are not so liable to be unseated, closing the manway and blocking the ventilation. The surplus is sometimes sent down the manways, leaving the loose coal in the center of the breast undisturbed, until the limit is reached. Single-Chute Battery.— To prevent the coal from running out through the chutes, the opening into the breast is closed by a battery constructed by, laying heavy logs across the openings, as shown at &, Fig. 26, or else built on' props, as shown at b, Fig. 27; a hole is left in the center, or at one side of the battery, through which the coal may be drawn. The battery closes all the. openings into the breast, except the space occupied by the jugular manways, and is made air-tight, or as nearly so as possible, by a covering of plank. Fig. 26 is a plan and section of a breast opened up by a single chute. The plan ^ is taken on the line m n shown on the section B, which section is taken on the line/^ shown on the plan A. The pitch is great and the seam is so thick that the breast must be kept full of loose coal for the men to work upon, the surplus being drawn off at the battery b and run into the car standing on the gangway g through the chute c. A manway w is made along each side of the breast, for the purpose of ventilation and affording a passage for the men to reach the working face. The heading a is used for an air- course between breasts. The main airway h is driven over the gangway g, where it will be well protected. By drawing the surplus coal through a central chute, the manways are not injured so much as when it is drawn off through side chutes, as the coal will move principally along the- middle of the breast. When the breast is worked up to its limit, all the loose coal is run out of the breast and the drawing back of the pillars is commenced, unless for some purpose they are allowed to stand for a time. Double-Chute Battery.— Fig. 27 shows a plan and section pf double-chute breasts used in very thick seams having a heavy dip. The breasts are entered by two main coal chutes c, c, each of which is provided with a battery 6, through which the coal is drawn. A manway chute m is driven up through the middle of the pillar for a few yards and is then branched in both directions until each branch (slant chute) intersects the foot of a breast near the battery 6, as shown. The jugu- lar manways n, n are started at this point and continued up each side of the breast. The main airway h is driven in the solid through the stump A above the gangway. By driving the main gangway g against the roof, as shown, the pitch of the chute is lessened, and the loading chute c is more readily controlled. When the main gangway is not driven against the roof, a gate is placed in the chute below the check-battery, which enables the loader to properly handle the coal. Coal in excess of the amount necessary to keep the miner up to the face may be drawn through the main battery, or sent down the manway chute, from which it is loaded through an air-tight check-battery. The main chutes are usually 8 or 9 ft. wide, but sometimes only for the first 6 or 8 ft.; above this they are driven about 6 ft. square. The manway and slant chutes are also about 6 ft. square. When the seam is not thick enough to carry the return airway h (Fig. 27) over the gangway, the chutes are driven up in the same manner as in Fig. 27, for a distance of about 30 ft., where they intersect the airway. The breast is opened out just above the airway, a battery being built in the airway Fig. 28. 310 METHODS OF WORKING. immediately above each chute. A manway is driven from the gangway up through the middle of the stump until it intersects the airway, and a trap door is placed at this point to confine the air. This manway is made about 4 ft. X 6 ft., or smaller. Fig. 28 shows a less complicated plan than Fig. 27. The main chutes n, n are driven up to the heading c, from which the breast is opened out; a log battery is built at the top of each chute at the points marked a, a. The chutes are used for drawing the batterj’^ coal, and for re- ceiving the manway coal, and are also used for trav- eling ways. A check-bat- tery h is placed in the chute to prevent the air-current from taking a short cut from the gangway through the chute to the breast air- ways. This check-battery is of great assistance to the loader when the chute has a very steep pitch, as he can readily control the flow of coal through the draw- hole. All these methods are open to the objection that in case of any accident to the breast manway, by which the flow of air, Fig. 29. shown by the arrows, is obstructed, there is no means of isolating the breast in which .the accident occurs, and the venti- lation of all the breasts beyond it is entirely stopped. To overcome this, sometimes the pil- lar A, shown in left- hand breast. Fig. 28, is left in each breast to protect the airway. Rock-Chute Mining. Fig. 29 shows a section of two seams, sepa- rated by a few yards of rock. Chutes from 4^ to 7 ft. high and 7 to 12 ft. wide are driven in the rock from the gangway or level g to the level I in the seam above, at such an angle that the coal will gravitate from the upper seam into the gangway g. The work- ing, otherwise, is sim- ilar to that previously described. Rock-chute mining contemplates the fol- lowing sequence of operation; 1. The opening of all gangways and air- ways in the lower seam, lying a few feet above it. Fig. 30. to develop coal as yet untouched in a thick seam ANTHRACITE MINING. 311 2. Developing the thick bed by a regular series of rock chutes driven from the gangway below; workings being opened out from chutes as in ordinary pillar-and-breast working— the panel system or some other plan may be found better than pillar-and-breast workings. 3. Driving the breasts to the limit of the lift and robbing out the pillars from a group of breasts as soon as possible, even if a localized crush is induced. 4. After one group of breasts is taken out and the roof has settled, open- ing a second series of chutes for the recovery of coal from any large pillars that were not taken out when the crush closed the workings. 5. While the work of recovering the pillar coal is in progress, a second group of breasts may be worked, and the process continued until all the area to be worked from that gangway has been exhausted. The same process is employed in opening lower lifts. 6. When all the upper bed of coal has been exhausted, the lower seam may be worked by the ordinary method. Workings in this seam may be Fig. 31. carried on simultaneously with the upper bed, but to avoid the possibility of a squeeze destroying these workings, very large pillars must be left. After exhausting tlie upper seam, these pillars may be advantageously worked by opening one or two breasts in the center of each, and when these are worked to the upper limit, attacking the thin rib on each side, com- mencing at the top and drawing back. When the roof of the lower bed is good, the cost of timbering and keeping open the gangways and airways will be considerably less than if these were driven in the upper seam, and this difference, in some cases, may be suf- ficient to pay for driving all the rock chutes. There are three undetermined points in this connection, viz.; (1) The 312 METHODS OF WORKING. maximum distance between the two beds, or the length of rock chute that can be driven with satisfactory financial results. (2) The maximum dip on which such working can be successfully opened. (3) The maximum thick- ness of the upper and also of the lower seam, which will yield results war- ranting the additional outlay when rock chutes are of considerable length. Fig. 30 shows how one or more seams are worked by connecting them by a “stone drift,” or “tunnel,” driven horizontally across the measures, through which the coal from the adjacent seams is taken to the haulage- way leading to the landing at the foot of the slope or shaft. Tunnels are sometimes driven horizontally through the measures from the surface, so as to cut one or more seams above water level. The lower seam of coal is worked from a gangway or level I, connected by a tunnel, or stone drift to the level or gangway g, in the thick seam. The stone drift may be extended right and left to open seams above and below the thick seam. This tunnel, or stone drift, is never driven under a breast in the upper seam, but directly under the middle of the pillar. In the upper and thicker seam, when the coal is very hard, a breast h is worked to the limit and the loose coal nearly all run out through the chute s into the gangway g. The “ monkey gangway ” m is driven near the top as a return airway, and is connected to the upper end of the chute s by a level heading n, and to the main gangway ^ by a heading v. These headings are driven for the purpose of ventilation and to provide access to the battery in case the chute s should be closed. In the lower seam, the breast is still being worked upwards in the ordinary way. The* J. L Williams method of working anthracite. Fig. 31, has been applied successfully by the originator at the Richards Mine, Mt. Carmel, Pa., and by it 90^ of the available coal is said to have been obtained. The method is a pil- lar-and-stall method with the following distinguishing points: (a) Timbering the gob with props set not more than 6 ft. apart, to keep up the roof during the extraction of the pillars. (6) Making holes from the crop, for the delivery of timber into the workings, (c) Removing the pillars in shorter lifts than is possible when the roof is supported with culm pillars, {d) Keep- ing the gob open with timber for dumping the fallen rock, that would have to be sent to the surface if the breasts were flushed. Both the floor and the roof of the mine were weak, so that it was not possible to make either the breasts or the pillars wide. In some cases, the floor consisted of 3 ft. of clod, and to prevent its lifting and sliding, every alternate prop was put through the clod and its foot set in the slate beneath, while the other props were set oh pieces of 2" plank 2 ft. in length to keep down the bottom. A small gangway X is driven to take out the chain pillar, and F is a small gangway for taking in timber. Running of Coal.— In large seams, when the coal is soft and shelly or slip- pery, and lies at an angle of more than 50°, and generates large quantities of firedamp, a danger to be guarded against is the sudden liberation of gas should a breast run; that is, should the coal at the face loosen and run out by its own gravity, only stopping when it chokes or fills up the open space below. To meet these conditions, the air-course may be driven above the gangway and used as a return, the fan being attached as an exhaust, and the working breasts ventilated in pairs. The inside manway of one of a pair of breasts is connected with the gangway for the intake, and the outside manway of the other breast with the return airway, giving each pair of breasts a separate split of the current. In collieries where this system of working is followed, the coal is soft. A new breast is worked up a few yards, but as soon as it is opened out, the coal runs freely and the manways are pushed up on each side as rapidly as possible, to keep up with the face. Two miners, one on either side, sometimes finish a breast without being able to cross to each other. The work is done exclusively with safety lamps, and when a breast “runs” the gas is liberated . in such quantities that it frequently fills breasts from the top to the airway before the men can get down the manway on the return side. When the gas reaches the cross-hole, it passes into the return airway without reaching any part where men are working. Should a run of coal block a breast by closing the mahway, it affects the current of one pair of breasts alone. As the gangway is the intake, leakage at the batteries passes into the breasts, as the cross-holes are above their level and the gas is thus kept above the starter when at the draw-hole. The gangway, chutes, and airway are supplied by wooden pipes, which connect with a door behind the inside chute. If a breast runs up to the surface, it does not affect the return airway, as it is in the solid. ANTHRACITE MINING, 313 Among the disadvantages urged against this system of working are the following: It increases the friction, as the air must pass in the airway all the distance from the breast to the fan, the area of the airway being small in comparison to the gangway or intake. As the faces of the breasts are so much higher than the return airway, the lighter gas must be forced down into the return against the buoyant power of its smaller specific gravity. The reduction of friction obtained by splitting is neutralized by each split running up one small manway and down another; the advantage of running through several pillar headings and thus securing a shorter course being lost. This can be partly obviated by ventilating the breasts in groups, but the dangers avoided in splitting are increased. Blackdamp, which accumulates in the empty or partly empty breasts, works its way down and mixes with the intake current, as there is no return current in the breast strong enough to carry it away, the return being closed in the airway. All things considered, when the seam is soft and has a pitch of 40° and upwards, and emits large quantities of gas in sudden outbursts, as in running breasts, this system is the best that can be adopted. When the Coal Is Hard and Gas Is Not Freely Evolved.— The reverse of the system just described is followed at some collieries where the coal is hard and but little gas is encountered. The. airway is driven over the gangway or against the top, the fan being used to force the air inward to the end of the airway. The air is distributed as it returns, being held up at intervals by distributing doors placed along the gangway. Among the advantages claimed for this plan are the following: As the pressure is outward, it forces smoke and gas out at any openings that may exist from crop-hole falls or other causes. The warm air from the interior of the mine returning up the hoisting slope or shaft prevents it from freezing. As the current is carried from the fan to the end of each lift without pass- ing through working places, the opening of doors as cars are passing, etc. does not interfere with the current. If a locomotive is used, the smoke and gases generated by it are carried away from the men toward the bottom. Locomotives are generally used only from the main turnout to the bottom. An objection to this system is that the gangway, as the return, is apt to be smoky. Starters and loaders are forced to work in more or less smoke, and even the mules work to disadvantage, while if gas is given off, it is passed out over the lights of those working in the gangway. However, in places where there is but little gas, and airways of large area can be driven, this plan works very satisfactorily, and some of the best ven- tilated collieries are worked upon it. An objection advanced by some against forcing fans is that they increase the pressure, thus damming the gas back in the strata. In case the speed of the fan is slacked off, the accumulated gas may respond to the lessened pres- sure and spring out in large volumes from its pent-up state. This argument, however, works both ways. An exhaust fan running at a given speed is taking off pressure, and if anything occurs to block the intake, the pressure is diminished, and the gas responds to the decrease on the same principle. Hints for the Smaller Seams When They Are Small and Lie From Horizontal to About 10°.— Two gangways may be driven, the lower or main gangway being the intake. Branch gangways should then be driven diagonally or at a slant, with a panel or group of working places on each slant gangway. Large headings should connect the panels. In this system, the air is carried directly to the face of the gangway and up into the breasts, returning back through the working places. The intake and return are separated by a solid pillar, the only openings being the slant gangways on which are the panels. The advantages of this plan are several: The main gangway is solid, with the exception of the small cross-holes connecting with the gangway above; these furnish air to the gangway and are small and easily kept tight. These stoppings should be built of brick, and made strong enough to withstand concussion. A full trip of wagons can be loaded and coupled in each panel or section without interfering with, or detaining the traffic on, the main road; one trip can be loaded while another is run out to the main gangway for transpor- tation to the bottom. 314 METHODS OF WORKING. The only break in the intake current is when a tri^ of cars is taken out from, or returns to, a panel or section; this can be partially provided against by double doors, set far enough apart to permit one to close after the trip before the other is opened. This distance can be secured by opening the tirst three breasts on a back switch above the road through the gangway pillar, or by running each branch over the other far enough to obtain the distance for the double doors. If it is not desired to carry the whole volume of air to the end of the air- way, a split can be made at each branch road. These will act as unequal splits in reducing friction, and, although not theoretically correct, are prefer- able to dragging the whole current the full length of the workings. The objections urged to this plan are that it involves too much expense in the large amount of narrow work at high prices necessary to open out a colliery, that it necessitates a double track the whole length of the lift, and that the grade ascends into each panel or section. But the latter criticism falls, because the loss of powder hauling the empty wagons up a slight grade is more than made up by the loaded wagons running down while the mules are away putting a trip into another panel or section. For a large colliery this is without doubt the best and cheapest system. When the Seam is Small and Lies at an Angle of More Than i0°.— In small seams lying at an angle of more than 10°, and too small to permit an airway over the chutes, it is more difficult to maintain ventilation. If air holes are put through every few breasts, and a fresh start obtained by closing the back holes, or if an opening can be gotten through to the last lift as often as the current becomes weak, an adequate amount of air can be maintained, because the lift worked can be used as the intake, and the abandoned lift above as the return. To ventilate fresh ground, the filling of the chutes with coal will have to be depended on, or a brattice must be carried along the gangway. This can be done for a limited distance only, as a brattice leaks too much air. As a rule, collieries worked on this plan are run along until the smoke accumulates and the ventilation becomes poor; then a new hole is run through and the brattice removed and used as before for the next section. This operation is repeated until the lift is worked out. Some- times, to make the chutes tight, canvas covers are put on the draw holes, but as they are usually left to the loaders to adjust, they are often very imperfectly applied. Then, as the coal is frequently very large, the air wdll leak through the batteries. This plan works very satisfactorily if the openings are made at short intervals, say as frequent as every fifth breast, but the distance is usually much greater to save expense. As the power of the current decreases as the distance between the air holes is increased, good ventilation is entirely a question of how often a cut-off is obtained. An effective ventilation could be maintained in a small seam at a heavy angle by working with short lifts, say two lifts of 50 yd. instead of one of 100 yd., as at present. The gangways should be frequently connected, and one used as an intake and the other as a return. This would necessitate driving two gangways where one is now made to do, but the additional expense would be made up in the greater proportion of coal won. FLUSHING OF CULM. From 15 9^ to 20^ of the coal taken out of an anthracite mine, according to the methods used in the past, became so fine in the course of preparation through the breaker that it could not be used or sold, and had to be piled away as refuse. Recently, the coarser portions of these culm piles have been screened out and sold for use as steam sizes, while the finer part, together with the fine material from the breaker, has been carried back into the mines with water to fill the abandoned portions of the underground workings. This culm is carried through a system of conveyors to the hopper, usually an old oil barrel, and the stream of water is conducted into the same hopper by a 3" pipe. The culm is then carried by the water through a pipe from 4 to 6 in. in diameter, which passes into the mine through the shaft, bore hole, or other opening, thence along the gangways to the chambers through the cross-cuts, and to the point where it is desired to deposit the culm. The bottoms or outlets of the chambers to be filled are closed by board partitions fitted closely, or by walls of slate or mine rubbish. The culm, as it issues CVLM FLUSHING. 315 from the end of the pipe, takes a very flat slope, and it is carried a long dis- tance hy the water, which ultimately filters through the deposited culm to the lower portion of the mine, to he pumped to the surface. When the chamber is filled to the roof, the pipe is withdrawn and extended to the next place to be filled, and so on. Wrought-iron pipe is said to be the best, and the life of the pipe depends on the nature of the water used and the material treated. With fresh water and small culm from the buckwheat screen, it lasts 18 months; when carrying culm from the bank, ranging from dust to pea coal and some chestnut, 9 months; and when mixed with ashes, 6 months. The smaller the material the better. The amount of water used depends on the distance to which the culm is carried and the slope of the pipe. From li to If lb. of water is required to flush 1 lb. of culm to level and down-hill places; 3 to 6 lb. of water to 1 lb. of culm to flush up-hill for heights varving from 10 to 100 ft. above the level of the shaft bottom. Any ele- vation of the pipe very materially increases the amount of water necessary. Mr, James B. Davis, superintendent of the Dodson and Black Diamond mines, has ascertained by experiment that 1 cu. ft. of anthracite coal ground to culm can be flushed into a space of nearly li cu. ft., and it is therefore impossible to compress the culm more than one-third. In addition to acting as a filling and a support, to prevent squeezes and crushing, flushing has been advantageously used for fighting and sealing off mine fires. No instance has been recorded where spontaneous combustion has taken place in the flushed culm. The Dodson culm plant, which was a pioneer, cost S7,473.42, with the capacity of flushing 119 tons per day, while the Black Diamond culm plant is capable of flushing 287 tons per day and cost ^6,280.12, but plants can probably be put up much more cheaply than this. The saving from the flushing of culm over depositing it on the surface varies for the ordinary anthracite colliery from |5 to ^15 per day. The average cost of putting in stoppings in a 9' vein is given by Mr. Davis as ^9.50, including material. To remove the pillars after the intervening breasts have been filled with culm, the face of the pillar along the gangway is attacked, and a road driven up through the pillar, splitting it {z, Fig. 32). This road may be the full width of the pillar, but in general it is necessary to leave a narrow stump of coal on either side to keep up the fine flushed material in the adjoining breasts. The thickness of this supi)orting coal depends entirely on the condition of the flushed material behind it. If that is fine, it will set firmly and form a compact mass that will not run. In such a case, the pillar may be entirely taken out, leaving a vertical wall of solidly packed flushed culm. When the flushed material is of a size larger than buckwheat, it will not set compactly, but will run when it is opened up, and when such material fills the adjoining breasts, the thin pillar of coal must be left to keep back the culm. Timbers are placed flush up against the culm or the coal stumps, as the case may be, and if there is a tendency for the culm to run, lagging is placed behind the timbers. In some cases, as much as 700 ft. of timber have been used per 100 ft. of pillar taken out. As the pillar is removed, the top settles until it finally rests upon the flushed culm, and as the weight from the top and the pres- sure from the sides comes upon these props, they are broken, while the coal that has been left will also be crushed. At the Black Dia- mond colliery, the props us^d are 16 ft. long, ^ . and at this colliery the top settles about 4 ft. if the flushed material is packed tightly before the roof pressure comes on it. After this settling, new props 12 ft. in length are put in close up against the culm and the broken stump of the original pillar, and they serve to keep the road open up to the working face. Fig. 32. 316 MINING MINERAL DEPOSITS, METHODS OF MINING MINERAL DEPOSITS. Much of what has already been given under the heading of Coal Mining applies equally to the mining of mineral deposits. It will therefore not be repeated under this heading, and the only methods here given will be those that have not already been covered. Highly inclined deposits are mined out as follows: Horizontal passages called drifts, levels, or galleries are driven through the ore at regular intervals, and connected by openings at right angles to the levels, which, in the case of perpendicular or highly fnclined deposits, are called winzes or raises, according as they are sunk from above or raised from below. These parallel openings divide the ore body into a series of rectangles, thus serving to test its value. (See also Overhaiid-Stoping Method, page 304.) Levels.— The distance between the individual levels depends on the material being mined. They are placed nearer together in high-grade ore than in low-grade material. The width of the vein also has considerable influence on the distance between the levels. In veins where it is necessary to break into walls to afford working room in the levels, they are usually placed as far apart as is consistent with the economical handling of the material in chutes and convenient access to the working faces of the stopes. The distance between the levels varies from 60 to 100 ft., and should be measured on the dip and not perpendicularly. Winzes or Raises. — The distance between the raises or winzes varies from 30 to 250 ft., depending largely on the character of the material and the method of getting it into the chutes or winzes. Where the material at the working faces is shoveled or thrown directly into the chutes, they are often placed as close as 30 ft., while if the material is carried from the working face to the chute or winze in a wheelbarrow, the chutes may be much farther apart. Sloping.— For narrow deposits, there are two general styles of stoping in regular use, called, respectively, underhand and overhand stoping. There are several minor divisions under each. Underhand stoping may be conveniently divided into underhand regular and underhand Cornish. The regular method of underhand stoping is illustrated in (a). Fig. 33, and may be described as follows: The miner selects a place in any given level or on the surface of the ore deposit from which to commence stoping. A cut 6 or 7 ft. in depth and from 6 to 8 ft. in length is made. This forms the first, or No. 1, bench in the stope. After this, he continues the work in each direction, supporting the track, if any exists above, upon stulls or timbering. After this No. 1 bench has proceeded a sufficient distance, he starts a similar cut in the bottom of it, which forms No. 2 bench, and is driven in both directions as before. At first the ore can be shoveled to the level above, but after considerable depth has been attained, it will be necessary to provide a winze, as shown at /, through whfch the ore from the lower benches can be hoisted. Stulls covered with lagging are placed across the stope behind each bench as platforms, to support the waste material. Under- hand stoping by the Cornish system is illustrated in (6), Fig. 33, and differs from the system just described only in that the level below has to be driven first, and a winze sunk to it. a is the lower level, b the winze, and c the upper level. The work is then carried on in successive benches, as described. OVERHAND STORING. 317 The advantages of the Cornish method are that any water that collects in the stope flows to the lower level and does not have to be taken care of in each individual stope. Also, the ore can be tumbled down through the raise to the lower level, thus avoiding the extra hoisting with a windlass, or small hoist. The advantages that apply to any system of underhand stoping are as follows: The ore can be extracted at once; while the stope is new, the miner is protected from the roof by stulls and stagings; the loss of fine and valuable mineral is reduced, owing to the opportunity for sorting afforded during the handling of the broken ore. The disadvantages are as follows: The manner in which the ore must be handled is expensive; an individual pumping plant will be necessary in each stope of a wet mine with the regular system; should the mine be abandoned for any length of time, the stulls become loose and allow the rock stowed upon them to fall on the face of the ore, rendering the mine unsafe, and burying the ore so as to require a large expenditure of time and money to reopen the workings; in a wet stope, the water flows down over the working faces, interfering with the workmen and forcing them to stand continually in water. Overhand Sloping.— In this system of stoping, the ore is broken down from above as the work progresses. Work is usually started from the bottom of a raise, as B, Fig. 34. After the lower level A has been driven, the miner stands on top of the lagging over the caps and works out a slice (7 5 or 6 ft. high, this being followed by succeeding slices, as D and E. Chutes are timbered or cribbed at intervals, through which the material may be thrown down and any waste packed in the space between the chutes, as at F. In cases where the entire deposit is of value, a portion of the broken ore is allowed to accumulate as a platform upon which the men stand while Fig. 34. working, only enough being sent through the chutes to provide working room. After overhand stoping is started, the work may be carried on by means of breast holes, as shown at E. The force of gravity assists in break- ing the rock, and reduces the powder necessary for blasting. Where rich ore is broken, platforms of planks, or sheets of canvas or bull hide covered with plank, may be placed over the filling to receive the broken ore, thus preventing the loss of fine and valuable material in the filling. One argument which is usually presented against overhand stoping is that the roof is not secured by timbering, but this is offset by the fact that the workmen are always close to the roof and thus examine its condition and break off any dangerous portions or give them such support as may be needed with temporary timbers. Overhand stoping may be carried on in a number of modified forms, all of which involve the principle of breaking down the material in such a manner that the work is aided by gravitation. Sometimes, where practically the entire deposit is removed, temporary platforms supported on stulls are com structed close to the working face for the workmen. The advantages of overhand stoping are that no hoisting or pumping is required in the block of ore being worked, as with underhand stoping with- out a winze; water gives no trouble in the stopes; less timbering is required than in the underhand stoping, because no platforms are required to store waste, and the timbering in working stagings is usually recovered; where the mine is abandoned for a time, the working face is usually left in better 318 MINING MINERAL DEPOSITS. shape with overhand than with underhand stoping. In the overhand system, gravity assists in the breaking of the ore. The disadvantages are that the miner is forced to work under an unsup- ported roof, though the fact that he is close to it enables him to examine it and take care of any dangerous portions. There may be greater loss of the fine and valuable material that becomes mixed with the waste than in underhand stoping, though this may be largely prevented by the use of boards or canvas. Flat or Slightly Inclined Deposits.— Where flat or slightly inclined ore bodies are being worked, the working drifts (corresponding to levels in steeper deposits) are driven comparatively close together (about 30 ft. apart) and the material between them removed in successive steps, as in underhand or overhand stoping, the space behind the miner being packed with waste mate- rial to support the roof, or the roof being supported by timbering until the ore is removed. Sometimes pillars of ore have to be left to aid in the support of the roof, and when this is the case, the miners try to leave the pillars where the ore is low grade. When a deposit of ore is of uniform value throughout, and the roof of a somewhat flexible character, it may be let down without much, if any, stowing, as in the longwall system of coal mining. In other cases, the material is removed like square work or by pillars and rooms, the pillars in either case being robbed as closely as possible before leaving the workings. LARGE DEPOSITS OVER 8 FEET THICK. With a deposit much over 8 ft. in thickness, it is impossible to keep the walls in place by stulls or single sticks of timber. Large masses of mineral frequently contain very valuable ma- terial, and engineers have developed a number of methods for the removal of their valuable contents. The method depends largely on the value per ton of the material being removed, and local conditions as to the cost of labor, timber, filling material, char- acter of wall rock, etc. The methods used for these deposits are square work, filling, caving, and square-set timbering Fig. 35. The advantages are that it Square work, also called the cham- ber-and-pillar system, is illustrated in Fig. 35. Galleries are driven through the ore as shown, the deeper galleries being smaller than the upper ones, the object being to leave larger pillars for the support of the material above the workings. Galleries are then driven at right angles to these, to leave square pillars, as shown. When this svstem is applied to a bed that is only 30 or 40 ft. thick, from three-fourths to eight-ninths of all the material in the deposit can be removed, the remainder being left as pillars; but where it be- comes necessary to leave floors be- tween the succeeding levels, as shown in (6), Fig. 35, scarcely one-half of the deposit can be removed, even when it is of such a firm nature that the gal- leries can be driven considerably wider than the thickness of the pil- lars. This system of mining is applied to the removal of salt, gypsum, build- ing stone, and various low-grade ores, and is very similar to the room-and- pillar system (see page 280). 3 no timbering, and that, owing to the MINING THICK DEPOSITS. 319 larger size of the chambers, the material can he removed at a low cost per ton. The disadvantages are that a large portion of the deposit has to be left untouched, and that where the formation being mined is at all soft, it is not safe to work these large chambers. Filling Methods.— Sometimes a filling of worthless material is substituted for the worked-out ore. This system may be carried on by any one of a number of different plans. Slicing Method. — In some cases, comparatively small drifts or chambers (from 6 ft. X 6 ft. to 10 ft. X 10 ft.) are driven through the ore across the aeposit, and then tightly packed with broken rock, after which other drifts or chambers are driven beside the first ones and also packed or filled. This P rocess is continued until a slice has been removed from under the entire eposit. The process is then repeated on top of the filling, taking out suc- cessive chambers and filling them, until another slice has been removed. This method has been used in the copper mines of Spain, and has also been tried at some mines in the United States with varying degrees of success, Fig. 36. Fig. 37. depending principally on the cost of the stowing material compared with the value per ton of the deposit being removed. In this process, the filling material should be composed entirely of large pieces, so that it can be packed closely. Transverse Rooming With Filling.— In other cases, a filling system is used in which rooms or chambers are driven across the deposit and then con- tinued upwards by overhand stoping, the ore being thrown to a lower level through a chute cribbed up as the work progresses, and the excavated space filled up with broken rock brought down through a chute from above, as shown in Fig. 36. After the rooms are worked out between two levels, the pillars are removed in the same manner. Longitudinal Back Stoping With Filling.— In this case, the deposit is worked as a series of overhand stopes, Fig. 37, the space below the workmen being filled with broken rock a brought down through raises b from above, the ore being thrown to a level c, which has been timbered through the filling material on 320 MINING MINERAL DEPOSITS. the first or lower floor of the stope. This method has been very successfully applied to some of the large iron mines of the Lake Superior region of the United States. The filling material used in any one of the various filling methods may be obtained at the surface, may be partially or wholly obtained from the waste rock associated with the vein material and from drifts or passages that have to be driven in barren ground, or it may be obtained by driving drifts into the hanging wall, and opening chambers there, from which the waste may be obtained. (See also Flushing of Culm, page 314. ) Caving Methods. — The longwall method of mining coal is really a caving system, but where this system is applied to the mining of large masses, it becomes necessary to introduce some special features. There are two general systems in use, caving a hack of ore and caving the gob or waste only. Caving a Back of Ore. — In this system, drifts or levels are run through the ore a few feet below the top of the deposit, as though the material above were to be removed by overhand stoping, but in place of breaking the m,aterial down, it is allowed to cave by gravity. When a back of ore is thick (20 ft. or more), the entire stope is sometimes allowed to cave full and then the broken ore removed by driving heavily timbered drifts through to the farther side and drawing the crushed material into the face of the drift. When the overlying worthless material appears, op-* erations are continued by removing the last set in the drift and drawing the ore from nearer the shaft. This method is continued until practically all the broken ore has been removed. Where the back of the ore is comparatively thin (less than 20 ft.), the caving is usually accomplished at the face of the drift only, the drift being driven a short distance beyond the timbering without support. The ore above this unsupported portion will cave in and can be removed. When the waste rock and old timber from above appear, the operator retreats, removing one set of timber from the drift, caving and remov- ing the ore over it. In this manner, operations are contin- ued until all the ore over the drift or stope has been caved, when another drift or stope is driven beside the first and the ore over it caved. In this method, blasting has to be re- sorted to only in driving the drifts, from one-half to three- fourths of the ore being obtained without the use of powder. The advantages of this system are that little blasting is re- quired; practically the entire deposit is recovered; the mining cost per ton is very low. The disadvantages are that the ore is liable to become mixed with more or less dirt, which caves down with it; only one level of the mine can be operated at a time, and the surface of the ground is allowed to cave into the openings, thus rendering it unfit for ordinary surface uses. Caving the Waste Only.— In this system. Fig. 38, drifts A and galleries B are driven through the top of the ore body immediately under the waste rock. After one of these drifts or galleries is completed, the floor is covered with a lagging of plank or poles, and the waste material allowed to cave on to this platform. Subsequently, other drifts are driven beside the first one, the floor covered with lagging, and the waste allowed to cave. This process is continued until a slice has been removed over the entire surface of the ore deposit, when more drifts are driven lower down and another slice removed. After the first slice has been removed, the broken or waste mate- rial is supported on the lagging laid on the floors of the first drifts, and hence the miners have only to support this lagging in order to support the waste. The caving of any individual drift crushes the ore on either side to a con- siderable extent, thus materially reducing the blasting expense, Fig. 38. IRREGULAR DEPOSITS, 321 The advantages of this system are that the entire deposit is recovered; little blasting is required; the ore obtained is clean; the mining expense is comparatively low per ton. The disadvantages are that only one level of a mine can be producing at a time; the surface is allowed to cave, thus rendering it unfit for surface uses. SQUARE-SET SYSTEM. Frequently, large masses of material are encountered, which it is neces- sary to remove, and at the same time support the surrounding material. At times, it is not desirable to fill the TT l/Xit; VXi C XO UCXXig iCXXXWVcCl, and, at the same time, it is impossible to support the walls by single sticks or Stulls. To overcome these diffi- culties, the square-set system has been evolved, which consists in the sup- porting of the walls by means of a series of square frames, from 6 to 9 ft. square, which are placed in position as fast as the ore is removed. The use of these frames reduces the length of the individual sticks, and so produces a firm structure. The timbers may be square-sawed material or round logs. If the walls are soft, the sides and top may require lagging, and if the floor is soft or composed of ore, sills will be necessary under the posts. The mining is carried on by overhand- stoping system, removing one block at a time and replacing it with the square set. Fig. 39 represents a stope, the Fig. 39. walls and roof of which are supported by square sets that are lagged from the outside. In this case, the square sets are made from round timber. IRREGULAR DEPOSITS. Coyoting, or Gophering.— Bodies of valuable material frequently occur that cannot be mined by any regular system. These are recovered by simply following the ore throughout its irregularities and removing it with the use of as little supporting timber or other material as possible. Owing to the crooked and irregular passages that occur in such mines, the work has been called coyoting, or gophering. Sometimes regular levels are driven at stated intervals, and the coyoting, or gophering, carried on from them. Many of the small gold and silver mines of the West, the mines of Mexico and South America, and the Missouri lead and zinc deposits are worked by this system, the object being to remove as much of the ore as possible without the use of timbering or the driving of unnecessary passages. Probably one of the best examples of working irregular deposits is the mining practice in the Joplin zinc district, Missouri. The deposits of zinc blende are irregularly distributed through a limestone rock, and the mining is carried on in a very crude and irregular fashion. After an ore body has been found by drilling, a shaft 5 ft. X 5 ft. to 6 ft. X 9 ft. in the clear is sunk by the contractor, the price being $4 per foot for soft and ^9 per foot for hard ground for the first 50 to 80 ft., the contractor doing all the work in sinking and timbering. Through the soft ground, the shaft is timbered by 4" round poles or by 2" X 4" or 2" X 6" timbers laid flatwise, skin to skin. The mines are divided into four kinds. (1) Very hard mines that require all the ore to be drilled with air drills and blasted out, and require no timbering. (2) Mines that are hard but have open crevices between the strata where a hand drill can be driven and a charge of dyna- mite lodged and exploded, throwing down a large amount of dirt and so jarring the surrounding ground that it may be easily cut down with the miner’s pick. This kind of ground needs no timber. (3) Mines that are moderately soft and where the miner can place a blast anywhere by driving 322 COSTS OF MINING ANTHRACITE. a spud, throwing down a large amount of ore. The drifts are carried 10 ft. X 12 ft. in the clear, and are cut ahead from 6 to 10 ft. before putting in the sets of timber and laggings to hold the roof. (4) Mines that are very soft and where a drift cannot be carried over 8 ft. X 10 ft. in size, where the getting of the ore is all performed by pick and shovel, and where it is neces- sary to timber close and drive spiling overhead as well as along the sides and to resort to mud -sills in the floor of the drift. When the shaft reaches the ore and the drift is extended for some dis- tance to prove the ore body, underhand stoping is used and 15' holes are drilled by hand in the bottom. A charge of 50 lb. of 40^ dynamite lifts a stope 10 ft. X 10 ft. The cost of 75 tons of ore, hoisting it and dumping it on the mill platform during a shift of 9 hours in the two classes of hard mines mentioned, is, according to Mr. E. Hedburg, as follows: 1 ground boss $ 2.50 2 miners at ^2.00 : 4.00 2 miners at S1.75 3.50 2 shovelers at $1.75 3.50 1 hoister 1.75 1 engineer, who also sharpens picks and drills 2.25 1 engineer 1.50 Dynamite 6.00 Fuel 2.50 Oil and supplies 2.50 Superintendent 3.50 Total $33.40 Or 44.5 cents per ton of rough ore; this includes pumping the mine. In very soft ground, a drift 8 ft. to 10 ft. high is driven, a spiling put in the top and sides. When one level is worked out, the whole drift is then caved from the surface and allowed to settle down on the floor of timbers. The cost of mining in soft ground is about the same as in hard ore, as the saving of labor and dynamite is expended in timber and time. A typical primitive mining plant in this region, which has a shaft 150 ft. deep* with pump, hoisting engines, and boilers, and including hand jigs, screens, and tools, costs from $2,000 to $3,000; more modern plants are however now being erected, costing $8,000 to $10,000. SPECIAL METHODS. Frozen Ground.— When the material of placer deposits is frozen, as in Alaska and Siberia, it is mined by building a fire on the surface, which thaws the earth to a depth of from 1 ft. to 14 in. The embers are then scraped away and the thawed material removed. By repeating this operation, a shaft can be sunk, and then, by building a fire against one side, a drift can be started and continued by thawing the face, 1 ft. at a time. It has been found that 1 ft. of timber piled against the face of a drift will thaw to a depth of about 1 ft. The latest practice thaws the frozen ground by means of a steam jet instead ot by fire. The openings have to be securely, but not heavily, timbered. Leaching Methods.— Salt, copper, and sulphur have been mined by leaching methods. In the case of salt, a hole is drilled into the salt formation, water allowed to flow down and dissolve the salt, and is then pumped out as a con- centrated brine. For excavating upward in salt, a jet of water is made to play upon the roof of the level to be raised, and the resulting brine is carried off in launders. When old workings containing the sulphides of copper are left exposed to the action of air and to percolating waters, part of the copper is converted into soluble sulphate. Water pumped from such mines may be a profitable source of the metal, for by passing it over iron bars or scrap iron the copper will be separated and deposited as cement copper in the bottom of the vessel containing the iron. In the case of sulphur, superheated steam is forced down to melt the sulphur, which is then pumped out. LEHIGH REGION. 323 COSTS OF MINING ANTHRACITE. The following costs include only labor and supplies, and do not include, ill general, improvements, royalties, taxes, and other similar fixed charges that independent of the method of mining. LEHIGH REGION (PENNA.). The costs for the Lehigh region, though based on the results of a single 'Company, are believed to be very fairly representative of the entire region. 'They are the mean costs of two collieries where about 2,000 men were employed inside and outside, and apply to the year 1897, when the con- dition at all anthracite mines was very unfavorable to economical working, as the mines were then working on very short time. The tonnage at these collieries for the year was as follows: January, 29,775.04 May, 34,090.02 September, 27,406.94 1 February, 30,872.97 June, 35,761.89 October, 56,710.04 f Total, March, 42,827.04 July, 44,409.13 November, 48,177.94 [ 463,672.08. April, 38,553.08 August, 37,500.97 December, 37,587.02 J The following tables show the distribution of this output by sizes during the year, and the costs per ton itemized under the several headings given: Percentages of Different Sizes. Month. Lump. Broken. Egg. Stove. Chestnut. Pea. January 10.56 23.59 18.27 18.69 14.21 14.68 February 12.34 22.54 18.11 17.98 14.50 14.53 March 11.85 19.26 18.81 19.69 13.18 17.21 April 12.81 19.21 18.35 19.48 11.14 19.01 May 13.81 19.11 18.35 19.01 11.32 18.40 June 15.29 18.60 17.73 19.08 11.23 18.07 July 14.26 19.89 17.41 18.30 11.25 18.89 August 13.56 20.26 18.10 17.72 11.49 18.87 September 12.31 20.41 18.27 18.28 11.61 19.12 October 12.21 18.01 19.15 18.89 12.28 19.46 November 11.40 18.53 19.78 19.79 12.01 18.49 December 10.78 19.56 20.09 20.32 12.07 17.18 Year 12.58 19.71 18.59 18.99 12.15 17.98 Costs of Mining and Preparation. Month. Outside. Inside. Total Cost. Credits. Net Cost Labor. Supplies. Total. Labor. Supplies. Total. January ... .300 .109 .409 .951 .196 1.147 1.595 .100 1.495 February.. .297 .085 .382 .909 .190 1.099 1.519 .063 1.456 March .243 .047 .290 .844 .151 .995 1.311 .088 1.223 April .242 .071 .313 .822 .137 .959 1.303 .075 1.228 May .251 .100 .351 .852 .166 1.018 1.397 .103 1.294 June .300 .079 .379 .500 .203 .703 1.576 .103 1.473 July .240 .063 .303 .487 .162 .649 1.485 .084 1.401 August .... .248 .095 .343 .709 .182 .891 1.579 .085 1.494 September .278 .096 .374 .682 .158 .840 1.588 .054 1.534 October.... .228 .093 .321 .721 .129 .850 1.580 .072 1.508 N ovember .247 .093 .340 .806 .210 ' 1.016 1.846 .091 1.755 December. .290 .061 .351 .833 .220 1.053 1.883 .090 1.793 Year .271 .092 .363 1.109 .162 1.271 1.634 .088 1.546 324 COSTS OF MINING ANTHRACITE, Cost per Ton of Supplies Used Inside. Distribution. j Jan. Feb. Mar. Apr.j May. i Jun. Jul. Oils .010 .011 .007 .010 .007 .009 .006 Powder .036 .030 .031 .026 .030 .032 .029 Lumber - .007 I .025 .011 .004 .002 .008 .007 Props .040 .027 .021 .015 .022 .027 .019 Feed .039 .018 .019 .017 .023 .022 .022 Mules killed, etc .010 .005 .014 .019 .013 .009 .015 T rails, frogs, etc .005 .012 .007 .009 .018 .010 .010 Wire ropes .018 .016 .025 .013 General supplies .019 .021 .014 .009 .018 .021 .013 Total general supplies .166 .167 i t .140 1 .109 .133 .163 .134 Pumping machiuerv Hoisting machinery .009 1 .005 .004 .012 .016 .023 .004 Ventilating machinery Boilers 1 Mine cars Engines .018 .007 , .016 .017 .017 .024 Total repairs .030 .023 .011 ; .028 .033 .040 .028 Total cost inside .196 ! .190 ! .151 .137 .166 1 .203 .162 Credits .100 1 .063 1 .088 1 .075 .103 1 .103 .084 Net cost inside .096 .127 1 .063 i : .062 1 .063 : .100 [ .078 Cost per Ton of Supplies Used Outside. Distribution. Jan. Feb. Mar.' : 1 Apr. May. Jun. Jul. Oils .010 .008 .007 .006 .009 .009 .008 Lumber - .022 .0-25 .003 .016 .015 .005 .012 Feed .008 .004 .005 .004 .005 .005 .006 Mules killed, etc T rails, frogs, etc .001 .003 .004 .005 .002 Wire ropes General supplies .020 .021 .015 .008 .040 .016 .019 Total general supplies .060 [ .058 .031 .037 .073 .040 .047 Pumping machiners^ .001 Hoisting machinery .008 .002 .001 .001 .003 .008 .001 Ventilating machinerv .003 Breaker machinery....* .028 .012 .008 .014 .017 .011 .008 Boilers .006 .005 .002 .013 .001 .011 .005 Breaker .006 .008 .005 .006 .005 .006 .002 Tracks and sidings .001 Miscellaneous Total repairs .049 .027 .016 .034 .027 .039 .016 Total cost outside .109 .085 .047 .071 .100 .079 .063 Credits Net cost outside .109 .085 .047 .071 .100 .079 .063 In the two tables above and the one following, the fibres were available for seven months of the year only, but an average for these months gives a fair average for the year. WYOMING REGION. 325 Itemized Cost of Outside Labor. Occupations. Jan. Feb. March. April- May. June. July. Foreman and assistants .013 .012 .007 .006 .006 .006 .003 Clerks, shipper and supply .004 .004 .003 .003 .002 .002 .002 Hoisting engineers .009 .022 .018 .021 .019 .026 .021 Pump and fan engineers .003 .003 .003 .002 .003 J)03 Locomotive engineers and helpers .014 .014 .011 .009 .011 .013 .011 Firemen and ashmen .078 .071 .056 .060 .063 .069 .057 Stablemen .005 .005 .003 .003 .004 .005 .003 Watchmen .007 .006 .004 .005 .006 .006 .004 Total miscellaneous .133 .137 .105 .109 .114 .130 .101 Topmen and footmen .004 .004 .002 .003 .003 .004 .003 Top drivers and oilers .007 .007 .006 .006 .007 .008 .007 Dumpmen .002 .003 .002 .002 .002 .003 .002 Platform and docking boss .014 .013 .013 .012 .012 .012 .012 Chute bosses .006 .006 .005 .006 .005 .004 .006 Slate pickers .059 .063 .058 .053 .048 .056 .057 Car loaders .007 .007 .007 .006 .006 .008 .008 Breaker engineer .003 .003 .002 .002 .002 .001 .002 Dirt and plane engineer .007 .001 .001 .001 .001 .001 * .001 Rock and dirt men .007 .009 .009 .006 .004 .005 .005 General laborers .012 .013 .009 .011 .020 .022 .012 Total breaker .128 .129 .114 .108 .110 .124 .115 Pumping machinery .001 .001 Hoisting machinery .010 .005 .005 .005 .006 .009 .005 Ventilating machinery .003 Breaker machinery .005 .004 .004 .006 .003 .002 .002 Boilers .004 .004 .001 .005 .002 Breakers .007 .009 .007 .005 .011 .019 .006 Tracks and sidings .008 .007 .007 .009 .007 .008 .007 Miscellaneous .004 .001 .002 Total repairs .039 .031 .024 .025 .027 .046 .024 Total cost outside labor .300 .297 .243 .242 .251 .300 .240 WYOMING REGION (PENNA.). The following tables of costs for the Wyoming region give mean results from a number of different collieries which are quite widely separated in location and at which the conditions of working are so different that the mean results given are thought to represent average results for the entire region. They also apply, approximately, to the Lackawanna Valley, where the general conditions are the same, although the seams are much nearer the surface than in the Wyoming region, and the amount of gas present in the coal is much less. These same figures are probably also fairly representative of the Schuylkill and Shamokin fields. The collieries for which the following figures are averages are all operated through shafts, varying in depth from 350 to 1,100 ft., and many of the mines are extremely gaseous. The number includes several entirely new and modern surface and underground plants, and the others, though not new, have been overhauled and modernized as much as possible. At these collieries 10,000 men were employed during the year 1895, for which the data are given, and during the same year the output was 1,862,144 tons, distributed during the year as follows: Month. Ton- nage. Days Worked. Month. Ton- nage. Days Worked. Month. Ton- nage. Days Worked. January. 107,952 7.94 May 179,752 12.84 September 161,213 11.52 February 98,109 7.37 June 164,062 11.92 October.... 198,161 13.90 March.... 141,991 9.95 July 145,445 10.59 November 228,433 17.15 April 136,375 9.69 August .. 177,241 12.96 December 123,406 8.87 326 COSTS OF MINING ANTHRACITE, Percentages of Different Sizes. Month. Lump. Steamer. Broken. Egg. Stove. Chestnut. Pea. January 8.21 .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 6.20 .55 17.64 20.04 20.65 18.00 16.92 April 7.01 .38 16.76 20.17 20.92 18.12 16.64 May 4.79 .27 18.63 20.33 21.42 18.23 16.33 June 3.29 .21 22.43 19.72 20.21 18.57 15.57 July 7.84 .42 19.42 19.54 19.46 18.58 14.74 August 5.05 .57 19.84 20.69 18.92 18.62 16.31 September 4.25 .27 18.81 21.98 19.98 19.32 15.39 October 4.72 .01 16.77 22.00 21.27 19.88 15.35 November 2.69 .16 15.56 22.42 22.66 20.71 15.80 December 4.40 .57 14.03 22.62 • 21.27 21.41 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. Total Cost. Credits. Net Cost. Labor. Supplies. Repairs. Total. Labor. Supplies. Repairs. Total. January .363 .042 .014 .419 .934 .249 .028 1.211 1.630 .120 1.510 February .376 .042 .014 .432 .947 .273 .030 1.250 1.682 .104 1.578 March .297 .031 .010 .338 .872 .182 .022 1.076 1.414 .096 1.318 April .305 .034 .023 .362 .870 .203 .020 1.093 1.455 .103 1.352 May .270 .022 .011 .303 .839 .164 .015 1.018 1.321 .101 1.220 June .290 .032 .011 .333 .874 .206 .018 1.098 1.431 .105 1.326 July .309 .046 .019 .374 .879 .266 .033 1.178 1.552 .098 1.454 August .286 .030 .017 .333 .873 .194 .026 1.093 1.426 .102 1.324 September ... .284 .039 .012 .335 .890 .201 .024 1.115 1.450 .105 1.345 October .267 .036 .013 .316 .856 .188 .020 1.064 1.380 .100 1.280 November .... .262 .029 .010 .301 .860 .214 .018 1.092 1.393 .104 1.289 December ... .344 .045 .018 .407 .954 .307 .028 1.289 -1.696 .120 1.576 Year .297 .034 .014 .345 .881 .214 .023 1.118 1.463 .104 1.359 Coal Production of United States. Year. Bituminous. Anthracite. Tons of 2,000 Lb. Value. Tons of 2,240 Lb. Value. 1890 1895 1897 1898 1899 111,302,322 135,118,193 147,609,985 166,592,023 193,321,987 $110,420,801 115,779,771 119,567,224 132,586,313 167,935,304 46,468,641 57,999,937 52,611,680 53,382,644 53,944,647 $66,383,772 82,019,272 79,301,954 75,414,537 88,142,130 PRICES OF COAL. The table on page 327, given by the U. 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. Average Prices per Short Ton for Coal at the Mines Since 1886. PRICES OF COAL. 327 pm mmmm r-^ r^(N i ^ ,0 o pm mmmm mwmw-i pm mmmmmwmw-% pm^- mmmm ^232^ ^§222^^223 !22^i^3ll^2^2 Pi22 ^^2^!-^S2S 2^2^1^213-5^2 pi 22 ^ 2223^^225 2 2 - PSIS 22l2§§^^25i i i^i-2i5§i2i Pii2 232222^221 I 2^1^211^1^! ,-1 >.>. I e e l2ii2 232232-221 I 2-1-22521^= oa» rH r-5 Q g |i II a Exclusive of colliery consumption, h Includes Alaska, c Includes Nebraska. 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 401 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 c.ars 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 2.04 Yard pumps .76 Cleaning tracks 1.20 Total 100.08 Mine. Per Cent. Mine. Per Cent. Room coal 52.15 Machinist .49 Drivers 8.07 Bookkeeping, i of total for Heading coal 11.15 mine and yard .49 Rope haulage 2.81 Outside labor 2.03 Roads 3.03 Stable boss .96 Mine bosses 1.31 Teams .65 Fire boss 1.44 Blacksmith .98 Timber 2.83 Carpenters 1.01 Trappers .43 Lamp cleaners .82 Superintendence, i of total Inside pumps .59 for mine and yard .49 Steam pumps .55 Cagers .66 Surveys .41 Runners and oilers .80 Extra men .51 Engineers 1.01 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. Tne cost of equipping a coke plant and opening a mine to furnish the coal in the Connellsville region is from S500 to |l,000 per oven, dependent on the kind of opening for the mine and local considerations. ^00 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; Copp6e, $1,000; Bernard, $1,000. Saving by-products: Simon Carves, $1,300; Semet-Solvay, $1,600; Huessner, $1,400; G. Seibel, $1,300; Otto-Hoffman, $1,600; Festner-Hoffinan, $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 Zf of moisture in transit between the ovens and the furp^ces, 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. I ts 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 Siaies. Saltpeter 75 66.0 64 62 66.6 70 64 Sulphur 10 12.5 16 20 16.7 18 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 unconfined, 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 thaAV 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 lOj^ dynamite means that the dyna- mite contains 10^ of nitroglycerine, etc. Safety explosives, or, as they are called in England, pemfffed explosives, are compounds intended for use in gaseous mines, and they are so constituted 830 EXPLOSIVES. that they \v*ill 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. Brand. Per Cent. Nitroglycerine. | 1 Repauno Gelatine. Hercules Powder. i Hercules Gelatine. Giant Powder. Giant Gelatine. Hecla Powder. (V 73 O PL a A 75 A No. 1 XX No. 1 XX Old No. 1 No.l A No. 1 XX B + 60 B + No. 1 No. 1 No. 1 A No.l No. 1 XS No.l B 50 B No. 2 SS No. 2 SS New No. 1 No. 2 No. 1 X No. 2 XX C-f 45 c + No. 2 S N0.2S No. 2 Extra N0.2X c 40 c No. 2 No. 2 No. 2 N0.3C No.l No. 2 D + 33 No. 2C No. 2C N0.2X No. 3 A D 30 No. 3 No. 3 No. 2 No. 3 E + 27 N0.3B XXX N0.3X N0.3B 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 Hoies.— 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 1^ 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 1" 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. 331 rammer on it with sufiBicient 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 2i" hole in a seam of bituminous coal 6 fit. 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, 2 X ^ X 2 X 2 X 6 X 12 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 ofit in the cartridge. The exploders are loaded with fulminate of 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 oif by high explosives are much worse m the case of deflagrating a cartridge. The electric exploder. Fig. 2, has wires A and B, which carry the current to the exploder. /> 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 Eiectricity.— Drill the number of holes desired to be Fig. 4. 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 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 neyer 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 m 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 334 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. 8. Fig. 9. 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, Noule, and Abel, tlie following approximate maximum l)ressures, 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 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 E ermit the easy handling of the drills and also to minimize the number of oles 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 the 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 g lans. The numbers of the holes correspond in the several views. The oles 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 4 simultaneously; (2) 5, 6, 7, 8; (3) 9, 10, 11, 12) (4) 13, lU, 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 egh by the shots 1, 2, 3, and 4; 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, 20, 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 37.59^, while the average yearly gain from 1891 to 1896 was only about 22/o. 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 of 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 to 6 ft. in thickness, the machine will undercut from 50 to 100 tons of coal i 11 10 hours. The cost of undercutting under these conditions has been given MS 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, 210 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 » wo men handling the same machine under ordinary conditions can make ()0 cuts pel 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 (5) ventilating methods and machinery. THE ATMOSPHERE. Composition.— Air consists chiefiy of oxygen and nitrogen, with small and varying amounts of carbonic-acid gas, ammonia ^as, 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 23.0 100.0 100.0 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 lb. 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 1.3253 X B ^ “ 459 + i ’ 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. w 1.3253 X 30 459 + 60 = .07661b. Table of Weight of Dry Air. Weight of 1 cu. ft. of dry air at different temperatures and barometric 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. 0 .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 .065*21 .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 .01423 .04587 .04751 .04915 400 .04166 .04321 .04475 .04629 THE BAROMETER. 339 Atmospheric Pressure. — ThQ ieim barometric pressure 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 lb. per sq. in., while the barometric pressure at the same level is 30 in. of mercury column, or simply 30 in. BarometriaVariations.— 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 Ailing a glass tube 3 ft. long, and having a bore of i 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 suppbrted 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 lb., 340 VENTILATION OF MINES. the atmospheric pressure that supports 30 in. of mercury column is .49 X 30 = 14.7 lb. 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- pheric pressure will support is 13.6 X f§ = ^4 ft. This is the theoretical height to which it is possible to raise water by means of a suction pump, but the length of the suction pipe should not exceed 75^ 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 verj^ 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: E = 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 = difierence of level in feet between the two stations. = 56.300(logiJ-log r)(l + ^-*). More simply: log = R - + logr. H = 49,000 mb 300 (900 + I 000 (900 + T + 0 — 900.HJ ‘ °00 )• ^ r49,000 (900 A T At) A 900 J71 ^ “ ^149,0 ‘ 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 Tuioir of the observed height for each degree above 32°; or, if the temperature is below 32°, add for each degree. Thus, 30.667 in. at 62° F. is equivalent to a reading of 30.555 in. at 32° F., ao QO 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: II = 55,000(l--y/^), in which the letters stand for the same factors as designated above. The most important use of the barometer in mining imictice, 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, ov 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 ihe 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. Ill 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 inereased; 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 volurnes 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. Qhemlpal Symbols and Equations.- To facilitate the writing of chemical 3i2 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 tirst 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. Symbol. Atomic Weight. Element. 1 Symbol. Atomic Weight. Aluminum Al 27.5 Manganese Mn 55.0 Antimony (stibium) Sb 120.0 Molybdenum Mo 96.0 Argon(?) A Neodymium(?) Nd Arsenic As 75.0 Nickel Ni 58.8 Barium Ba 137.0 Niobium Nb 94.0 Beryllium Be 9.4 Nitrogen N 14.0 Bismuth Bi 208.0 Osmium Os 191.0 Boron B 11.0 Oxygen 0 16.0 Bromine Br 80.0 Palladium Pd 106.5 Cadmium Cd 112.0 Phosphorus P 31.0 Caesium Cs 133.0 Platinum Pt 197.0 Calcium Ca 40.0 Potassium (kalium) K 39.0 Carbon C 12.0 Praseodymium (?) Pr Cerium Ce 138.0 Rhodium Rh 104.0 Chlorine Cl 35.5 Rubidium Rb 85.0 Chromium Cr 52.5 Ruthenium Ru 104.0 Cobalt Co 59.0 Samarium(?) Sa Columbium Cb 93.7 Scandium Sc Copper (cuprum) Cu 63.0 Selenium Se 79.0 Didymium D 147.0 Silicon Si 28.0 Erbium(?) Er 169.0 Silyer (argentum) ...... ^9 108.0 Fluorine F 19.0 Sodium (natrium) Na 23.0 Gallium Gcl 69.0 Strontium Sr 87.5 rioTTn Q n 1 n tn Ge Sulphur S 32.0 VJTt/l lildill CilU. Gold (aurum) An 196.7 Tantalum Ta 182.0 Helium(?) He Tellurium Te 127.0 Hydrogen H 1.0 Thallium Tl 205.0 Indium In 113.4 Thorium Th 231.5 Iodine I 127.0 Tin (stannum) Sn 108.0 Ttt ^iiTm Ir 193.0 Titanium Ti 48.0 Xli-AlltlllJ. Iron (ferrum) Fe 56.0 Tungsten (wolfram) ... W 184.0 Lanthanum La 139.0 Uranium U 240.0 Lead (plumbum) Pb 207.0 Vanadium V 51.2 Lithium Li 7.0 Ytterbium Yb Magnesium Mg 24.0 Yttrium Y 89.0 Mercury ( hydrargy- Zinc Zn 65.0 rum) Hg 200.0 Zirconium Zr 90.0 sianus lur r r two elements, carbon and oxygen. v. i ^ i + * A molecule is expressed by writing the symbols of its elementary atoms. , 1 o+/^TY^ rkf Q cnhctflnpp nr plp.mpnt entprs into ihp compo- sition of a molecule, tne numoer Ol aiums U1 sucii eiemuut is u\ 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 CO^. 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 l 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 + 0 + 4iV = CC 2 + 4: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 CO 2 . 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 4- leN = CO 2 -h 2 H. 2 O 4- UN In this equation, each molecule of marsh gas CH^ 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 CO 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 (MO), or 2 H 2 O. The nitro- gen in this equation is equal to 4 times the volume of the oxygen consumed, and is therefore written as UN, 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 CO 2 , we have as follows: CO 4 - 0 4 - 4iV = ( 7024 - 4 Ar Atomic volumes, 2+14-4= 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- 5 X 100 oxide gas, we write the proportion 2 : 5 : : 100 : 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 CO 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, ^4 + 40 + 16iVr = CO 2 + 2 H 2 O + 16A^ Atomic volumes, 2 + 4-1- 16 = 2 -|- 4 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 X 100 = 9.38/o of CH^. lU.DD 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 CHu 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 (4 X 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 CO 2 is .11712 lb. at the same temperature and pressure, the specific 11712 gravity of carbonic-acid gas is ‘ = 1.529. .07od 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 = .117121b. 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 (5) 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 PEESSUEE. 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 lb. per sq. in., the absolute pressure supported by the steam in the boiler will be 60 + 14.7 = 74.7 lb. per sq. in. Or, if the ventila- ting pressure in a mine is equal to 13 lb. per sq. ft., the absolute pressure supported by the air in the airways will be 13 + (14.7 X 144) = 2,129.8 lb. per sq. ft. Relation of Volume and Absolute Temperature {Charles' or Gay Lussac' slaw). 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.— T he intake current of a mine is 50,000 cu. ft. of air per minute; the ventilating pressure is 13 lb. 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 Or, (459 + 20) ; (459 + 70) ) . 2,116.8 : 2,129.8 j ' : 50,000 : x. 529 X 2,129.8 X 50,000 479 X 2,116.8 55,558 cu. ft. Example.— In a compressed-air plant, the gauge shows a pressure of 80 lb. 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 20 X 10 X 100 = — = 11-57 cu. ft. (cylinder pressure). The absolute pressure 1 j 7 on the air in the cylinder is 80 + 14.7 = 94.7 lb. The absolute pressure on the discharged air is simply the atmospheric pressure (14.7 lb.). Hence, we 94 7 ' 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: (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 62 5 = 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. = .434; or, the pressure per square inch due to 1 ft. of water column is .kSk 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 | 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. 1 3253 X 30 of air at this temperature and pressure w = = .0766 lb. The 459 -|- oO 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. 847 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 Cokresponding Mercury and Air Columns, and Pressure per Square Foot for Each Inch of Water Column. Water Gauge. Inches. Mercury Column. Inches. o am o ressure by 4, the work performed {pa) v will be multiplied by 2^ = 8. We til us 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, {h) 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 I 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 ME AS VREMENT OF PRESS VRE. 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. To obtain the quantity of air passing (cubic feet per minute), multi pl^^ 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? 1 320 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 Fig. 5. water level, and the upper water level will 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 a right 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 at A, Fig. 6. The brass tube forming 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 be observed that the water gauge records a difference of pressure, each end the water gauge being subject to atmospheric pressure, but one end in addition being subject to the ventilating pressure, which is the difference of Fig. 6. 366 VENTILATION OF MINES. pressure between the two entries. The water gauge thus enables us to measure the resistance of the mine inhye 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 onlj^ the resistance of that split. It never measures the resistance outhye 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 tne 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 0° and 80°, respectively. In the Centigrade, the freezing and boiling points are placed at 0° and 100°, respectively. To Convert Fahrenheit Into Centigrade.— (1) Subtract 32 and divide the remainder by 1.8, or multiply by |. If a Fahrenheit thermometer registers 167°, what will be the register by a Centigrade thermometer ? — g — = 75° Centigrade. ^ = 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. 5 To Convert Fahrenheit Into Reaumur.— (1) Subtract 32, and divide by 2.25, or multiply by f. If the Fahrenheit thermometer registers 113°, what will be the register by the Reaumur thermometer ? ^^2 25 Reaumur. — ^ - = 36° Reaumur. To Convert Reaumur Into Fahrenheit.— (1) Multiply by 2.25, or multiply by |, 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. 4 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, pr the unit of resistance, is the resistance offered by the unit of rubbing sur- face to a current of a velocity. This unit resistance has been variously estimated by different authorities (see following table). The value most iiniversally accepted, however, is that known as the Atkinson coefficient THE EQUIVALENT ORIFICE. 367 (.0000000217). (6) 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^. Table of Various Coefficients of Friction of Air in Mines. Pressure per Sq. Ft. Decimals of a Pound. J. J. Atkinson’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 Navier W. Fairley J. Stanley James.. D. Murgue .000000001955 .000000001872 .00000001 .00000000929 .000000008242 It will be observed that J. J. Atkinson’s coeificient is greatly in excess of any other, with the exception of Andre’s. Fairley’s is derived from an average taken between 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- gation, made by a commission of competent men, provides a standard coef- ficient, 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 = pav = 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. T he fo rmula expressing the velocity of flow through such an orifice is V = y 2gh\ 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 .621/2 the vena contracta of the flow. Reducing this to cubic feet per minute and inches of water gauge represented by t, we have, finally, the equation A = .0004 X — By this formula, Murgue has suggested assimilating the V i 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. Reard.)— Equations 8 and 27, 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 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 g, we have the following: With respect to pressure, With respect to power, Hence, we observe that, in any airway, /or a constant pressure, the quan- tity of air in circulation is proportional to the expression and, /or 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 - 4 = and are the potentials of the \/ p y u 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 he. 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 k', 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 Xp with respect to the pressure for each of these mines, or airways, we have, using the relative potential, -Xi = 6 X ^^-^6 + 8) X 10,000 "" ^2 = 6 X 2(6 -}- 12) X 8,000 = 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 non V 1 1^84 tion 20,000 : ga : : .62845 : 1.1384, and gg = ’ - = 36,229 cu. ft. per min. .62840 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 with respect to power for each of these 6x8 mines, using, as before, the relative potential. Thus, Xi = - ■ 6 y 12 r 2(6 + 8 ) X 10,000 = .7337, and X^ = , . — = 1.0905. Then, in this case, since the F 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 : 20,000 X 1.0905 92 = — ^ = 29,726 cu. ft. per min. .7337 .7337 : 1.0905, and 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 = X It will be observed that this second formula is a 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 case, is u = Or, the question may be asked, what quantity of air will be produced in a given airway by means of a certain power^ work applied to the airway. In this case, the formula used is 9 = H the ques- tion asks for the power required to produce a given velocity in a given air- way, the formula employed is = 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 ft.) a 20 sq. ft. Horsepower* h 2.959 H. P. Coefficient of friction f -.r k .0000000217 lb. Length of airway 1 2,000 ft. Perimeter of airway, 2('5 ft. + 4 ft.) 0 18 ft. Pressure (lb. per sq. ft.) P 9.765 lb. 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.-lb. Velocity (ft. per min.) V 500 ft. Water gauge i 1.87788 in. Equivalent orifice of the mine A 2.919 sq. ft. Potential for power 217.16 units. Potential for pressure 3,200 units. Weight of 1 CO. ft. of downcast air vf .08098 lb. Motive column (downcast air) M 120.5 ft. Depth of furnace shaft D 306.77 ft. Average temperature of the upcast column.. T 350° F. Average temperature of the downcast column t 32° F. *A horsepower is equal to 33,000 units of work. tThis 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: No. Formula. Specimen Calculation. Rubbing sur- face of an air- way. (Sq.ft.) 1 s = lo 2,000 X 18 = 36,000 sq. ft. Area of an airway. (Sq.ft.) 2 11 - = 20 sq. ft. of area. Velocity. (Ft. per min.) 3 a 4 si u ~ 'yjks 3 / 97,650 \ .0000000217 X 36,000 5 ^ = \k- \ ks 1 9.765 X 20 \ .0000000217 X 36,000 u 97,650 _ 9.765 X 20 6 ~ pa Pressure. 7 ksv- .0000000217 X 36,000 X 5002 ^ (Lh. per sq. ft.) 20 “ 8 ks(fi .0000000217 X 36,000 X 10,0002 203 = 9.765 lb. 9 u p = — <1 97,650 _ __ „ iPoo = 10 p = Mw 120.58 X .08098 = 9.765 lb. 11 p = 5.2 i 5.2 X 1.87788 = 9.765 lb. 12 11 13 Water gauge. (Inches.) 14 ^ 5.2 = 1.87788 in. Resistance of an airway. (Total pressure, lb.) 15 16 pa = k sv^ n pa = - ^ V .0000000217 X 36,000 X 5002 = 195.3 ib. 97,650 ^ „ FORMULAS. 371 To Find: No. Formula. Specimen Calculation. Quantity. (Cu.ft.per min) 17 q = a V 20 X 500 = 10,000 cu. ft. 18 u 97,650 Q = ~ P ■^7-65 19 1 9.765X20 q = ^ \ .0000000217 X 36,000 ^ = 10,000 cu. ft. 20 fcx- 3 / 97,050 \ .0000000217 X 36,000 ^ = 10,000 cu. ft. 21 11 1 SI 217.16 X if 97,650 = 10,000 cu. ft. 22 11 S if 3,2002 X 97,650 = 10,000 cu. ft. 23 q = Xpl/ p 3,200 X 1 / 9.765 = 10,000 cu. ft. Units of work per minute, or power on the 24 u = avp 20 X 500 X 9.765 = 97,650 ft.-lb. 25 u = qp 10,000 X 9.765 = 97,650 ft.-lb. air. (Ft.-lb.permin) 26 u = ksv^ .0000000217 X 36,000 X 500" = 97,650 ft.-lb. 27 u = ks q^ .0000000217 X 36,000 X 10,0003 203 = 97,650 ft.-lb. 28 u = ^33,000 2.959 X 33,000 = 97,650 ft.-lb. 29 u — q^ Xu^ S = 97.650 30 u = JL = 97.650 ft-lb. Xp^ 3,2002 ’ Horsepower. 31 h = u ?^- 2 959H P 33,000 “ Power poten- Xu = a 20 tial. (Units.) 32 217.16 units. -^ks r:6d00000217 X 36,600 33 Xu, = 3iq^ MJ -<1 9:765 - 217.16 units. 34 X — 10,000 — ^ ^ jg units fu U97,650 372 VENTILATION OF MINES. To Find: No. Formula. Specimen Calculation. Pressure poten- tial. (Units.) 35 36 II II 1 0000000217 X 36,000 = 3,200 units. - ^ ^ = 3,200 units. 1/9.765 Equivalent orifice. (Sq. ft.) 37 ^ _ .0004 Q i/r y 1.87788 Motivecolumn, downcast air. (Feet.) 38 39 ^“^^459 + T M = ^ w - 120.5 ft. Motivecolumn, upcast air. (Feet.) 40 39 M = ^ w + 198.7 ft. 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 tt, 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 same for each airway. The following rules may always be applied: For a constant pressure: v varies as Q. varies as (relative poten- tial for pressure). For a constant power: v varies as-^^; q varies as-r^ (relative potential V lo for power). For a constant velocity: q varies as a; p varies as — ; u varies as For a constant quantity: v varies inversely as a; p varies inversely slS, XJ (potential for power); u varies inversely as (potential for power) or directly as p. For the same airway: The following terms vary as each other: v, q, l/p, -^u. Similar Airways. r = length of similar side, or similar dimension. _ For a constant pressure: v varies as q varies as r^ X rvariesas Iv^t or Iq^. DISTRIBUTION OF AIR. 373 1 3 \T^ For a constant power; wanes as — — ; q varies as r X r varies as 3 IT^ Yy; r varies as For a constant velocity: q varies as r*; p varies as u varies as Ir; /-I w r vanes as y , or y For a constant quantity: v varies inversely as p and u vary inversely as Furnace Ventilation. _ p (motive column) varies as*" Z); q varies as i/X). 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^; u varies as n^. 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 p varies as n^-^. Complement of ^ciency {1 — K) varies as 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 gr 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 wdll 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; (ft) 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 sum 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 -1- X2 + etc.) by the expression Hence, p == 7.^^ ^ and u = (2 X^y this rule is 2 p express the pressure and power. 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 Xi 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, Xi 48 2(6+8)5,000 40 for split B, Xa 40 ^ 8)10, 000 and substituting these values, we have, .8888 = .8888 = .4961 and 2 X„ = 1.3849; qi = X 60,000 = 38,506 cu. ft. per min.; and 72 = X 60,000 1.3849 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. Calcul iting the respective relative potentials with respect to pressure, we have for split X, = 60^ 2(6 + - loTx 8,000 ^ for split B, X, = + 1^X16,00 0 = for split C, X, = 50^ 2(5 ^,oTx ' 6.000 = Adding these potentials, we have 2 = .9185 4- .8314 + .8333 = 2.5832. Then, applying the foregoing rule, we have 9185 qi = X 100,000 = 35,556 CU. ft. per min.; X 100,000 = 32,184 cu. ft. per min.; ^•OooZ QOOO and ^^3 = ~ X 100,000 = 32,260 cu. ft. per min. ^.UOO^ 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 he 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 50fc 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, k S 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, kso^ when passing its required amount of air, using the formula p = — 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.— T he 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 B, 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 D, 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, . , , .0000000217 X 2(6 -f 9)8,000 X 40,0002 for split A, p = ' ' 543 " ^ for split B,p = for split C, p = for split D,p = .0000000217 X 2(5 + 8)6,000 X 40,0002 403 .0000000217 X 2(9 -f 9)8,000 X 10,0002 813 .0000000217 X 2(6 + 8)10,000 X 30,0002 483 = 84.63 lb. per sq. ft.; = 1.176 lb. per sq. ft; = 49.45 lb. per sq. 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 lb. 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 = \/ 2 gh. 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 k s 0 ^ first calculated by the formula p = — 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 = The value of A thus obtained is V i 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 re^lator 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^ (6 X 10)=“ = 7.233 lb. per sq. ft. 7 233 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 = - — j— = V.6 .0004 g _ .0004 X 15,000 l /.6 = 7.746 sq. ft., area of opening. Size of Opening for a Door Reguiator.— The sectional area at the regulator is divided proportionately to the work to be performed in the respective splits according to the proportion Ai\ A^wui'. u^. Or since Ai-\- A^ = a, we have Ai : a : : Wi : and Ai = — ^ — ■ X a. This furnishes a method of pro- U\ “T U2 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 84.63 X 120,000 33,000 ' 307.745 H. P. 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. Natural Division. Required Division. Horsepower. Door Regulator. Box Regulator. Split A, 6 ft. X 9 ft., 8,000 ft. long Split B, 5 ft. X 8 ft., 6,000 ft. long Split Cy 9 ft. X 9 ft,, 8,000 ft. long Split Z>, 6 ft. X 8 ft.,10,000 ft. long Totals 28,277 22,360 47,423 21,940 40,000 40.000 10.000 30,000 64.145 102.582 .356 44.955 102.582 102.582 25.645 76.936 120,000 120,000 212.038 307.745 378 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. Potential for pressure. 35 (X 1 + X 2 + etc.). i 20 ^^\.0000000217X 14,400 ~ /'o\ on-t. / 4 1^1 ^^^.0000000217X21,600 ’ 5,060 + 4,131 = 9,191. Natural divi- sion. 41 (1) X 10,000 = 5,505 cu. ft. (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 = Xp}/ p. (1) 5,060 i/l.l838 = 5,505 CU. ft. (2) 4,131 1 / 1.1838 = 4,495 CU. ft. See formula (42). Pressure. 42 ^ (2Xy)2- Power. 43 “ (2X„)2- S = units- Quantity. 44 45 Q = 2 XpV'p- Q = f (2Xp)%. 9,191 p 1.1838 = 10,000 CU. ft. #'9,1912 X 11,838 = 10,000 CU. ft. Increase of quantity due to splitting. (Pressure con- stant.) 46 2 X„ Q = X Qo- Q 1Q1 ^ X 10,000 = 28,722 cu. ft. Increase in quantity due to splitting. ( Power con- stant. ) 47 Hm' 10,000 ^(^^y=20,mcn. ft. SPLITTING FORMULAS. 379 . Secondary Splits.— (1) 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 A:, when finding the quantity, as in formulas (49) to (51). 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 Calculation. Pressure due to friction. 13 (2) = 2.4757 lb. To accomplish this division of air, the pressure in split (1) mlist he 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 diff’erence between the natural pressures in these splits. Pressure due to the regulator in split (1). 53 11 1 2.4757 — .47845 = 1.99725 lb. Area of the opening in regulator. 37 , .0004 q 1.99725 \ 5.2 Secondary Splits.— (1) 4 ft. X5 ft., 800 ft. — 3,500 cu. ft. (2) 4 ft. X5 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 jxitential, multiply the result by fc, to obtain the pressure, or the power. Pressure due to friction. Free split-second- ary pressure. 13 (.1) . 0000000217 (^ 1 ^^^= .47848 lb. (2) .0000000217 1.0314 lb. (3) .0000000217 .31248 lb. (4) .0000000217 .0915461b. 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. 1 P 2 +P 3 . 1.0314 + .31248 = 1.34388. Pressure due to the regula- tors. P3-P4- (P2+P3)-Pl. (4) .31248 — .091546 = .220934 lb. (1) (1.0314 + .31248) — .47848 = .86540 lb. Areas of open- ings in the regulators. 37 , .0004 q Vi ■ m •<>«« X 2,500 /.220934 V 5.2 (1) = 3.4328 sq.ft. .8654 \ 6.2 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; {h) 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; (b) 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 thC 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 Zess. 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 : 6. If, now, the mine pressure is decreased to, say, 2 in., the effective rise and dip pressures will be, respectively, 2\ in. and li 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 f, 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 : ]/l.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, 4i 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 i/l.4 : \/ 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 dumib 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 50,000 60X20 41| sq. ft. 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 , and cubing and. dividing the result by 33,000; thus. H. P. = \X^I ^ 33,000 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 . over 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 cu^'ent from the mine is laden with blackdamp CO 2 , its weight will be much increased, since this gas is practically li 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 ventifating 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- 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 ressure in the mine airways, in natural or in furnace ventilation, is caused y 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 / 1.3253 X B 1.3253 X ^ ^ V 459 + « 459 + T * 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 ( = 18.32 lb. per sq. ft. Calculation of Motive Column or Air Column. — It is often convenient to express the ventilating pressure p (lb. 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 wofl cu. ft. of air, or = £• 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 th^ Fig. 7. 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 / 1 3253 X \ ventilating pressure by the weight of 1 cu. ft. of downcast air 459 _|.^ J » ( y I \ 459 + t ) ^ 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 / 1 3253 'X. E\ pressure by the weight of 1 cu. ft. of upcast air ( *459 + ' r ~)* obtain ( y I \ 7377 — 7 ) X D. which is the expression for motive column in terms of 459 + c / the upcast air. Influence of Furnace Stack.— To increase the height of the primary or furnace column, a stack is often 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 ot 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 qi and and the height of stack d, we have 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 ( 6 ) 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 {h) force fans or blowers. In each, the action of the fan is essentially the same; i. e., to credXe 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 (6) 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 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 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 6vase 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. 11. 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 6vase chimney, which was a feature of the Schiele fan, but vibration was so strong that a shutter was required at the cut-off below 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 radiallj^, 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. » Ventilator. — Fig. 13 consists of twin fans supported on the same 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 i§ 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 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 390 VENTILATION OF MINES. 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 abj 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 ab, 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 ^ and fs, 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 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 7^2 N/ 2 2 X 12 to the fan’s action is given by the equation h = ox i — g gx 1,000 ’ 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 jnS 1 - the theoretical work of the fan per minute: U = .001699 r— y V B?b n^, in which m = ratio between outer and inner diameters of fan (D = md), 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 163 600“ of efficiency of a ventilator is given by Beard as follows: K = C ^ -f- lo3,o(X)* 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 defiection 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 p assing per minute, d = fans, and d = -y/^ 00x T 78 5 4 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, = irdb. [The throat area is commonly made 1.25 times the total area of the intake orifices, which gives for breadth of blade b = | d for double intake, and 5 = 1 % 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 = and the effective head produced = h, h = KH = iT or w = From this 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 h = found the tangential speed required in feet per 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 = » in which V 1 + ^ 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 (/i) is easily calculated /gh from the formula u N, 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: m = 3 Q i , 163,600'^ \ 385,000,000 p KV'QV + 1 ; D = \/m^- |/m3 — 170 m __ 3,770 / p , a n \/Wv' 'X3 V e = 392 VENTILATION OF MINES. in which m = which is the ratio between the outer diameter of the fan a blades D and the inner diameter of the blade d, which equals the diameter of the intake orifice; h = 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 fiow 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 = — S v . in which D — diameter of fan; n = number revolu- ^ TT Dnh tions per minute; h = breadth of fan blade. The evase chimney reduces the velocity of the air, as it is discharged into the atmosphere, to a minimum. The chirnney 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 Testa.— A large number of fan tests hav$ 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 sufiicient 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 air bridge 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 HA VLAGE. 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- 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 i *ust as a flat rope on a reel does. On account of the fleeting of the rope, lowever, 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 liabilitjr 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- f rooved drums placed tandem instead of a single- riving 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 My F three times, then out to the fleet sheave (7, 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 c 0 < • 1 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 shaft. The power used for hoisting is generally steam for the main hoists. Elec- tricity is, however, coming rapidly into use, particularly for smaller 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 By loaded cage at top 0, empty cage plus rope at bottom D, small diameter of drum Xy and large diameter j/; then. Ax— By = Cy — Dx. Example.— In a shaft, the cage weighs 2 tons, the empty car 1 ton, the loaded car 3 tons, and the rope 2 tons. What should be the small diameter of a conical drum whose large diameter is 30 ft.? (2 + 2 -h 3)a; - (2 + 1)30 = (2 + 3)30 - (2 + 2 + l)Xy or 7 X — 90 = 150 — 5x. 12 a; = 240, a; = 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.). D = 1.97^/^, or P = \Pr . \ .7854: Frn 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 lb. per sq. in. and the stroke of the piston is twice its diameter ? D = 1.97 3ll52,580 \45X2 23.5 in. 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 frictional resistances, and call ihat 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 weight in lb. X speed in ft. per minute. 33,000 * addi for .contingencies, friction, etc. Example.— Having a shaft 600 ft. deep, gross weight of load 20,000 lb., to be hoisted in minutes, what horsepower is required ? 20 000 V 400 = * oo nnfi — = 243 H. P., nearly. To which add i for contingen- oOjOOO cies, and we have 324 H. P. In a shaft with two hoistways, use the net weight -h 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 i for friction, etc. HBAD-FRAMES, 397 Example.— G iven a pair of engines, cylinders 20 in, diameter by 40 in. stroke, the drum 12 ft. diameter, and the i)ressure at steam gauge 50 lb., steam cut-off at 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 -t- 452.4 = 2,677. I 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 -f i of 351,859 (or 175,930) = 527,789. The mean average pressure = 56.2 lb. 56.2 X (6 X 2) = 674.4. 527,789 -7- 674.4 = 782.6 sq. in., area of piston. 782.6 .7854 = 996. i/ ^ = 31.56 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, 1,500 ft. Then, 400 ^ 12 = 33.33. 33.33 X 31.416 = 1,047.1. 1,500 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 = 4,4801b.; depth, 1,500 ft.; period of wind- ing, 1.43 minutes. Then, 4,480 X 1,500 = 6,720,000. 6,720,000 -r- 1.43 = 4,699,301. 4,699,301 -r- 33,000 = 142-f 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 GH to the same scale to represent the pull of the engine, com- plete the parallelogram GHLK; 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 Fig. 4. possible parallel to this resultant line, and should be designed to withstand a compressive Strain equal to this resultant. Ile8d-9ne9v*9 are made of iron, being sometimes entirely cast, or else the 398 HOISTING AND HAULAGE. rim and hub are cast separately and wrought-iron 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- i scends, while the rope attached to the empty ^ car is wound on the drum and the car thus T hauled up the plane. The natural slope of nor/zontaL ground, in a large measure, determines Fig. 5. 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 lb. and that of the ascending load 2,800 lb. Or the inclination should not be less than h\io 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 5j^ to 10^, according to the loads. A load of 4,000 lb. on a 10^^ grade 2,000 ft. long will hoist a weight of 1,400 lb. 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. HAULAGE. 399 The acceleration f oi the haulage system is given by the formula /=: - X X sin a Pi + P2 ' where pi and p 2 are the descending and ascending pulls, respectively. The length of steep pitch is given by the formula 2 /’ I = 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 wl) a -Y {W wl) cos a X where W = weight of loaded trip; wl = weight of rope; a — slope angle; p = 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 ju, = the empty cars weighing 1,000 lb. each and carrying a load of 2,000 lb. each. Assuming w = .88 lb., T = (6,000 + .88 X 800) (.05 + .04994) = 671 lb. To find the nuipber of cars that must run in a trip on a self-acting incline, use the formula ^ (40 sin a + cos a) Wz (40 sin a — cos a) Wi — (40 sin a + cos a) Wf in which N = number of cars; a = angle of inclination of plane; Wi = weight in pounds of one loaded car; W 2 , = weight in pounds of one empty car; Wz = 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 lb., a loaded car weighs 3,000 lb., and an empty car weighs 1,800 lb. 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 - c ~ (40 X .13917 — .99027 ) 3,000 — (40 X .13917 + .99027)1,800 “ 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 Tracfc.— 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= ( ir+ ^^;^) (sin a + ju. cos a). 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 lb. each, and carrying a load of 2,000 lb. each, the inclination of the plane or the slope angle being 16° and its length 500 yd., assuming for the coefficient of friction /a = W = 30,000 lb., and assuming w = .89 lb., W + wl = 30,000 + (.89 X 1,500) = 31,335 lb. Sin a + = .27564 + = .29967. Hence, T = 31,320 X .29967 = 9,394 lb. 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 lb., and using a factor of safety of 6, we have for the breaking strain of the rope 18 788 X 6 - ’ — = 57 tons. In the table of wire ropes, a 1|-" plow-steel rope ^)UUU 400 HOISTING AND HAULAGE. presents % breaking strain of 56 tons. Since a Ij" rope weighs 2 lb. per lineal fo jt, we have W w I 80,000 + (2 X 1,500) = 33,000 lb. Then T = 33,000 X .29967 = 9,889 lb. . (b) 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 — sin a, and for the friction pull of the entire moving system {W -\-Wi-\-wr) ju. cos a, and L = {W — W\ -\- wl) sin a A- {W ^W\ A- y^l) y- cos a. Assuming the same conditions as given in the example of the preceding paragraph, we have for the load L on the engine, X = [10 X 2,000 + 2 x 1,500] .27564 + [10 X (3,000 + 1,000) + 2 X 1,500] X = 23,000 X .27564 4- 43,000 X .02403 = 7,373 lb. instead of 9,394, the unbalanced load for single track. (c) Engine at Foot of Incline.— 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 X, as before, we have, in this case, X = TT sin a + ( IF + 2 Z) /u. cos a. Assuming the conditions of the previous example and calculating the load on the engine for this case, we have X = 30,000 X .27564 + [30,000 -f 2(2 X 1,500)1.02103 = 9,1341b. 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 lb. ; 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 33,000 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 naulage 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 roi)e (ft.). a = slope angle of maximum grade. T = Tr(sin a + iu. cos a)+ (d + /X 0- 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°, fx = Assuming a rope, weighing .89 lb. per lineal ft. T = 60,000 (.17365 -1- -f .89 ( 3 OO = say 12,300 lb., or some- 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 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 1" 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 greatlJ^ 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 HA ULAOE. 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 0 = output (lb. per min.); = weight of mine car (lb.); speed of winding (ft. per min.); w = weight of rope (lb.); I = length of haulage road (ft.); c = Then, T ~ load on the rope (lb.); M = coefficient of friction. capacity of mine car (lb.); ^ = weight of material in transit; 2 ^ wi = weight of moving cars, loaded and empty; 2lw = weight of rope; ^ ^1 + + 2 wl = entire moving load. And if the coefficient of friction equals l}. H. P. = JU, I ^00 X (l + -p) + 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 /x = r = A (l + + 2 X 1.58 X 5,00oj = 1,697, say 1,700 lb. 1 + H. P. = 704 5,000 40 X 33,000 [3,333 ( 2X1,200\ 2,000 ) + 2 X 1.58 X 704] = 36.2 H.P. or. assuming an efficiency for the engine of 60/c, 36.2 .60 = 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 OA and the total work per minute u will be u = iOL^[o^l + ^ + 2 ic vj + 0 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 haulage way, we have « = 5 ^ 1 ^ 3 , 333(1 + - ^p^ ) + 2 X 1.58 X 704] + 3,333 X 100 = 1,528,050 ft.-lb. per minute = 46.3 H. P., or assuming an efficiency of 60^^ for the engine, = 77 H. P. .60 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 5?^ 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 pV-\-P^ storage: P' = ^ ; in which V = volume of storage on locomotive; X = volume of stationary storage desired; p — cylinder pressure; P = stationary storage pressure; and P' = 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 = in which d = diameter of cylinder; D = diameter of driver; I = 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. 7 8 1 1 3 1 1 4 1 8 5 10 24 6,000 1,020 990 920 835 710 530 325 6 10 24 8,500 1,470 1,425 1,320 1,200 1,020 760 445 7 12 26 13,000 2,200 2,150 1,990 1,810 1,540 1,140 700 8 12 26 18,000 2,880 2,750 2,600 2,360 2,000 1,510 900 9 14 26 25,000 4,340 4,140 3,840 3,490 2,960 2,220 1,350 10 14 26 32,000 5,280 5,150 4,740 4,310 3,660 2,630 1,670 11 16 28 42,000 6,770 6,450 5,980 5,440 4,620 3,470 2,140 12 16 28 52,000 8,050 7,800 7,200 6,550 5,580 4,150 2,550 On account of certain losses due to radiation, etc. for cut-oif 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 exi)osed, 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^ 800 ft. 0.30^ 700 ft. 2.4^ 400 ft. 600 ft. 1.77^ 1,025 ft. 3.5^ 425 ft. \.zio 800 ft. 0.90^ 300 ft. 1.2?^ 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^ -\-lfo = 4.b Tatory 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 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 capacitjr 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 of Blake Crushers. Fig. 1. 1 Size of Re- ceiving Ca- pacity. Approximate Prod- uct per Hour, Cubic Yards, to 2 Inches. Weight of Heaviest Piece. Total Weight. Extreme Dimensions. Proper Speed. j Horsepower Required. Length. Breadth. Height. Inches. Lb. Lb. Ft. In. Ft. In. Ft. In. 3X U Laboratory 40 100 1 1 0 6 0 10 250 1 2 6X 2 One 560 1,200 2 10 2 1 2 3 250 4 10 X 4 Three 1,800 4,900 4 0 3 3 3 9 250 6 10 X 7 Five 3,800 8,000 5 1 3 9 4 5 250 8 15 X 9 Eight 7,400 15,500 6 6 5 0 5 11 250 15 15X10 Nine 7,800 16,000 6 6 5 5 5 11 250 15 20 X 6 Ten 5,300 11,200 5 3 2 11 4 6 250 15 20X 10 Ten 8,100 18,300 6 10 5 9 5 11 250 20 12X30 Sixteen 14,200 33,000 7 10 8 4 6 4 250 30 15X30 Twenty 14,200 35,000 7 10 8 4 6 4 250 30 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 large 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. Fig. 2. 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 Crushek. No. Size of Jaw Opening. Diameter of Pulleys. Width of Belt Used. Horsepower Required. No. Tons per Hour, Nut Size. Revolutions per Minute. Weight Complete. Inches. Inches. Inches. 1 4X 6 20 4 2 to 4 itol 275 1,200 2 7X 9 24 5 4 to 8 1 to 3 235 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. ~B is a sectional view of a Sturtevant roll-jaw crusher. The rolling motion of the jaw subjects the material to a rolling and squeezing action, instead of a direct squeeze. The product of this crusher is approximately sized and there is no greater producer of sized output. The adjustment of the machine for fine crushing neces- sarily contracts the space for dis- charge, and thereby lessens its capacity. When set wide, or for material from 1 to inches in size, the discharge is very free and the capacity is claimed to be greater than that of any other jaw and toggle machine. Gyratory Crushers. — These crush- ers, Fig. 4, are all large capacity, con- tinuous-action crushers, a is a ring or hopper against which the material is crushed by a conical head c, which fits on a shaft g, 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 receiving hopper h, and the machine is thus automatically fed. nOLLS. 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 betw'een 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 li" to 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, 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 of 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 (D - 1 ^ r- (D oo ]oo rir © © 1 Tgo: jo© m (D 0 ill Fig. 5. 422 ORE DRESSING AND PREPARATION OF COAL. teeth. In one test it was found that less fine coal was produced at 800 ft. per minute, but that the rolls blocked at this speed and hence had to be driven 1,000 ft. per minute. In one case a pair of main rolls 24 in. in diameter, 36 in. face, running at 1,000 ft. per min- ute, handled 2,500 tons of coal in 24 hours. A pair of 19" X 24" main rolls run at 1,000 ft. per minute handled 300 tons mine run in 10 hours. A well-known maker of rolls for crushing bitumi- nous coal gives a speed of 100 to 150 R. P. M., according to the output re- quired, for rolls 24 in. in diameter and 33 in. long. As a rule, cracking rolls are never run up to their full capacity, as is the case with crushing rolls. The /orm of the teeth varies greatly, but, as a rule, the larger rolls have straight pointed teeth of the spar- row-bill or some similar form. Fig. 6 a. The old curved, or hawk-billed, teeth. Fig. 6 b, have now gone almost wholly out of use. On small sized rolls, rectangular teeth with a height equal to one side of the square base are frequently em- ployed, and these may be cast in seg- 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. Indicated Horsepower. Granite, Ore. Limestone. Diameter of Hopper. Inches. Space Occupied by Breaker. Inches. JO q:^Suaq •amujj JO qipiAV •jaddoH dox oj auiujjj uio:^^og uiojj jqSian •iCaitnj SuiAiici JO suoijniOAOH Dimensions of Driving Pulley. Inches. Face. Diam. •8J0 JO 3[OOH JO oj Suipioooy ‘JguiH ‘ni SUTSSBJ ‘-qq; 000‘S JO suox ui ‘inoH JOd 2 to 4 4 to 8 6 to 12 10 to 20 15 to 30 25 to 40 30 to 60 50 to 125 100 to 150 weight Breaker. Pounds. 500 3,300 5,600 7,800 13.800 21.500 30.000 40.500 65.800 89.000 :inoqv ‘pouiq -raoo sSuTuado Sni -AioooH eojqx JO suoisuaraia Inches. xxxxxxxxxx jnoqv ‘Suiuodo SuT -Apo8H qo«a JO suoisuaraiQ Inches. xxxxxxxxxx •azis gOrH«Ot^QO 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 | 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 a b form a slight spiral about the body of the roll. The other Fig. 6. 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. These swing out by centrifugal force and strike blows upon the coal to be broken. When it is reduced sufficiently fine, it is discharged through bars 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 advent of the rolled- steel shells, it became possible to employ larger diameters and higher speeds. Rolls of the Cornish type vary from 4" 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 tlj^e 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 _ t — 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; tt = 3.14; = number of revo- lutions in the given time; I = length of rolls; w = space between rolls; and i = 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 27" rolls. T = 7.725 J7S. 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 Ipwest possible production of very fine material, rolls are the best form of MOLLS. 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. 20X12 E. P. Allis Co 26X 14 30X14 36X14 800 Cornish. E. P. Allis Co 20X12 1,885 4,000 for hard Narrow face, high speed. Colorado Ironworks 27X 14 36X16 40X16 600 rock. 4,800 for very hard rock. Cornish. Colorado Ironworks 36X6 ’ 42X6 54X8 2,100-2,800 Narrow face, high speed. Denver Engineering Works Co 16X10 to 42X16 350-100 3,500-4,500 Cornish. Gates Iron Works .... 9X4 26X15 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. 1 16 qOO e ®'= 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 diiference of from 1" to i" 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. 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 d. In order to prevent the accumulation CRUSHING MILLS. 427 Fig. 10. 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 of ball mills; (1) those in which the crushing is per- formed by balls traveling in a fixed path, and (2) those 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. STAMPS. Fig. 11. Gravity stamps are especially well suited for material the valuable portion of which does not have a tendency to slime. The fact that these stamps are very simple in construction, easy to transport and erect, as well as to operate, gives them a decided advantage over other forms of 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 h 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 i)yrites 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 venuers or bumping tables, and subsequently treated by chlorination or sm If the apron plates do not catch the major portion of the values, the “"ailings 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 7" 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 li to 2 cents per lb. 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 lb., weigh from 150 to 155 lb., and measure about 9 in. in diameter by 7i to 8 in. long. The neck is from 4i 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 lb. lighter than the above weights. The chrome steel dies weigh from 110 to 125 lb., and measure (where shoes of the above dimensions are used) 9 in. in diameter by 4 to 4i in. in height, with a rectangular foot-plate lOi in. by 91 in. by i in. thick. Iron shoes usually weigh from 20 to 25 lb. 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 hffight 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 11 in. or 1 in. in thickness, and weigh about 25 or 40 lb. Old dies usually wear down to about 11 in. in thickness, and weigh from 20 to 50 lb. 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 11 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 11 to 3 lb. 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 lb. 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 li miner’s inches per battery should be provided. In 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 4i 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 13i 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 X wgt. of each stamp X No. of drops per min. X drop of each in in. 12X33,000 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 Sl.OO per ton up. The Montana Co., Limited, operating a 60-stamp combination mill, in 1888 treated 40,530 tons of ore at S1.13 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 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 bn 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 mTTI piston, thus urging it down with greater force than its own j weight would. These steam stamps can be run at a much higher speed than gravity stamps, and hence have a greater |tT|4 capacity. In the figure shown, three screens are employed, one in front and one at each end of the mortar. There" are j 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 Fig. 14. classed under one of the previous heads, but there are some 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. 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 ^ace 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. 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 ttie 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 1| 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 f in. to | in. In the Pittsburg region of Pennsylvania, all coal passing through screen is called slack, while, on the Monongahela River, coal passing through ip' screen is called slack and. is used in stokers. iMany 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 li" screen; nut, all coal passing through ip' openings and over openings; slack, all coal passing through screen. If a pea-coal screen is used, all coal passing over I", i", and f" would be pea coal, and that passing through or f" would be slack. Adjustable Rars.— 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- 5'ijj wards and the bars do not therefore require nearly the same i inclination as fixed bars. — N 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 i in. to 2 in. per foot, the average being about f 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. Fig. 16. 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 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 according 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 ^ven 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^" 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 A; Iron Co. Kind of Coal. Round. Round. Square. Steamboat 5|" 5" Steamboat. Lump 4V' 4i// 4" Large broken. Broken 3i" zl" 2r' Small broken. Egg 2tV' 2" Egg. Stove 1|" IF' If" Stove. Chestnut 16// V' 7// T r Chestnut. Pea tV' j.// Pea. Buckwheat H" tb" i// Buckwheat. Rice tV^ tV' 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 w^hich 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. Pentagonal 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 PREPARATION 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 11 sq. ft. per 10 hours. Chestnut coal, 1 ton per li sq. ft. per 10 hours. Pea coal, 1 ton per 2 sq. ft. per 10 hours. Buckwheat coal, 1 ton per 21 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 1" mesh, and through mesh. Buckwheat passes over 1" mesh, and through i" mesh. Pea passes over i" mesh, and through 1" mesh. Chestnut passes over 1" mesh, and through If" mesh. Stove passes over If" mesh, and through 2" mesh. Egg passes over 2" mesh, and through 21" mesh. * Grate passes over 21" 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 aiul “lump” size are seldom made, and there is no uniformity whatever in the sizes called by these names. HYDRAULIC 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 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 a pipe a and discharges against the discharge 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 pass out through the spigot. A shield c reflects upward currents and confines the agitation to the bottom. The pulp flowing in the direction of the arrows is deflected downwards by the 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 through directly spigot d, 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 mast 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 (7, 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. someter H back into the washer. (As mentioned elsewhere, it is poor practice to use this w^ater 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 clear, 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 hie. With coal passing over f" perforations, the results were a reduction of 48;i in ash, 15^ in sulphur, and a gain of hio 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 ivas 35.1 gallons and the cost was 2.25 cents per ton for washing 400 tons, itemized as follows: Labor at washer, S2.00; labor at boiler, fuel, etc., ^.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 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 li 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 600 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 coal is fed with water at the upper end of the trough, and by the action of the fiowing 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 fiuid 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 dov/n 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 gr, 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 and the barren portion or gangue will 438 ORE DRESSING AND PREPARATION OF COAL, be carried over the discharge. Formerly, the concentrates were discharged from 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, 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 6, 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 h, 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. 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 ofisuction. 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 1 / 1){8 — 1) , for roundish grains; V = 2.14^/ 1){8 — 1) , for average grains; V — 2.37 1 / D(6 — 1), for long grains; V = 1.92 1 / D{8 — 1), for flat grains, in which V — velocity in m-eters per second; i) = diameter of particles in meters, and 5 = 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. % Velocity in Inches per Second. OJ 02 5 o 1 2 3 4 5 6 7 8 9 *s o ft m Author’s Multipliers. g| Anthracite 1.473 .500 .352 .225 .213 .288 Epidote 3.380 1.57 1.35 1.05 1.13 1.50 1.61 1.56 1.56 1.47 1.45 Sphalerite 4.046 1.46 1.05 1.17 1.62 1.64 1.68 1.66 1.56 1.85 Pyrrhotite 4.508 1.73 1.29 1.48 2.00 2.22 2.26 2.13 2.08 2.14 Chal cocite 5.334 1.90 1.47 1.62 2.07 2.28 2.41 2.44 2.17 2.64 Arsenopyrite ... 5.627 1.90 1.57 1.89 2.42 2.56 2.72 2.84 2.94 2.82 Cassiterite 6.261 2.11 1.79 2.00 2.73 2.93 3.03 3.05 3.12 3.32 Anitmony 6.706 2.71 2.00 2.00 2.73 2.93 3.03 2.98 3.00 3.48 Wolframite 6.937 2.71 1.83 2.07 2.86 3.04 3.21 3.28 3.26 3.64 Galena 7.856 2.71 1.83 2.26 3.00 3.42 3.65 3.76 3.75 4.01 Copper Quartz 8.479 2.640 2.71 2.00 2.36 3.00 3.20 3.58 3.76 3.75 4.56 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 OBE DBESSINO AND PBEPARATION OP 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 than for the quartz, and it will therefore be much less impeded in its fall than the quartz; hence, the I)articles of galena found adjacent to the particles of quartz will be Fig. 23. 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 xV 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 thinkness 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 same 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 inmcated 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 fiattened, 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 Collom 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 sieve 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: firsts 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 jig, 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 20^ 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 lie 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 fiour pyrites fioats 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- piined 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. 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. 44 : 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, in. per ft.; for stove or chestnut coal, 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 22i° from the hori- zontal. If chutes for hard coal are lined with glass, the angle can be reduced from SO47 9.98075 4 4 30 2.0 1.5 57 9.46469 41 9.48398 45 0.51602 9.98071 4 3 40 2.7 2.0 58 9.46511 42 9.48443 45 0.51557 9.98067 4 2 50 3.3 2.5 59 9.46552 41 42 9.48489 46 45 0.51511 9.98063 4 3 1 60 9.46594 9.48534 0.51466 9.98060 0 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. / P. P. 73 ' LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 170 509 / L. Sin. 0 9.46594 1 9.46635 2 9.46676 3 9.46717 4 9.46758 5 9.46800 6 9.46841 7 9.46882 8 9.46923 9 9.46964 10 9.47005 11 9.47045 12 9.47086 13 9.47127 14 9.47168 15 9.47209 16 9.47249 17 9.47290 18 9.47330 19 9.47371 20 9.47411 21 9.47452 22 9.47492 23 9.47533 24 9.47573 25 9.47613 26 9.47654 27 9.47694 28 9.47734 29 9.47774 30 9.47814 31 9.47854 32 9.47894 33 9.47934 34 9.47974 35 9.48014 36 9.48054 37 9.48094 38 9.48133 39 9.48173 40 9.48213 41 9.48252 42 9.48292 43 9.48332 44 9.48371 45 9.48411 46 9.48450 47 9.48490 48 9.48529 49 9.48568 50 9.48607 51 9.48647 52 9.48686 53 9.48725 54 9.48764 55 9.48803 56 9.48842 57 9.48881 58 9.48920 59 9.48959 60 9.48998 L. Cos. L.Tang. 9.48534 9.48579 9.48624 9.48669 9.48714 9.48759 9.48804 9.48849 9.48894 9.48939 9.48984 9.49029 9.49073 9.49118 9.49163 9.49207 9.49252 9.49296 9.49341 9.49385 9.49430 9.49474 9.49519 9.49563 9.49607 9.49652 9.49696 9.49740 9.49784 9.49828 9.49872 9.49916 9.49960 9.50004 9.50048 9.50092- 9.50136 9.50180 9.50223 9.50267 9.50311 9.50355 9.50398 9.50442 9.50485 9.50529 9.50572 9.50616 9.50659 9.50703 9.50746 9.50789 9.50833 9.50876 9.50919 9.50962 9.51005 9.51048 9.51092 9.51135 9.51178 Cotg; d. c. L. Cotg. L. Cos. P. P. 45 45 45 45 45 45 45 45 45 45 45 44 45 45 44 45 44 45 44 45 44 45 44 44 45 44 44 44 44 44 44 44 44 44 44 44 44 43 44 44 44 43 44 43 44 43 44 43 44 43 43 44 43 43 43 43 43 44 43 43 d. c. 0.51466 0.51421 0.51376 0.51331 0.51286 0.51241 0.51196 0.51151 0.51106 0.51061 9.98060 9.98056 9.98052 9.98048 9.98044 9.98040 9.98036 9.98032 9.98029 9.98025 0.51016 0.50971 0.50927 0.50882 0.50837 9.98021 9.98017 9.98013 9.98009 9.98005 0.50793 0.50748 0.50704 0.50659 0.50615 9.98001 9.97997 9.97993 9.97989 9.97986 0.50570 0.50526 0.50481 0.50437 0.50393 9.97982 9.97978 9.97974 9.97970 9.97966 0.50348 0.50304 0.50260 0.50216 0.50172 9.97962 9.97958 9.97954 9.97950 9.97946 0.50128 0.50084 0.50040 0.49996 0.49952 9.97942 9.97938 9.97934 9.97930 9.97926 0.49908 0.49864 0.49820 0.49777 0.49733 9.97922 9.97918 9.97914 9.97910 9.97906 0.49689 0.49645 0.49602 0.49558 0.49515 9.97902 9.97898 9.97894 9.97890 9.97886 0.49471 0.49428 0.49384 0.49341 0.49297 9.97882 9.97878 9.97874 9.97870 9.97866 0.49254 0.49211 0.49167 0.49124 0.49081 9.97861 9.97857 9.97853 9.97849 9.97845 0.49038 0.48995 0.48952 0.48908 0.48865 9.97841 9.97837 9.97833 9.97829 9.97825 0. 48822 L.Tang. L. Sin. 45 4.5 5.3 6.0 6.8 7.5 15.0 22.5 30.0 37.5 4.4 5.1 5.9 6.6 7.3 14.7 22.0 29.3 36.7 43 4.3 5.0 5.7 6.5 7.2 14.3 21.5 28.7 35.8 42 4.2 4.9 5.6 6.3 7.0 14.0 21.0 28.0 35.0 40 4.0 4.7 5.3 6.0 6.7 13.3 20.0 26.7 83.3 41 4.1 4.8 5.5 6.2 6.8 13.7 20.5. 27.3 34.2 39 3.9 4.6 5.2 5.9 6.5 13.0 19.5 26.0 32.5 11 5 4 3 10 6 0.5 0.4 0.3 9 7 0.6 0.5 0.4 8 8 0.7 0.5 0.4 7 9 0.8 0.6 0.5 6 10 0.8 0.7 0.5 5 20 1.7 1.3 1.0 4 30 2.5 2.0 1.5 3 40 3.3 2.7 2.0 2 50 4.2 3.3 2.5 1 0 ' P. P. 7r 510 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 18 ° / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. 0 9.48998 9.51178 0.48822 9.97821 1 9.49037 39 9.51221 43 0.48779 9.97817 2 9.49076 39 9.51264 43 0.48736 9.97812 3 9.49115 39 9.51306 42 0.48694 9.97808 4 9.49153 38 39 9.51349 43 43 0.48651 9.97804 5 9.49192 9.51392 0.48608 9.97800 6 9.49231 39 9.51435 43 0.48565 9.97796 7 9.49269 38 9.51478 43 0.48522 9.97792 8 9.49308 39 9.51520 42 0.48480 9.97788 9 9.49347 39 38 9.51563 43 43 0.48437 9.97784 10 9.49385 9.51606 0.48394 9.97779 11 9.49424 39 9.51648 42 0.48352 9.97775 12 9.49462 38 9.51691 43 0.48309 9.97771 13 9.49500 38 9.51734 43 0.48266 9.97767 14 9.49539 39 38 9.51776 42 43 0.48224 9.97763 15 9.49577 9.51819 0.48181 9.97759 16 9.49615 38 9.51861 42 0.48139 9.97754 17 9.49654 39 9.51903 42 0.48097 9.97750 18 9.49692 38 9.51946 43 0.48054 9.97746 19 9.49730 38 38 9.51988 42 43 0.48012 9.97742 20 9.49768 9.52031 0.47969 9.97738 21 9.49806 38 9.52073 42 0.47927 9.97734 22 9.49844 38 9.52115 42 0.47885 9.97729 23 9.49882 38 9.52157 42 0.47843 9.97725 24 9.49920 38 38 9.52200 43 42 0.47800 9.97721 25 9.49958 9.52242 0.47758 9.97717 26 9.49996 38 9.52284 42 0.47716 9.97713 27 9.50034 38 9.52326 42 0.47674 9.97708 28 9.50072 38 9.52368 42 0.47632 9.97704 29 9.50110 38 38 9.52410 42 42 0.47590 9.97700 30 9.50148 9.52452 0.47548 9.97696 31 9.50185 37 9.52494 42 0.47506 9.97691 32 9.50223 38 9.52536 42 0.47464 9.97687 33 9.50261 38 9.52578 42 0.47422 9.97683 34 9.50298 37 38 9.52620 42 41 0.47380 9.97679 35 9.50336 9.52661 0.47339 9.97674 36 9.50374 38 9.52703 42 0.47297 9.97670 37 9.50411 37 9.52745 42 0.47255 9.97666 38 9.50449 38 9.52787 42 0.47213 9.97662 39 9.50486 37 37 9.52829 42 41 0.47171 9.97657 40 9.50523 9.52870 0.47130 9.97653 41 9.50561 38 9.52912 42 0.47088 9.97649 42 9.50598 37 9.52953 41 0.47047 9.97645 43 9.50635 37 9.52995 42 0.47005 9.97640 44 9.50673 38 37 9.53037 42 41 0.46963 9.97636 45 9.50710 9.53078 0.46922 9.97632 46 9.50747 37 9.53120 42 0.46880 9.97628 47 9.50784 37 9.53161 41 0.46839 9.97623 48 9.50821 37 9.53202 41 0.46798 9.97619 49 9.50858 37 38 9.53244 42 41 0.46756 9.97615 50 9.50896 9.53285 0.46715 9.97610 51 9.50933 37 9.53327 42 0.46673 9.97606 52 9.50970 37 9.53368 41 0.46632 9.97602 53 9.51007 37 9.53409 41 0.46591 9.97597 54 9.51043 36 37 9.53450 41 42 0.46550 9.97593 55 9.51080 9.53492 0.46508 9.97589 56 9.51117 37 9.53533 41 0.46467 9.97584 57 9.51154 37 9.53574 41 0.46426 9.97580 58 9.51191 37 9.53615 41 0.46385 9.97576 59 9.51227 36 37 9.53656 41 41 0.46344 9.97571 60 9.51264 9.53697 0.46303 9.97567 Cos. d. L. Cotg. d. e. 'L.Tang. L. Sin. P. P. 43 4.3 5.0 5.7 6.5 7.2 14.3 21.5 28.7 35.8 42 4.2 4.9 5.6 6.3 7.0 14.0 21.0 28.0 35.0 4f 4.1 4.8 5.5 6.2 6.8 13.7 20.5 27.3 34.2 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 5 6 0.5 7 0.6 8 0.7 9 0.8 10 0.8 20 I 1.7 30 I 2.5 40 i 3.3 50 I 4.2 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 P. P. 71 ° LOGARITUm OF TRIGONOMETRIC FUNCTIONS. 511 19 ° / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P .P, 0 9.51264 9.53697 0.46303 9.97567 60 1 9.51301 37 9.53738 41 0.46262 9.97563 4 59 2 9.51338 37 9.53779 41 0.46221 9.97558 5 58 3 9.51374 36 9.53820 41 0.46180 9.97554 4 57 41 40 4 9.51411 37 36 9.53861 41 41 0.46139 9.97550 4 56 6 7 4.1 4.8 4.0 4.7 5 9.51447 9.53902 0.46098 9.97545 D 55 8 5!5 6 9.51484 37 9.53943 41 0.46057 9.97541 4 54 9 6.2 6.0 7 9.51520 36 9.53984 41 0.46016 9.97536 5 53 10 6.8 6.7 8 9.51557 37 9.54025 41 0.45975 9.97532 4 52 20 13.7 13.3 9 9.51593 36 36 9.54065 40 41 0.45935 9.97528 4 51 30 20.5 20.0 10 9.51629 9.54106 0.45894 9.97523 O 50 40 27.3 26.7 11 9.51666 37 9.54147 41 0.45853 9.97519 4 49 50 34.2 33.3 12 9.51702 36 9.54187 40 0.45813 9.97515 4 48 13 9.51738 36 9.54228 41 0.45772 9 97510 5 47 14 9.51774 36 37 9.54269 41 40 0.45731 9.97506 4 46 39 15 9.51811 9.54309 0.45691 9.97501 0 45 6 3.9 16 9.51847 36 9.54350 41 0.45650 9.97497 4 44 7 4.6 17 9.51883 36 9.54390 40 0.45610 9.97492 5 43 8 6.2 18 9.51919 36 9.54431 41 0.45569 9.97488 4 42 9 5.9 19 9.51955 36 36 9.54471 40 41 0.45529 9.97484 4 41 10 6.5 20 9.51991 9.54512 0.45488 9.97479 D 40 20 13.0 21 9.52027 36 9.54552 40 0.45448 9.97475 4 39 30 19.5 22 9.52063 36 9.54593 41 0.45407 9.97470 5 38 40 26.0 23 9.52099 36 9.54633 40 0.45367 9.97466 4 37 60 32.5 24 9.52135 36 36 9.54673 40 41 0.45327 9.97461 5 A 36 25 9.52171 9.54714 0.45286 9.97457 35 26 9.52207 36 9.54754 40 0.45246 9.97453 4 84 37 36 27 9.52242 35 9.54794 40 0.45206 9.97448 5 33 6 3.7 3.6 28 9.52278 36 9.54835 41 0.45165 9.97444 4 32 7 4.3 4.2 29 9.52314 36 9.54875 40 0.45125 9.97439 5 31 8 4.9 4.8 36 40 A 5.4 A A 9.52350 9.54915 0.45085 9.97435 30 y 1 A u.o A 0 31 9.52385 35 9.54955 40 0.45045 9.97430 5 29 lU 9A o.z 19 ^ O.U 19 A 32 9.52421 36 9.54995 40 0.45005 9.97426 4 28 QA i-Z.O 1 ft jLZ.U 1 ft A 33 9.52456 35 9.55035 40 0.44965 9.97421 5 27 oU A(\ ±0.0 24 7 lo.U OA A 34 9.52492 36 35 9.55075 40 40 0.44925 9.97417 4 5 26 4:U 60 3o!8 30.0 35 9.52527 9.55115 0.44885 9.97412 25 36 9.52563 36 9.55155 40 0.44845 9.97408 4 24 37 9.52598 35 9.55195 40 0.44805 9.97403 5 23 38 9.52634 36 9 55235 40 0.44765 9.97399 4 22 69 34 39 9.52669 35 36 9.55275 40 0.44725 9.97394 5 4 21 6 7 3.5 4.1 3.4 4.0 40 9.52705 9.55315 0.44685 9.97390 20 8 4!7 4!5 41 9.52740 35 9.55355 40 0.44645 9.97385 5 19 9 5.3 5.1 42 9.52775 35 9.55395 40 0.44605 9.97381 4 18 10 5.8 5.7 43 9.52811 36 9.55434 39 0.44566 9.97376 5 17 20 11 7 11.3 44 9.52846 35 35 9.55474 40 40 0.44526 9.97372 4 5 16 30 17.5 17.0 45 9.52881 9.55514 0.44486 9.97367 15 40 23.3 22.7 46 9.52916 35 9.55554 40 0.44446 9.97363 4 14 50 29.2 28.3 47 9.52951 35 9.55593 39 0.44407 9.97358 5 13 48 9.52986 35 9.55633 40 0.44367 9.97353 5 12 49 9.53021 35 35 9.55673 40 0.44327 9.97349 4 5 11 5 4 50 9.53056 9.55712 0.44288 9.97344 SO 6 0.5 0.4 51 9.53092 36 9.55752 40 0.44248 9.97340 4 9 7 0.6 0.5 52 9.53126 34 9.55791 39 0.44209 9.97335 5 8 8 0.7 0.5 53 9.53161 35 9.55831 40 0.44169 9.97331 4 7 9 0.8 0.6 54 9.53196 35 35 9.55870 39 40 0.44130 9.97326 5 4 6 10 0.8 0.7 55 9.53231 9.55910 0.44090 9.97322 5 20 1.7 1.3 56 9.53266 35 9.55949 39 0.44051 9.97317 5 4 30 2.5 2.0 57 9.53301 35 9.55989 40 0.44011 9.97312 5 3 40 3.3 2.7 58 9.53336 35 9.56028 39 0.43972 9.97308 4 2 50 4.2 3.3 59 9.53370 34 35 9.56067 39 40 0.43933 9.97303 5 4 1 60 9.53405 9.56107 0.43893 9.97299 0 L. Cos. ~d.' L. Cotg. d. c. L.Tang. L. Sin. d. ' P. P. 70 ^ 512 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 200 / L. Sin. 0 9.53405 1 9.53440 2 9.53475 3 9.53509 4 9.63544 5 9.53578 6 9.53613 7 9.53647 8 9.53682 9 9.53716 10 9.53751 11 9.53785 12 9.53819 13 9.53854 14 9.53888 15 9.53922 16 9.53957 17 9.53991 18 9.54025 19 9.54059 20 9.54093 21 9.54127 22 9.54161 23 9.54195 24 9.54229 25 9.54263 26 9.54297 27 9.54331 28 9.54365 29 9.54399 30 9.54433 31 9.54466 32 9.54500 33 9.54534 34 9.54567 35 9.54601 36 9.54635 37 9.54668 38 9.54702 39 9.54735 40 9.54769 41 9.54802 42 9.54836 43 9.54869 44 9.54903 45 9.54936 46 9.54969 47 9.55003 48 9.55036 49 9.55069 50 9.55102 51 9.55136 52 9.55169 53 9.55202 54 9.55235 55 9.55268 56 9.55301 57 9.55334 58 9.55367 59 9.55100 60 9.55433 L. Cos. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 9.56107 0.43893 9.97299 60 9.56146 39 0.43854 9.97294 5 59 9.56185 39 0.43815 9.97289 5 58 9.56224 39 0.43776 9.97285 4 57 4U 39 9.56264 40 0.43736 9.97280 5 A 56 6 7 4.0 4.7 3.9 4.6 9.56303 0.43697 9.97276 55 8 5^3 5.2 9.56342 39 0.43658 9.97271 5 54 9 6.0 5.9 9.56381 39 0.43619 9.97266 5 53 To 6.7 6.5 9.56420 39 0.43580 9.97262 4 52 ‘JO 13.3 13.0 9.56459 39 39 0.43541 9.97257 5 51 30 20.0 19.5 9.56498 0.43502 "9.97252 o 50 40 26.7 26.0 9.56537 39 0.43463 9.97248 4 49 50 33.3 32.5 9.56576 39 0.43424 9.97243 6 48 9.56615 39 0.43385 9.97238 5 47 9.56654 39 39 0.43346 9.97234 4 PL 46 38 37 9.56693 0.43307 9.97229 O 45 6 3.8 3.7 9.56732 39 0.43268 9.97224 5 44 7 4.4 4.3 9.56771 39 0.43229 9.97220 4 43 8 5.1 4.9 9.56810 39 0.43190 9.97215 5 42 9 5.7 5.6 9.56849 39 0.43151 9.97210 5 A 41 10 6.3 6.2 9.5^887 0.43113 9.97206 '± 40 20 12.7 12.3 9.56926 39 0.43074 9.97201 5 39 30 19.0 18.5 9.56965 39 0.43035 9.97196 5 38 40 25.3 24.7 9.57004 39 0.42996 9.97192 4 37 50 31.7 30.8 9.57042 38 39 0.42958 9.97187 6 36 9.57081 0.42919 9.97182 o 35 9.57120 39 0.42880 9.97178 4 34 35 9.57158 38 0.42842 9.97173 5 33 6 3.5 9.57197 39 0.42803 9.97168 5 32 7 4.1 9.57235 38 39 0.42765 9.97163 5 A 31 8 4.7 9.57274 0.42726 9.97159 30 y in 5.3 K Q 9.57312 38 0.42688 9.97154 5 29 lU on O.o 117 9.57351 39 0.42649 9.97149 5 28 on 11. / 17 9.57389 38 0.42611 9.97145 4 27 ou An 1/ .D OQ Q 9.57428 39 QQ 0.42572 9.97140 5 r; 26 Zo.o 90 9 9.57466 OO 0.42534 9.97135 0 25 9.57504 38 0.42496 9.97130 6 24 9.57543 39 0.42457 9.97126 4 23 9.57581 38 0.42419 9.9712] 5 22 34 33 9.57619 38 0.42381 9.97116 5 5 21 6 7 3.4 4.0 3.3 3.9 9.57658 oy 0.42342 9.97111 20 8 4!5 4^4 9.57696 38 0.42304 9.97107 4 19 9 5.1 5.0 9.57734 38 0.42266 9.97102 6 18 10 5.7 5.5 9.57772 38- 0.42228 9.97097 5 17 20 11.3 11.0 9.57810 38 QQ 0.42190 9.97092 5 5 16 30 17.0 16.5 9.57849 Oif 0.42151 9.97087 15 40 22.7 22.0 9.57887 38 0.42113 9.97083 4 14 60 28.3 27.5 9.57925 38 0.42075 9.97078 5 13 9.57963 38 0.42037 9.97073 5 12 9.58001 38 0.41999 9.97068 5 5 11 1 4 9.58039 OO 0.41961 9.97063 10 6 0.5 0.4 9.58077 38 0.41923 9.97059 4 9 7 0.6 0.5 9.58115 38 0.41885 9.97054 5 8 8 0.7 0.5 9.58153 38 0.41847 9.97049 6 7 9 0.8 0.6 9.58191 38 0.41809 9.97044 6 5 6 10 0.8 0.7 9.58229 OO 0.41771' 9.97039- 5 20 1.7 1.3 9.58267 38 0.41733 9.97035 4 4 30 2.5 2.0 9.58304 37 0.41696 9.97030 5 3 40 3.3 2.7 9.58342 38 0.41658 9.97025 5 2 50 4.2 3.3 9.58380 38 38 0.41620 9.97020 5 5 1 9.58418 0.41582 9.97015 0 L. Cotg. L.Tang. I.. Sin. “dr ' P, . P. d. d. ^ 9 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 21 ° 518 / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. 0 9.55433 9.58418 0.41582 9.97015 60 1 9.55466 33 9.58455 37 0.41545 9.97010 5 59 2 9.55499 33 9.58493 38 0.41507 9.97005 5 58 3 9.55532 33 9.58531 38 0.41469 9.97001 4 57 4 9.55564 32 9.58569 38 37 0.41431 9.96996 5 5 56 5 9.55597 9.58606 0.41394 9.96991 55 6 9.55630 33 9.58644 38 0.41356 9.96986 5 54 7 9.55663 33 9.58681 37 0.41319 9.96981 5 53 8 9.15695 32 9.58719 o8 0.41281 9.96976 5 52 9 9.55728 33 33 9.58757 38 37 0.41243 9.96971 5 5 51 10 9.55761 9.58794 0.41206 9.96966 50 11 9.55793 32 9.58832 38 0.41168 9.96962 4 49 12 9.55826 33 9.58869 37 0.41131 9.96957 5 48 13 9.55858 32 9.58907 38 0.41093 9.96952 5 47 14 9.55891 33 9.58944 37 37 0.41056 9.96947 5 5 46 15 9.55923 9.58981 0.41019 9.96942 45 16 9.55956 33 9.59019 38 0.40981 9.96937 5 44 17 9.55988 32 9.59056 37 0.40944 9.96932 5 43 18 9.56021 33 9.59094 38 0.40906 9.96927 5 42 19 9.56053 32 32 9.59131 37 37 0.40869 9.96922 5 5 41 20 9.56085 9.59168 0.40832 9.96917 40 21 9.56118 33 9.59205 37 0.40795 9.96912 5 39 22 9.56150 32 9.59243 38 0.40757 9.96907 5 38 23 9.56182 32 9.59280 37 0.40720 9.96903 4 37 24 9.56215 33 32 9.59317 37 37 0.40683 9.96898 5 5 36 25 9.56247 9.59354 0.40646 9.96893 35 26 9.56279 32 9.59391 37 0.40609 9.96888 5 34 27 9.56311 32 9.59429 38 0.40571 9.96883 5 33 28 9.56343 32 9.59466 37 0.40534 9.96878 5 32 29 9.56375 32 9.59503 37 37 0.40497 9.96873 5 5 31 30 9.56408 oo 9.59540 0.40460 9.96868 30 31 9.56440 32 9.59577 37 0.40423 9.96863 5 29 32 9.56472 32 9.59614 37 0.40386 9.96858 5 28 33 9.56504 32 9.59651 37 0.40349 9.96853 5 27 34 9.56536 32 Q9 9.59688 37 37 0.40312 9.96848 5 5 26 35 9.56568 Oii 9.59725 0.40275 9.96843 25 36 9.56599 31 9.59762 37 0.40238 9.96838 5 24 37 9.56631 32 9.59799 37 0.40201 9.96833 5 23 38 9.56663 32 9.59835 36 0.40165 9.96828 5 22 39 9.56695 32 32 9.59872 37 37 0.40128 9.96823 5 5 21 40 9.56727 9.59909 0.40091 9.96818 20 41 9.56759 32 9.59946 37 0.40054 9.96813 5 19 42 9.56790 31 9.59983 37 0.40017 9.96808 5 18 43 9.56822 32 9.60019 36 0.39981 9.96803 5 17 44 9.56854 32 32 9.60056 37 37 0.39944 9.96798 5 5 16 45 9.56886 9.60093 0.39907 9.96793 15 46 9.56917 31 9.60130 37 0.39870 9.96788 5 14 47 9.56949 32 9.60166 36 0.39834 9.96783 5 13 48 9.56980 31 9.60203 37 0.39797 9.96778 5 12 49 9.57012 32 32 9.60240 37 36 0.39760 9.96772 6 5 11 50 9.57044 9.60276 0.39724 9.96767 10 51 9.57075 31 9.60313 37 0.39687 9.96762 5 9 52 9.57107 32 9.60349 36 0.39651 9.96757 5 8 53 9.57138 31 9.60386 37 0.39614 9.96752 5 7 54 9.57169 31 32 9.60422 36 37 0.39578 9.96747 5- 5 6 55 9.57201 9.60459 0.39541 9.96742 5 56 9.57232 31 9.60495 36 0.39505 9.96737 5 4 57 9.57264 32 9.60532 37 0.39468 9.96732 5 3 58 9.57295 31 9.60568 36 0.39432 9.96727 5 2 59 9.57326 31 32 9.60605 37 36 0.39395 9.96722 5 5 1 80 9.57358 9.60641 0.39359 9.96717 0 L. Cos, d. L. Cotg. d. c. L.Tang. L. Sin. d. / P. P. 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 37 3.7 4.3 4.9 5.6 6.2 12.3 18.5 24.7 30.8 33 3.3 3.9 4.4 5.0 5.5 11.0 16.5 22.0 27.5 32 3.2 3.7 4.3 4.8 5.3 10.7 16.0 21.3 26.7 31 3.1 3.6 4.1 4.7 5.2 10.3 15.5 20.7 25.8 0.4 0.5 0.5 0.6 0.7 1.3 2.0 2.7 3.3 P. P. 68 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 22 ° 5U / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. 0 9.57358 9.60641 0.39359 9.96717 60 1 9.57389 31 9.60677 36 0.39323 9.96711 6 59 2 9.57420 31 9.60714 3 / 0.39286 9.96706 5 58 3 9.57451 31 9.60750 36 0.39250 9.96701 5 57 4 9.57482 31 32 9.60786 36 37 0.39214 9.96696 5 56 5 9.57514 9.60823 0.39177 9.96691 0 '55 6 9.57545 31 9.60859 36 0.39141 9.96686 5 54 7 ■9.57576 31 9.60895 36 0.39105 9.96681 5 53 8 9.57607 31 9.60931 36 0.39069 9.96676 5 52 9 9.57638 31 31 9.60967 36 37 0.39033 9.96670 6 51 10 9.57669 9.61004 0.38996 9.96665 0 50 11 9.57700 31 9.61040 36 0.38960 9.96660 5 49 12 9.57731 31 9.61076 36 0.38924 9.96655 5 48 13 9.57762 31 9.61112 36 0.38888 9.96650 5 47 14 9.57793 31 31 9.61148 36 36 0.38852 9.96645 5 c 46 15 9.57824 9.61184 0.38816 9.96640 0 45 16 9.57855 31 9.61220 36 0.38780 9.96634 6 44 17 9.57885 30 9.61256 36 0.38744 9.96629 5 43 18 9.57916 31 9.61292 36 0.38708 9.96624 5 42 19 9.57947 31 9.61328 36 36 0.38672 9.96619 5 c 41 20 9.57978 9.61364 0.38636 9.96614 0 40 21 9.58008 30 9.61400 36 0.38600 9.96608 6 39 22 9.58039 31 9.61436 36 0.38564 9.96603 5 38 23 9.58070 31 9.61472 36 0.38528 9.96598 5 37 24 9.58101 31 30 9.61508 36 36 0.38492 9.96593 5 36 25 9.58131 9.61544 0.38456 9.96588 5 35 26 9.58162 31 9.61579 35 0.38421 9.96582 6 34 27 9.58192 30 9.61615 36 0.38385 9.96577 5 33 28 9.58223 31 9.61651 36 0.38349 9.96572 5 32 29 9.58253 30 31 9.61687 36 35 0.38313 9.96567 5 31 30 9.58284 9.61722 0.38278 9.96562 0 30 31 9.58314 30 9.61758 36 0.38242 9.96556 6 29 32 9.58345 31 9.61794 36 0.38206 9.96551 5 28 33 9.58375 30 9.61830 36 0.38170 9.96546 5 27 34 9.58406 31 30 9.61865 35 36 0.38135 9.96541 5 a 26 35 9.58436 9.61901 0.38099 9.96535 0 2.5 36 9.58467 31 9.61936 35 0.38064 9.96530 5 24 37 9.58497 30 9.61972 36 0.38028 9.96525 5 23 38 9.58527 30 9.62008 36 0.37992 9.96520 5 22 39 9.58557 30 31 9.62043 35 36 0.37957 9.96514 6 c 21 40 9.58588 9.62079 0.37921 9.96509 o 20 41 9.58618 30 9.62114 35 0.37886 9.96504 5 19 42 9.58648 30 9.62150 36 0.37850 9.96498 6 18 43 9.58678 30 9.62185 35 0.37815 9.96493 5 17 44 9.58709 31 30 9.62221 36 35 0.37779 9.96488 5 K 16 45 9.58739 9.62256 0.37744 9.96483 0 15 46 9.58769 30 9.62292 36 0.37708 9.96477 6 14 47 9.58799 30 9.62327 35 0.37673 9.96472 5 13 48 9.58829 30 9.62362 35 0.37638 9.96467 5 12 49 9.58859 30 30 9.62398 36 35 0.37602 9.96161 6 5 11 50 9.58889 9.62433 0.37567 9.96456 10 51 9.58919 30 9.62468 35 0.37532 9.96451 5 9 52 9.58949 30 9.62504 36 0.37496 9.96445 6 8 53 9.58979 30 9.62539 3o 0.37461 9.96440 5 7 54 9.59009 30 30 9.62574 35 35 0.37426 9.96435 5 6 55 9.59039 9.62609 0.37391 9.9(>429 5 56 9.59069 30 9.62645 36 0.37355 9.96424 5 4 57 9.59098 29 9.62680 35 0.37320 9.96419 5 3 58 9.59128 30 9.62715 35 0.37285 9.96413 6 2 59 9.59158 30 30 9.62750 35 35 0.372^50 9.96408 5 5 1 60 9.59188 9.62785 0.37215 9.96403 0 L. Cos. 1 d. L. Cotg. d. c. L.Tang. L. Sin. d. / 67 ° P. P. 37 36 6 3.7 3.6 7 4.3 4.2 8 4.9 4.8 9 5.6 5.4 10 6.2 6.0 20 12.3 12.0 30 18.5 18.0 40 24.7 24.0 50 30.8 30.0 35 6 3.5 7 4.1 8 4.7 9 5.3 10 5.8 20 11.7 30 17.5 40 23.3 50 29.2 32 31 6 3.2 3.1 7 3.7 3.6 8 4.3 4.1 9 4.8 4.7 10 5.3 5.2 20 10.7 10.3 30 16.0 15.5 40 21.3 20.7 50 26.7 25.8 30 29 6 3.0 2.9 7 3.5 3.4 8 4.0 3.9 9 4.5 4.4 10 5.0 4.8 20 10.0 9.7 30 15.0 14.5 40 20.0 19.3 50 25.0 24.2 6 5 6 ' 0.6 0.5 7 I 0.7 0.6 8 0.8 0.7 9 0.9 0.8 10 1.0 0.8 20 2.0 1.7 30 3.0 2.5 40 I 4.0 3.3 50 I 5.0 4.2 P. P. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 23 ^ 515 / L. Sin.'. d. L.Tang. d. c. L. Cotg. L. Cos. d. 0 9.59188 9.62785 0.37215 9.96403 60 1 9.59218 30 9.62820 35 0.37180 9.96397 6 59 2 9.59247 29 9.62855 35 0.37145 9.96392 5 58 3 9.59277 30 9.62890 35 0.37110 9.96387 5 57 4 9.59307 30 29 9.62926 36 35 0.37074 9.96381 6 K 56 5 9.59336 9.62961 0.37039 9.96376 o 55 6 9.59366 30 9.62996 35 0.37004 9.96370 6 54 7 9.59396 30 9.63031 35 0.36969 9.96365 5 53 8 9.59425 29 9.63066 35 0.36934 9.96360 5 52 9 9.59455 30 29 9.63101 35 34 0.36899 9.96354 6 51 10 9.59484 9.63135 0.36865 9.96349 O 50 11 9.59514 30 9.63170 35 0.36830 9.96343 6 49 12 9.59543 29 9.63205 35 0.36795 9.96338 5 48 13 9.59573 30 9.63240 35 0.36760 9.96333 5 47 14 9.59602 29 30 9.63275 35 35 0.36725 9.96327 6 46 15 9.59632 9.63310 0.36690 9.96322 O 45 16 9.59661 29 9.63345 35 0.36655 9.96316 6 44 17 9.59690 29 9.63379 34 0.36621 9.96311 5 43 18 9.59720 30 9.63414 35 0.36586 9.96305 6 42 19 9.59749 29 29 9.63449 35 35 0.36551 9.96300 5 41 20 9.59778 9.63484 0.36516 9.96294 0 40 21 9.59808 30 9.63519 35 0.36481 9.96289 5 39 22 9.59837 29 9.63553 34 0.36447 9.96284 5 38 23 9.59866 29 9.63588 35 0.36412 9.96278 6 37 24 9.59895 29 29 9.63623 35 34 0.36377 9.96273 5 a 36 25 9.59924 9.63657 0.36343 9.96267 0 35 26 9.59954 30 9.63692 35 0.36308 9.96262 5 34 27 9.59983 29 9.63726 34 0.36274 9.96256 6 33 28 9.60012 29 9.63761 35 0.36239 9.96251 5 32 29 9.60041 29 29 9.63796 35 34 0.36204 9.96245 6 31 30 9.60070 9.63830 0.36170 9.96240 O 30 31 9.60099 29 9.63865 35 0.36135 9.96234 6 29 32 9.60128 29 9.63899 34 0.36101 9.96229 5 28 33 9.60157 29 9.63934 35 0.36066 9.96223 6 27 34 9.60186 29 29 9.63968 34 35 0.36032 9.96218 5 g 26 35 9.60215 9.64003 0.35997 9.96212 25 36 9.60244 29 9.64037 34 0.35963 9.96207 5 24 37 9.60273 29 9.64072 35 0.35928 9.96201 6 23 38 9.60302 29 9.64106 34 0.35894 9.96196 5 22 39 9.60331 29 28 9.64140 34 35 0.35860 9.96190 6 5 21 40 9.60359 9.64175 0.35825 9.96185 20 41 9.60388 29 9.64209 34 0.35791 9.96179 6 19 42 9.60417 29 9.64243 34 0.35757 9.96174 5 18 43 9.60446 29 9.64278 35 0.35722 9.96168 6 17 44 9.60474 28 29 9.64312 34 34 0.35688 9.96162 6 5 16 45 9.60503 9.64346 0.35654 9.96157 15 46 9.60532 29 9.64381 35 0.35619 9.96151 6 14 47 9.60561 29 9.64415 34 0.35585 9.96146 5 13 48 9.60589 28 9.64449 34 0.35551 9.96140 6 12 49 9.60618 29 28 9.64483 34 34 0.35517 9.96135 5 6 11 50 9.60646 9.64517 0.35483 9.96129 10 51 9.60675 29 9.64552 35 0.35448 9.96123 6 9 52 9.60704 29 9.64586 34 0.35414 9.96118 5 8 53 9.60732 28 9.64620 34 0.35380 9.96112 6 7 54 9.60761 29 28 9.64654 34 34 0.35346 9.96107 5 Q 6 55 9.60789 9.64688 0.35312 9.96101 5 56 9.60818 29 9.64722 34 0.35278 9.96095 6 4 57 9.60846 28 9.64756 34 0.35244 9.96090 5 3 58 9.60875 29 9.64790 34 0.35210 9.96084 6 2 59 9.60903 28 28 9.64824 34 34 0.35176 9.96079 5 g 1 60 9.60931 9.64858 0.35142 9.96073 0 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. / P. P. 36 3.6 4.2 4.8 5.4 6.0 12.0 18.0 24.0 30.0 35 3.5 4.1 4.7 5.3 5.8 11.7 17.5 23.3 29.2 34 3.4 4.0 4.5 5.1 5.7 11.3 17.0 22.7 28.3 30 3.0 3.5 4.0 4.5 5.0 10.0 15.0 20.0 25.0 29 2.9 3.4 3.9 4.4 4.8 9.7 14.5 ]9.3 24.2 28 2.8 3.3 3.7 4.2 4.7 9.3 14.0 18.7 23.3 6 5 6 0.6 0.5 7 0.7 0.6 8 0.8 0.7 9 0.9 0.8 10 1.0 0.8 20 2.0 L7 30 3.0 2.5 40 4.0 3.3 50 5.0 4.2 P. P. 66 ° 516 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 24 ° / L. Sin. 0 9.60931 1 9.60960 2 9.60988 3 9.61016 4 9.61045 5 9.61073 6 9.61101 7 9.61129 8 9.61158 9 9.61186 10 9.61214 11 9.61242 12 9.61270 13 9.61298 14 9.61326 15 9.61354 16 9.61382 17 9.61411 18 9.61438 19 9.61466 20 9.61494 21 9.61522 22 9.61550 23 9.61578 24 9.61606 25 9.61634 26 9.61662 27 9.61689 28 9.61717 29 9.61745 30 9.61773 31 9.61800 32 9.61828 33 9.61856 34 9.61883 35 9.61911 36 9.61939 37 9.61966 38 9.61994 39 9.62021 40 9.62049 41 9.62076 42 9.62104 43 9.62131 44 9.62159 45 9.62186 46 9.62214 47 9.62241 48 9.62268 49 9.62296 50 9.62323 51 9.62350 52 9.62377 53 9.62405 54 9.62432 55 9.62459 56 9.62486 57 9.62513 58 9.62541 59 9.62568 60 '9.62595 L. Cos. d. L.Tang. 29 28 28 29 28 28 28 29 28 28 28 28 28 28 28 28 29 27 28 28 28 28 28 28 28 28 27 28 28 28 27 28 28 27 28 28 27 28 27 28 27 28 27 28 27 28 27 27 28 27 27 27 28 27 27 27 27 28 27 27 9.64858 9.64892 9.64926 9.64960 9.64994 9.65028 9.65062 9.65096 9.65130 9.65164 9.65197 9.65231 9.65265 9.65299 9.65333 9.65366 9.65400 9.65434 9.65467 9.65501 9.65535 9.65568 9.65602 9.65636 9.65669 9.65703 9.65736 9-65770 9.65803 9.65837 9.65870 9.65904 9.65937 9.65971 9.66004 9.66038 9.66071 9.66104 9.66138 9.66171 9.66204 9.66238 9.66271 9.66301 9.66337 9.66371 9.66404 9.66437 9.66470 9.66503 9.66537 9.66570 9.66603 9.66636 9.66669 9.66702 9.66735 9.66768 9.66801 9^6^ 9.66867 L- C(^ d. c. 34 34 34 34 34 34 34 34 34 33 34 34 34 34 33 34 34 33 34 34 33 34 34 33 34 33 34 33 34 33 34 33 34 33 34 33 33 34 33 33 34 33 33 33 34 33 33 33 33 34 33 33 33 33 33 33 33 33 33 33 d.^cT L. Cotg. L. Cos. d. ] P. P. 0.35142 9.96073 60 0.35108 9.96067 6 59 0.35074 9.96062 5 58 0.35040 9.96056 6 57 A 04 Q A 00 Q Q 0.35006 9.96050 6 5 56 O 7 O.'l 4.0 0.0 3.9 0.34972 9.96045 55 8 4.5 4.4 0.34938 9.96039 6 54 9 5.1 5.0 0.34904 9.96034 5 53 10 5.7 5.5 0.34870 9.96028 6 52 20 11.3 11.0 0.34836 9.96022 6 5 51 30 17.0 16.5 0.34803 9.96017 50 40 22.7 22.0 0.34769 9.96011 6 49 50 28.3 27.5 0.34735 9.96005 6 48 0.34701 9.96000 5 47 0.34667 9.95994 6 6 46 29 0.34634 9.95988 45 6 2.9 0.34600 9.95982 6 44 7 3.4 0.34566 9.95977 5 43 8 3.9 0.34533 9.95971 6 42 9 4.4 0.34499 9.95965 6 5 41 10 4.8 0.34465 9.95960 40 20 9.7 0.34432 9.95954 6 39 30 14.5 0.34398 9.95948 6 38 40 19.3 0.34364 9.95942 6 37 50 24.2 0.34331 9.95937 5 a 36 0.34297 9.95931 O 35 0.34264 9.95925 6 34 28 0.34230 9.95920 5 33 6 2.8 0.34197 9.95914 6 32 J 3.3 0.34163 9.95908 6 31 8 3.7 0.34130 9.95902 6 30 9 in 4.2 A 7 0.34096 9.95897 5 29 lU on Q Q 0.34063 9.95891 6 28 on M n 0.34029 9.95885 6 27 OU An 1ft 7 0.33996 9.95879 6 Q 26 50 lo. / 23.3 0.33962 9.95873 25 0.33929 9.95868 5 24 0.33896 9.95862 6 23 0.33862 9.95856 6 22 C! 0.33829 9.95850 6 (j 21 t) 7 2.7 3.2 0.33796 9.95844 20 3!6 0.33762 9.95839 5 19 t 5 4.1 0.33729 9.95833 6 18 10 4.5 0.33696 9.95827 6 17 20 9.0 0.33663 9.95821 6 6 16 30 13.5 0.33629 9.95815 15 40 18.0 0.33596 9.95810 5 14 50 22.5 0.33563 9.95804 6 13 0.33530 9.95798 6 12 0.33497 9.95792 6 g 11 6 5 0.33463 9.95786 10 6 0.6 0.5 0.33430 9.95780 6 9 7 0.7 0.6 0.33397 9.95775 6 8 8 0.8 0.7 0.33364 9.95769 6 7 9 0.9 0.8 0.33331 9.95763 6 6 6 10 1.0 0.8 0.33298 9.95757 5 20 2.0 1.7 0.33265 9.95751 6 4 30 3.0 2*5 0.33232 9.95745 6 3 40 4.0 3.3 0.33199 9.95739 6 2 60 5.0 4.2 0.33166 9.95733 6 5 1 0.33133 9.95728 0 1 L.Tang. L. Sin. / P. P. 65 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 25 ° 517 / L. Sin. d. L.Tanff. d. c. L. Cotg. L. Cos. d. 0 9.62595 9.66867 0.33133 9.95728 60 1 9.62622 27 9.66900 33 0.33100 9.95722 6 59 2 9.62649 27 9.66933 33 0.33067 9.95716 6 58 3 9.62676 27 9.66966 33 0.33034 9.95710 6 57 4 9.62703 27 27 9.66999 33 33 0.33001 9.95704 6 56 5 9.62730 9.67032 0.32968 9.95698 O 55 6 9.62757 27 9.67065 33 0.32935 9.95692 6 54 7 9.62784 27 9.67098 33 0.32902 9.95686^ ^ 6 53 8 9.62811 27 9.67131 33 0.32869 9.95680 6 52 9 9.62838 27 27 9.67163 32 33 0.32837 9.95674 6 51 10 9.62865 9.67196 0.32804 9.95668 D 50 11 9.62892 27 9.67229 33 0.32771 9.95663 5 49 12 9.62918 26 9.67262 33 0.32738 9.95657 6 48 13 9.62945 27 9.67295 33 0.32705 9.95651 6 47 14 9.62972 27 27 9.67327 32 33 0.32673 9.95645 6 46 15 9.62999 9.67360 0.32640 9.95639 o 45 16 9.63026 27 9.67393 33 0.32607 9.95633 6 44 17 9.63052 26 9.67426 33 0.32574 9.95627 6 43 18 9.63079 27 9.67458 32 0.32542 9.95621 6 42 19 9.63106 27 27 9.67491 33 33 0.32509 9.95615 6 41 20 9.63133 9.67524 0.32476 9.95609 6 40 21 9.63159 26 9.67556 32 0.32444 9.95603 6 39 22 9.63186 27 9.67589 33 0.32411 9.95597 6 38 23 9.63213 27 9.67622 33 0.32378 9.95591 6 37 24 9.63239 26 27 9.67654 32 33 0.32346 9.95585 6 36 25 9.63266 9.67687 0.32313 9.95579 6 35 26 9.63292 26 9.67719 32 0.32281 9.95573 6 34 27 9.63319 27 9.67752 33 0.32248 9.95567 6 33 28 9.63345 26 9.67785 33 0.32215 9.95561 6 32 29 9.63372 27 26 9.67817 32 33 0.32183 9.95555 6 R 31 30 9.63398 9.67850 0.32150 9.95549 0 30 31 9.63425 27 9.67882 32 0.32118 9.95543 6 29 32 9.63451 26 9.67915 33 0.32085 9.95537 6 28 33 9.63478 27 9.67947 32 0.32053 9.95531 6 .27 34 9.63504 26 27 9.67980 33 32 0.32020 9.95525 6 £* 26 35 9.63531 9.68012 0.31988 9.95519 O 25 36 9.63557 26 9.68044 32 0.31956 9.95513 6 24 37 9.63583 26 9.68077 33 0.31923 9.95507 6 23 38 9.63610 27 9.68109 32 0.31891 9.95500 7 22 39 9.63636 26 26 9.68142 33 32 0.31858 9.95494 6 R 21 40 9.63662 9.68174 0.31826 9.95488 O 20 41 9.63689 27 9.68206 32 0.31794 9.95482 6 19 42 9.63715 26 9.68239 33 0.31761 9.95476 6 18 43 9.63741 26 9.68271 32 0.31729 9.95470 6 17 44 9.63767 26 27 9.68303 32 33 0.31697 9.95464 6 6 16 45 9.63794 9.68336 0.31664 9.95458 15 46 9.63820 26 9.68368 32 0.31632 9.95452 6 14 47 9.63846 26 9.68400 32 0.31600 9.95446 6 13 48 9.63872 26 9.68432 32 0.31568 9.95440 6 12 49 9.63898 26 26 9.68465 33 32 0.31535 9.95434 6 rj 11 50 9.63924 9.68497 0.31503 9.95427 4 10 51 9.63950 26 9.68529 32 0.31471 9.95421 6 9 52 9.63976 26 9.68561 32 0.31439 9.95415 6 8 53 9.64002 26 9.68593 32 0.31407 9.95409 6 7 54 9.64028 26 26 9.68626 33 32 0.31374 9.95403 6 R 6 55 9.64054 9.68658 0.31342 9.95397 O 5 56 9.64080 26 9.68690 82 0.31310 9.95391 6 4 57 9.64106 26 9.68722 32 0.31278 9.95384 7 3 58 9.64132 26 9.68754 32 0.31246 9.95378 6 2 59 9.64158 26 26 9.68786 32 32 0.31214 9.95372 6 6 1 60 9.64184 9.68818 0.31182 9.95366 0 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. / P. P. 33 32 6 3.3 3.2 7 3.9 3.7 8 4.4 4.3 9 5.0 4.8 10 5.5 5.3 20 11.0 10.7 30 16.5 16.0 40 22.0 21.3 50 27.5 26.7 27 6 2.7 7 3.2 8 3.6 9 4.1 10 4.5 20 9.0 30 13.5 40 18.0 50 22.5 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 6 0.7 7 0.8 8 0.9 9 1.1 10 1.2 20 2.3 30 3.5 40 4.7 50 5.8 6 5 6 0.6 0.5 7 0.7 0.6 8 0.8 0.7 9 0.9 0.8 10 1.0 0.8 20 2.0 1.7 30 3.0 2.5 40 4.0 3.3 50 5.0 4.2 P. P. 64 ° 518 ' LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 26 ° / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. 0 9.64184 9.68818 0.31182 9.95366 60 1 9.64210 26 9.68850 32 0.31150 9.95360 6 59 2 9.64236 26 9.68882 32 0.31118 9.95354 6 58 3 9.64262 26 9.68914 32 0.31086 9.95348 6 57 4 9.64288 26 25 9.68946 32 32 0.31054 9.95341 7 8 56 6 9.64313 9.68978 0.31022 9.95335 55 6 9.64339 26 9.690m 32 0.30990 9.95329 6 54 7 9.64365 26 9.690^ 32 0.30958 9.95323 6 53 8 9.64391 26 9.69074 32 0.30926 9.95317 6 52 9 9.64417 26 25 9.69106 32 32 0.30894 9.95310 7 51 10 9.64442 9.69138 0.30862 9.95304 D 50 11 9.64468 26 9.69170 32 0.30830 9.95298 6 49 12 9.64494 26 9.69202 32 0.30798 9.95292 6 48 13 9.64519 ^5 9.69234 32 0.30766 9.95286 6 47 14 9.64545 26 9.69266 32 0.30734 9.95279 7 46 15 9.64571 26 9.69298 32 0.30702 9.95273 6 45 16 9.64596 25 9.69329 31 0.30671 9.95267 6 44 17 9.64622 26 9.69361 32 0.30639 9.95261 6 43 18 9.64647 25 9.69393 32 0.30607 9.95254 7 42 19 9.64673 26 25 9.69425 32 32 0.30575 9.95248 6 41 20 9.64698 9.69457 0.30543 9.95242 0 40 21 9.64724 26 9.69488 31 0.30512 9.95236 6 39 22 9.64749 25 9.69520 32 0.30480 9.95229 7 38 23 9.64775 26 9.69552 32 0.30448 9.95223 6 37 24 9.64800 25 96 9.69584 32 31 0.30416 9.95217 6 36 25 9.64826 9.69615 0.30385 9.95211 D 35 26 9.64851 25 9.69647 32 0.30353 9.95204 7 34 27 9.64877 26 9.69679 32 0.30321 9.95198 6 33 28 9.64902 25 9.69710 31 0.30290 9.95192 6 32 29 9.64927 25 26 9.69742 32 0.30258 9.95185 7 a 31 30 9.64953 9.69774 OZi 0.30226 9.95179 0 30 31 9.64978 25 9.69805 31 0.30195 9.95173 6 29 32 9.65003 25 9.69837 32 0.30163 9.95167 6 28 33 9.65029 26 9.69868 31 0.30132 9.95160 7 27 34 9.65054 25 25 9.69900 32 32 0.30100 9.95154 6 6 26 35 9.65079 9.69932 0.30068 9.95148 25 36 9.65104 25 9.69963 31 0.30037 9.95141 7 24 37 9.65130 26 9.69995 32 0.30005 9.95135 6 23 38 9.65155 25 9.70026 31 0.29974 9.95129 6 22 39 9.65180 25 25 9.70058 32 31 0.29942 9.95122 7 21 40 9.65205 9.70089 0.29911 9.95116 o 20 41 9.65230 25 9.70121 32 0.29879 9.95110 6 19 42 9.65255 25 9.70152 31 0.29848 9.95103 7 18 43 9.65281 26 9.70184 32 0.29816 9.95097 6 17 44 9.65306 25 25 9.70215 31 32 0.29785 9.95090 7 g 16 45 9.65331 9.70247 0.29753 9.95084 15 46 9.65356 25 9.70278 31 0.29722 9.95078 6 14 47 9.65381 25 9.70309 31 0.29691 9.95071 7 13 48 9.65406 25 9.70341 32 0.29659 9.95065 6 12 49 9.65431 25 25 9.70372 31 32 0.29628 9.95059 6 7 11 50 9.65456 9.70404 0.29596 9.95052 10 51 9.65481 25 9.70435 31 0.29565 9.95046 6 9 52 9.65506 25 9.70466 31 0.29534 9.95039 7 8 53 9.65531 25 9.70498 32 0.29502 9.95033 6 7 54 9.65556 25 24 9.70529 31 31 0.29471 9.95027 6 7 6 55 9.65580 9.70^0 0.29440 9.95020 5 56 9.65605 25 9.70592 32 0.29408 9.95014 G 4 57 9.65630 25 9.70623 31 0.29377 9.95007 7 3 58 9.65655 25 9.70654 31 0.29346 9.95001 6 2 59 9.65680 25 25 9.70685 31 32 0.29315 9.94995 6 7 1 60 9.65705 9.70717 0.29283 9.94988 0 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. ■d. / P . P. 32 31 6 3.2 3.1 7 3.7 3.6 8 4.3 4.1 9 4.8 4.7 10 5.3 5.2 20 10.7 10.3 30 16.0 15.5 40 21.3 20.7 50 26.7 25.8 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 25 6 2.5 7 2.9 8 3.3 9 3.8 10 4.2 20 8.3 30 12.5 40 16.7 50 20.8 24 6 2.4 7 2.8 8 3.2 9 3.6 10 4.0 20 8.0 30 12.0 40 16.0 50 20.0 7 6 6 0.7 0.6 7 0.8 0.7 8 0.9 0.8 9 1.1 0.9 10 1.2 1.0 20 2.3 2.0 30 3.5 3.0 40 4.7 4.0 50 5.8 5.0 P. P. 63 ‘ / L. Sill. ”F 9.65705 1 9.65729 2 9.65754 3 9.65779 4 9.65804 5 9.65828 6 9.65853 7 9.65878 8 9.65902 9 9.65927 10 9.65952 11 9.65976 12 9.66001 13 9.66025 14 9.66050 15 9.66075 16 9.66099 17 9.66124 18 9.66148 19 9.66173 20 9.66197 2i 9.66221 22 9.66246 23 9.66270 24 9.66295 25 , 9.66319 26 9.66343 27 9.66368 28 9.66392 29 9.66416 30 9.66441 31 9.66465 32 9.66489 33 9.66513 34 9.66537 35 9.66562 36 9.66586 37 9.66610 38 9.66634 39 9.66658 40 9.66682 41 9.66706 42 9.66731 43 9.66755 44 9.66779 45 9.66803 46 9.66827 47 9.66851 48 9.66875 49 9.66899 50 9.66922 51 9.66946 52 9.66970 53 9.66994 54 9.67018 55 9.67042 56 9.67066 57 9.67090 58 9.67113 59 9.67137 60 9.67161 L. Cos. LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 27 ° 519 L. Cotg. L. Cos. d. 0.29283 9.94988 6 60 0.29252 9.94982 59 0.29221 9.94975 7 58 0.29190 9.94969 6 57 0.29159 9.94962 7 g 56 0.29127 9.94956 55 0.29096 9.94949 7 54 0.29065 9.94943 6 53 0.29034 9.94936 7 52 0.29003 9.94930 6 7 51 0.28972 9.94923 50 0.28941 9.94917 6 49 0.28910 9.94911 6 48 0.28879 9.94904 7 47 0.28847 9.94898 6 7 46 0.28816 9.94891 45 0.28785 9.94885 6 44 0.28754 9.94878 7 43 0.28723 9.94871 7 42 0.28692 9.94865 6 y 41 0.28661 9.94858 6 40 0.28630 9.94852 39 0.28599 9.94845 7 38 0.28569 9.94839 6 37 0.28538 9.94832 7 g 36 0.28507 9.94826 35 0.28476 9.94819 7 34 0.28445 9.94813 6 33 0.28414 9.94806 7 32 0.28383 9.94799 7 6 31 0.28352 9.94793 30 0.28321 9.94786 7 29 0.28291 9.94780 6 28 0.28260 9.94773 7 6 7 27 0.28229 9.94767 26 0.28198 9.94760 25 0.28167 9.94753 7 24 0.28137 9.94747 6 23 0.28106 9.94740 7 6 7 22 0.28075 9.94734 21 0.28045 9.94727 20 0.28014 9.94720 7 19 0.27983 9.94714 6 18 0.27952 9.94707 7 17 0.27922 9.94700 7 6 16 0.27891 9.94694 15 0.27860 9.94687 7 14 0.27830 9.94680 7 13 0.27799 9.94674 6 12 0.27769 9.94667 7 y 11 0.27738 9.94660 10 0.27707 9.94654 6 9 0.27677 9.94647 7 8 0.27646 9.94640 7 7 0.27616 9.94634 6 7 6 0.27585 9.94627 5 0.27555 9.94620 7 4 0.27524 9.94614 6 3 0.27494 9.94607 7 2 0.27463 9.94600 7 7 1 o.274iiir 9.9I593 1 0 L.Tang. L. Sin. d.^ L.Tang. 9.70717 9.70748 9.70779 9.70810 9.70841 9.70873 9.70904 9.70935 9.70966 9.70997 9.71028 9.71059 9.71090 9.71121 9.71153 9.71184 9.71215 9.71246 9.71277 9.71308 9.71339 9.71370 9.71401 9.71431 9.71462 9.71493 9.71524 9.71555 9.71586 9.71617 9.71648 9.71679 9.71709 9.71740 9.71771 9.71802 9.71833 9.71863 9.71894 9.71925 9.71955 9.71986 9.72017 9.72048 9.72078 9.72109 9.72140 9.72170 9.72201 9.72231 9.72262 9.72293 9.72323 9.72354 9.72384 9.72415 9.72445 9.72476 9.72506 9.72537 9.72567 L. Cotg. d. 0^ P. P. 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 d. c. 32 3.2 3.7 4.3 4.8 5.3 10.7 16.0 21.3 26.7 31 3.1 3.6 4.1 4.7 5.2 10.3 15.5 20.7 25.8 30 3.0 3.5 4.0 4.5 5.0 10.0 15.0 20.0 25.0 25 2.5 2.9 3.3 3.8 4.2 8.3 12.5 16.7 20.8 24 2.4 2.8 3.2 3.6 4.0 8.0 12.0 16.0 20.0 23 2.3 2.7 3.1 3.5 3.8 7.7 11.5 15.3 19.2 6 0.6 0.7 0.8 0.9 1.0 2.0 3.0 4.0 5.0 P. P. 520 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 28 ° ' 1 L. Sin. 0 9.67161 1 9.67185 2 9.67208 3 9.67232 4 9.67256 5 9.67280 6 9.67303 7 9.67327 8 9.67350 9 9.67374 iO 9.67398 11 9.67421 12 9.67445 13 9.67468 14 9.67492 15 9.67515 16 9.67539 17 9.67562 18 9.67586 19 9.67609 20 9.67633 21 9.67656 22 9.67680 23 9.67703 24 9.67726 25 9.67750 26 9.67773 27 9.67796 28 9.67820 29 9.67843 30 9.67866 31 9.67890 32 9.67913 33 9.67936 34 9.67959 35 9.67982 36 9.68006 37 9.68029 38 9.68052 39 9.68075 40 9.68098 41 9.68121 42 9.68144 43 9.68167 44 9.68190 45 9.68213 46 9.68237 47 9.68260 48 9.68283 49 9.68305 50 9.68328 51 9.68351 52 9.68374 53 9.68397 54 9.68420 55 9.68443 56 9.68466 57 9.68489 58 9.68512 59 9.68534 60 9.68557 L. Cos. L.Tang. d. c. L. Cotg. L. Cos. d. P.P. 9.72567 9.72598 9.72628 9.72659 9.72689 9.72720 9.72750 9.72780 9.72811 9.72841 9.72872 9.72902 9.72932 9.72963 9.72993 9.73023 9.73054 9.73084 9.73114 9.73144 9.73175 9.73205 9.73235 9.73265 9.73295 9.73326 9.73356 9.73386 9.73416 9.73446 9.73476 9.73507 9.73537 9.73567 9.73597 9.73627 9.73657 9.73687 9.73717 9.73747 9.73777 9.73807 9.73837 9.73867 9.73897 9.73927 9.73957 9.73987 9.74017 9.74047 9.74077 9.74107 9.74137 9.74166 9.74196 9.74226 9.74256 9.74286 9.74316 9.74345 9.74375 31 30 31 30 31 30 30 31 30 31 30 30 31 30 30 31 30 30 30 31 30 30 30 30 31 30 30 30 30 30 31 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 29 30 30 30 30 30 29 30 0.27433 0.27402 0.27372 0.27341 0.27311 9.94593 9.94587 9.94580 9.94573 9.94567 0.27280 0.27250 0.27220 0.27189 0.27159 9.94560 9.94553 9.94546 9.94540 9.94533 0.27128 0.27098 0.27068 0.27037 0.27007 9.94526 9.94519 9.94513 9.94506 9.94499 0.26977 0.26946 0.26916 0.26886 0.26856 9.94492 9.94485 9.94479 9.94472 9.94465 0.26825 0.26795 0.26765 0.26735 0.26705 9.94458 9.94451 9.94445 9.94438 9.94431 0.26674 0.26644 0.26614 0.26584 0.26554 9.94424 9.94417 9.94410 9.94404 9.94397 0.26524 0.26493 0.26463 0.26433 0.26403 9.94390 9.94383 9.94376 9.94369 9.94362 0.26373 0.26343 0.26313 0.26283 0.26253 9.94355 9.94349 9.94342 9.94335 9.94328 0.26223 0.26193 0.26163 0.26133 0.26103 9.94321 9.94314 9.94307 9.94300 9.94293 0.26073 0.26043 0.26013 0.25983 0.25953 9.94286 9.94279 9.94273 9.94266 9.94259 0.25923 0.25893 0.25863 0.25834 0.25804 9.94252 9.94245 9.94238 9.94231 9.94224 0.25774 0.25744 0.25714 0.25684 0.25655 9.94217 9.94210 9.94203 9.94196 9.94189 L. Cotg. d. c. 0.25625 L.Tang. 31 3.1 3.6 4.1 4.7 5.2 10.3 15.5 20.7 25.8 30 3.0 3.5 4.0 4.5 5.0 10.0 15.0 20.0 25.0 29 2.9 3.4 3.9 4.4 4.8 9.7 14.5 19.3 24.2 24 2.4 2.8 3.2 3.6 4.0 8.0 12.0 16.0 20.0 23 2.3 2.7 3.1 3.5 3.8 7.7 11.5 15.3 19.2 22 2.2 2.6 2.9 3.3 3.7 7.3 11.0 14.7 18.3 7 6 i 0.7 7 ' 0.8 8 i 0.9 P. P. 61 ° 521 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 29 ° / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. ^ P. P. 0 1 2 3 4 9.68557 9.68580 9.68603 9.68625 9.68648 23 23 22 23 23 23 22 23 23 22 23 22 23 23 22 23 22 23 22 23 22 23 22 23 22 22 23 22 23 22 22 23 22 22 22 23 22 22 22 22 23 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 22 9.74375 9.74405 9.74435 9.74465 9.74494 30 30 30 29 30 30 29 30 30 30 29 30 30 29 30 30 29 30 29 30 29 30 30 29 30 29 30 29 30 29 30 29 30 29 29 30 29 30 29 29 30 29 30 29 29 30 29 29 29 30 29 29 29 30 29 29 29 30 29 29 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 7 7 7 7 7 7 7 8 7 7 7 7 7 7 7 7 7 7 8 7 7 7 7 7 7 7 8 7 7 7 7 7 8 7 7 7 7 8 7 7 7 8 7 7 7 7 8 7 7 8 7 7 7 8 7 60 59 58 57 56 55 54 53 52 51 30 6 3.0 7 3.5 8 4.0 9 4.5 10 5.0 20 10.0 30 15.0 40 20.0 50 25.a 29 6 2.9 7 3.4 8 3.9 9 4.4 10 4.8 20 9.7 30 14.5 40 19.3 50 24.2 23 6 2.3 7 2.7 8 3.1 9 3.5 10 3.8 20 7.7 30 11.5 40 15.3 50 19.2 22 6 2.2 7 2.6 8 2.9 9 3.3 10 3.7 20 7.3 30 11.0 40 14.7 50 18.3 8 7 6 0.8 0.7 7 0.9 0.8 8 1.1 0.9 9 1.2 1.1 10 1.3 1.2 20 2.7 2.3 30 4.0 3.5 40 5.3 4.7 50 6.7 5.8 5 6 7 8 9 9.68671 9.68694 9.68716 9.68739 9.68762 9.74524 9.74554 9.74583 9.74613 9.74643 0.25476 0.25446 0.25417 0.25387 0.25357 9.94147 9.94140 9.94133 9.94126 9.94119 10 11 12 13 14 9.68784 9.68807 9.68829 9.68852 9.68875 9.74673 9.74702 9.74732 9.74762 9.74791 0.25327 0.25298 0.25268 0.25238 0.25209 9.94112 9.94105 9.94098 9.94090 9.94083 50 49 48 47 46 15 16 17 18 19 9.68897 9.68920 9.68942 9.68965 9.68987 9.74821 9.74851 9.74880 9.74910 9.74939 0.25179 0.25149 0.25120 0.25090 0.25061 9.94076 9.94069 9.94062 9.94055 9.94048 45 44 43 42 41 20 21 22 23 24 9.69010 9.69032 9.69055 9.69077 9.69100 9.74969 9.74998 9.75028 9.75058 9.75087 0.25031 0.25002 0.24972 0.24942 0.24913 9.94041 9.94034 9.94027 9.94020 9.94012 40 39 38 37 36 25 26 27 28 29 9.69122 9.69144 9.69167 9.69189 9.69212 9.75117 9.75146 9.75176 9.75205 9.75235 0.24883 0.24854 0.24824 0.24795 0.24765 9.94005 9.93998 9.93991 9.93984 9.93977 35 34 33 32 31 30 31 32 33 34 9.69234 9.69256 9.69279 9.69301 9.69323 9.75264 9.75294 9.75323 9.75353 9.75382 0.24736 0.24706 0.24677 0.24647 0.24618 9.93970 9.93963 9.93955 9.93948 9.93941 30 29 28 27 26 35 36 37 38 39 9.69345 9.69368 9.69390 9.69412 9.69434 9.75411 9.75441 9.75470 9.75500 9.75529 0.24589 0.24559 0.24530 0.24500 0.24471 9.93934 9.93927 9.93920 9.93912 9.93905 25 24 23 22 21 40 41 42 43 44 9.69456 9.69479 9.69501 9.69523 9.69545 9.75558 9.75588 9.75617 9.75647 9.75676 0.24442 0.24412 0.24383 0.24353 0.24324 9.93898 9.93891 9.93884 9.93876 9.93869 20 19 18 17 16 45 46 '47 48 49 9.69567 9.69589 9.69611 9.69633 9.69655 9.75705 9.75735 9.75764 9.75793 9.75822 0.24295 0.24265 0.24236 0.24207 0.24178 9.93862 9.93855 9.93847 9 93840 9.93833 15 14 13 12 11 50 51 52 53 54 9.69677 9.69699 9.69721 9.69743 9.69765 9.75852 9.75881 9.75910 9.75939 9.75969 0.24148 0.24119 0.24090 0.24061 0.24031 9.93826 9.93819 9.93811 9.93804 9.93797 10 9 8 7 6 55 66 57 58 59 9.69787 9.69809 9.69831 9.69853 9.69875 9.75998 9.76027 9.76056 9.76086 9.76115 0.24002 0.23973 0.23944 0.23914 0.23885 9.93789 9.93782 9.93775 9.93768 9.93760 5 4 3 2 1 60 9.69897 9.76144 0.23856 9.93753 0 L. Cos. d. L. Cotg. d.c. L.Tang. L. Sin. d. ' P. P. 60 ' 522 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 30 ° t L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. 1 d. 0 9.69897 9.76144 0.23856 9.93753 60 1 9.69919 22 9.76173 29 0.23827 9.93746 7 59 2 9.69941 22 9.76202 29 0.23798 9.93738 8 58 3 9.69963 22 9.76231 29 0.23769 9.93731 7 57 4 9.69984 21 22 9.76261 30 29 0.23739 9.93724 7 <7 56 5 9.70006 9.76290 0.23710 9.93717 55 6 9.70028 22 9.76319 29 0.23681 9.93709 8 54 7 9.70050 22 9.76348 29 0.23652 9.93702 7 53 8 9.70072 22 9.76377 29 0.23623 9.93695 7 52 9 9.70093 21 22 9.76406 29 29 0.23594 9.93687 8 >7 51 10 9.70115 9.76435 0.23565 9.93680 50 11 9.70137 22 9.76464 29 0.23536 9.93673 7 49 12 9.70159 22 9.76493 29 0.23507 9.93665 8 48 13 9.70180 21 9.76522 29 0.23478 9.93658 7 47 14 9.70202 22 22 9.76551 29 29 0.23449 9.93650 8 <7 46 15 9.70224 9.76580 0.23420 9.93643 45 16 9.70245 21 9.76609 29 0.23391 9.93636 7 44 17 9.70267 22 9.76639 30 0.23361 9.93628 8 43 18 9.70288 21 9.76668 29 0.23332 9.93621 7 42 19 9.70310 22 22 9.76697 29 28 0.23303 9.93614 7 8 41 20 9.70332 9.76725 0.23275 9.93606 40 21 9.70353 21 9.76754 29 0.23246 9.93599 7 39 22 9.70375 22 9.76783 29 0.23217 9.93591 8 38 23 9.70396 2d\. 9.76812 29 0.23188 9.93584 7 37 24 9.70418 22 21 9.76841 29 29 0.23159 9.93577 7 8 36 25 9.70439 9.76870 0.23130 9.93569 35 26 9.70461 22 9.76899 29 0.23101 9.93562 7 34 27 9.70482 21 9.76928 29 0.23072 9.93554 8 33 28 9.70504 22 9.76957 29 0.23043 9.93547 7 32 29 9.70525 21 22 9.76986 29 29 0.23014 9.93539 8 31 30 9.70547 9.77015 0.22985 9.93532 30 31 9.70568 9.77044 29 0.22956 9.93525 7 29 32 9.70590 22 9.77073 29 0.22927 9.93517 8 28 33 9.70611 21 9.77101 28 0.22899 9.93510 7 27 34 9.70633 22 21 9.77130 29 29 0.-22870 9.93502 8 'j 26 35 9.70654 9.77159 0.22841 9.93495 25 36 9.70675 21 9.77188 29 0.22812 9.93487 8 24 37 9.70697 22 9.77217 29 0.22783 9.93480 7 23 38 9.70718 21 9.77246 29 0.22754 9.93472 8 22 39 §.70739 21 22 9.77274 28 29 0.22726 9.93465 7 8 21 40 9.70761 9.77303 0.22697 9.93457 20 41 9.70782 21 9.77332 29 0.22668 9.93450 7 19 42 9.70803 21 9.77361 29 0.22639 9.93442 8 18 43 9.70824 21 9.77390 29 0.22610 9.93435 7 17 44 9.70846 22 21 9.77418 28 29 0.22582 9.93427 8 <7 16 45 9.70867 9.77447 0.22553 9.93420 15 46 9.70888 21 9.77476 29 0.22524 9.93412 8 14 47 9.70909 21 9.77505 29 0.22495 9.93405 7 13 48 9.70931 22 9.77533 28 0.22467 9.93397 8 12 49 9.70952 21 21 9.77562 29 29 0.22438 9.93390 7 8 11 50 9.70973 9.77591 0.22409 9.93382 10 51 9.70994 21 9.77619 28 0.22381 9.93375 7 9 52 9.71015 21 9.77648 29 0.22352 9.93367 8 8 53 9.71036 21 9.77677 29 0.22323 9.93360 7 7 54 9.71058 22 21 9.77706 29 28 0.22294 9.93352 8 8 6 55 9.71079 9.77734 0.22266 9.93344 5 56 9.71100 21 9.77763 29 0.22237 9.93337 7 4 57 9.71121 21 9.77791 28 0.22209 9.93329 8 3 58 9.71142 21 9.77820 29 0.22180 9.93322 7 2 59 9.71163 21 21 9.77849 29 28 0.22151 9.93314 8 1 60 9.71184 9777877 0.22123 9.93307 0 L. Cos. 1 d. L. Cotg. ! d. c. L.Tang. L.'Sin. rd.“ / P. P. 30 29 6 3.0 2.9 7 3.5 3.4 '8 4.0 3.9 9 4.5 4.4 10 5.0 4.8 20 10.0 9.7 30 15.0 14.5 40 20.0 19.3 50 25.0 24.2 • 28 6 2.8 7 3.3 8 3.7 9 4.2 10 4.7 20 9.3 30 14.0 40 18.7 50 23.3 22 6 2.2 7 2.6 8 2.9 9 3.3 10 3.7 20 7.3 30 11.0 40 14.7 50 18.3 21 6 2.1 7 2.5 8 2.8 9 3.2 10 3.5 20 7.0 30 10.5 40 14.0 50 17.5 8 7 6 0.8 0.7 7 0.9 0.8 8 1.1 0.9 9 1.2 1.1 10 1.3 1.2 20 2.7 2.3 30 4.0 3.5 40. 5.3 4.7 50 6.7 5.8 P. P. 53 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 523 31 ° / L. Sin. d. L.Taiig. d. c. L. Cotg. L. Cos. d. P. P. 0 1 2 3 4 9.71184 9.71205 9.71226 9.71247 9.71268 21 21 21 21 21 21 21 21 21 20 21 21 21 21 21 21 20 21 21 21 20 21 21 21 20 21 21 20 21 21 20 21 20 21 20 21 20 21 21 20 20 21 20 21 20 21 20 20 21 20 20 21 20 20 21 20 20 21 20 20 9.77877 9.77906 9.77935 9.77963 9.77992 29 29 28 29 28 29 28 29 29 28 29 28 29 28 29 28 29 28 28 29 28 29 28 29 28 28 29 28 29 28 28 29 28 28 29 28 28 29 28 28 28 29 28 28 28 29 28 28 28 28 29 28 28 28 28 28 29 28 28 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 7 8 8 7 8 8 7 8 8 ■ 7 8 8 7 8 8 7 8 8 7 8 8 7 8 8 8 7 8 8 8 7 8 8 8 8 7 8 8 8 7 8 8 8 8 8 7 8 8 8 8 8 8 7 8 8 8 8 60 59 58 57 56 55 54 53 52 51 29 6 2.9 7 3.4 8 3.9 9 4.4 10 4.8 20 9.7 30 14.5 40 19.3 50 24.2 28 6 2.8 7 3.3 8 3.7 9 4.2 10 4.7 20 9.3 30 14.0 40 18.7 50 23.3 21 6 2.1 7 2.5 8 2.8 9 3.2 10 3.5 20 7.0 30 10.5 40 14.0 50 17.5 20 6 2.0 7 2.3 8 2.7 9 3.0 10 3.3 20 6.7 30 10.0 40 13.3 50 16.7 8 7 6 0.8 0.7 7 0.9 0.8 8 1.1 0.9 9 1.2 1.1 10 1.3 1.2 20 2.7 2.3 30 4.0 3.5 40 5.3 4.7 50 6.7 5.8 5 6 7 8 9 9.71289 9.71310 9.71331 9.71352 9.71373 9.78020 9.78049 9.78077 9.78106 9.78135 0.21980 0.21951 0.21923 0.21894 0.21865 9.93269 9.93261 9.93253 9.93246 9.93238 10 11 12 13 14 9.71393 9.71414 9.71435 9.71456 9.71477 9.78163 9.78192 9.78220 9.78249 9.78277 0.21837 0.21808 0.21780 0.21751 0.21723 9.93230 9.93223 9.93215 9.93207 9.93200 50 49 48 47 46 45 44 43 42 41 15 16 17 18 19 9.71498 9.71519 9.71539 9.71560 9.71581 9.78306 9.78334 9.78363 9.78391 9.78419 0.21694 0.21666 0.21637 0.21609 0.21581 9.93192 9.93184 9.93177 9.93169 9.93161 20 21 22 23 24 9.71602 9.71622 9.71643 9.71664 9.71685 9.78448 9.78476 9.78505 9.78533 9.78562 0.21552 0.21524 0.21495 0.21467 0.21438 9.93154 9.93146 9.93138 9.93131 9.93123 40 39 38 37 36 2.5 26 27 28 29 9.71705 9.71726 9.71747 9.71767 9.71788 9.78590 9.78618 9.78647 9.78675 9.78704 0.21410 0.21382 0.21353 0.21325 0.21296 9.93115 9.93108 9.93100 9.93092 9.93084 35 34 33 32 31 30 31 32 33 34 9.71809 9.71829 9.71850 9.71870 9.71891 9.78732 9.78760 9.78789 9.78817 9.78845 0.21268 0.21240 0.21211 0.21183 0.21155 9.93077 9.93069 9.93061 9.93053 9.93046 30 29 28 27 26 35 36 37 38 39 9.71911 9.71932 9.71952 9.71973 9.71994 9.78874 9.78902 9.78930 9.78959 9.78987 0.21126 0.21098 0.21070 0.21041 0.21013 9.93038 9.93030 9.93022 9.93014 9.93007 25 24 23 22 21 40 41 42 43 44 9.72014 9.72034 9.72055 9.72075 9.72096 9.79015 9.79043 9.79072 9.79100 9.79128 0.20985 0.20957 0.20928 0.20900 0.20872 9.92999 9.92991 9.92983 9.92976 9.92968 20 19 18 17 16 15 14 13 12 11 45 46 47 48 49 9.72116 9.72137 9.72157 9.72177 9.72198 9.79156 9.79185 9.79213 9.79241 9.79269 0.20844 0.20815 0.20787 0.20759 0.20731 9.92960 9.92952 9.92944 9.92936 9.92929 5Q 51 52 53 54 9.72218 9.72238 9.72259 9.72279 9.72299 9.79297 9.79326 9.79354 9.79382 9.79410 0.20703 0.20674 0.20646 0.20618 0.20590 9.92921 9.92913 9.92905 9.92897 9.92889 10 9 8 7 6 55 56 57 58 59 9.72320 9.72340 9.72360 9.72381 9.72401 9.79438 9.79466 9.79495 9.79523 9.79551 0.20562 0.20534 0.20505 0.20477 0.20449 9.92881 9.92874 9.92866 9.92858 9.92850 5 4 3 2 1 60 9.72421 9.79579 0.20421 9.92842 0 L. Cos. d. L. Cotg. d. c. L.Tcang. L. Sin. dr P. P. 58 ° 524 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 32° / L. Sin. 0 9.72421 1 9.72441 2 9.72461 3 9.72482 4 9.72502 5 9.72522 6 9.72542 7 9.72562 8 9.72582 9 9.72602 iO 9.72622 11 9.72643 12 9.72663 13 9.72683 14 9.72703 15 9.72723 16 9.72743 17 9.72763 18 9.72783 19 9.72803 20 9.72823 21 9.72843 22 9.72863 23 9.72883 24 9.72902 25 9.72922 26 9.72942 27 9.72962 28 9.72982 29 9.73002 30 9.73022 31 9.73041 32 9.73061 33 9.73081 34 9.73101 35 9.73121 36 9.73140 37 9.73160 38 9.73180 39 9.73200 40 9.73219 41 9.73239 42 9.73259 43 9.73278 44 9.73298 45 9.73318 46 9.73337 47 9.73357 48 9.73377 49 9.73396 50 9.73416 51 9.73435 52 9.73455 53 9.73474 54 9.73494 55 9.73513 56 9.73533 57 9.73552 58 9.73572 59 9.73591 60 9.73611 L.Cos. d. 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 L.Tang. 9.79579 9.79607 9.79635 9.79663 9.79691 9.79719 9.79747 9.79776 9.79804 9.79832 9.79860 9.79888 9.79916 9.79944 9.79972 9.80000 9.80028 9.80056 9.80084 9.80112 9.80140 9.80168 9.80195 9.80223 9.80251 9.80279 9.80307 9.80335 9.80363 9.80391 9.80419 9.80447 9.80474 9.80502 9.80530 9.80558 9.80586 9.80614 9.80642 9.80669 9.80697 9.80725 9.80753 9.80781 9.80808 9.80836 9.80864 9.80892 9.80919 9.80947 9.80975 9.81003 9.81030 9.81058 9.810 86 9.81113 9.81141 9.81169 9.81196 9.81224 9.81252 L. Cotg, d. c. 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 d.cT L. Cotg. 0.20421 0.20393 0.20365 0.20337 0.20309 0.20281 0.20253 0.20224 0.20196 0.20168 0.20140 0.20112 0.20084 0.20056 0.20028 0.20000 0.19972 0.19944 0.19916 0.19888 0.19860 0.19832 0.19805 0.19777 0.19749 0.19721 0.19693 0.19665 0.19637 0.19609 0.19581 0.19553 0.19526 0.19498 0.19470 0.19442 0.19414 0.19386 0.19358 0.19331 0.19303 0.19275 0.19247 0.19219 0.19192 0.19164 0.19136 0.19108 0.19081 0.19053 0.19025 0.18997 0.18970 0.18942 0.18914 0.18887 0.18859 0.18831 0.18804 0.18776 0.18748 L.Tang. L. Cos. d 9.92842 9.92834 9.92826 9.92818 9.92810 9.92803 9.92795 9.92787 9.92779 9.92771 9.92763 9.92755 9.92747 9.92739 9.92731 9.92723 9.92715 9.92707 9.92699 9.92691 9.92683 9.92675 9.92667 9.92659 9.92651 9.92643 9.92635 9.92627 9.92619 9.92611 9.92603 9.92595 9.92587 9.92579 9.92571 9.92563 9.92555 9.92546 9.92538 9.92530 9.92522 9.92514 9.92506 9.92498 9.92490 9.92482 9.92473 9.92465 9.92457 9.92449 9.92441 9.92433 9.92425 9.92416 9.92408 9.92400 9.92392 9.92384 9.92376 9.92367 9.92359 L. Sin. d. P. P. 29 2.9 3.4 3.9 4.4 4.8 9.7 14.5 19.3 24.2 28 2.8 3.3 3.7 4.2 4.7 9.3 14.0 18.7 23.3 27 2.7 3.2 3.6 4.1 4.5 9.0 13.5 18.0 22.5 21 2.1 2.5 2.8 3.2 3.5 7.0 10.5 14.0 17.5 20 2.0 2.3 2.7 3.0 3.3 6.7 10.0 13.3 16.7 6 1.9 7 2.2 8 2.5 9 2.9 10 3.2 20 6.3 30 9.5 40 12.7 50 15.8 9 8 6 0.9 0.8 7 1.1 0.9 8 1.2 1.1 9 1.4 1.2 10 1.5 1.3 20 3.0 2.7 30 4.5 4.0 40 6.0 5.3 50 7.5 6.7 P. P. 5T LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 33 ° 525 / L. Sin. 0 9.73611 1 9.73630 2 9.73650 3 9.73669 4 9.73689 5 9.73708 6 9.73727 7 9.73747 8 9.73766 9 9.73785 10 9.73805 11 9.73824 12 9.73843 13 9.73863 14 9.73882 15 9.73901 16 9.73921 17 9.73940 18 9.73959 19 9.73978 20 9.73997 21 9.74017 22 9.74036 23 9.74055 24 9.74074 25 9.74093 26 9.74113 27 9.74132 28 9.74151 29 9.74170 30 9.74189 31 9.74208 32 9.74227 33 9.74246 34 9.74265 35 9.74284 36 9.74303 37 9.74322 38 9.74341 39 9.74360 40 9.74379 41 9.74398 42 9.74417 43 9.74436 44 9.74455 45 9.74474 46 9.74493 47 9.74512 48 9.74531 49 9.74549 50 9.74568 51 9.74587 52 9.74606 53 9.74625 54 9.74644 55 9.74662 56 9.74681 57 9.74700 58 9.74719 59 9.74737 60 9.74756 L. Cos. L. Cotg. L. Cos. 0.18748 9.92359 0.18721 9.92351 0.18693 9.92343 0.18665 9.92335 0.18638 9.92326 0.18610 9.92318 0.18582 9.92310 0.18555 9.92302 0.18527 9.92293 0.18500 9.92285 0.18472 9.92277 0.18444 9.92269 0.18417 9.92260 0.18389 9.92252 0.18362 9.92244 0.18334 9.92235 0.18307 9.92227 0.18279 9.92219 0.18252 9.92211 0.18224 9.92202 0.18197 9.92194 0.18169 9.92186 0.18142 9.92177 0.18114 9.92169 0.18087 9.92161 0.18059 9.92152 0.18032 9.92144 0.18004 9.92136 0.17977 9.92127 0.17949 9.92119 0.17922 9.92111 0.17894 9.92102 0.17867 9.92094 0.17839 9.92086 0.17812 9.92077 0.17785 9.92069 0.17757 9.92060 0.17730 9.92052 0.17702 9.92044 0.17675 9.92035 0.17648 9.92027 0.17620 9.92018 0.17593 9.92010 0.17565 9.92002 0.17538 9.91993 0.17511 9.91985 0.17483 9.91976 0.17456 9.91968 0.17429 9.91959 0.17401 9.91951 0.17374 9.91942 0.17347 9.91934 0.17319 9.91925 0.17292 9.91917 0.17265 9.91908 0.17238 9.91900 0.17210 9.91891 0.17183 9.91883 0.17156 9.91874 0.17129 9.91866 0.17101 9.91857 L.Tang. L. Sin. L.Tang. d. c. P. P. 19 20 19 20 19 19 20 19 19 20 19 19 20 19 19 20 19 19 19 19 20 19 19 19 19 20 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 19 18 19 19 19 19 19 18 19 19 19 18 19 9.81528 9.81556 9.81583 9.81611 9.81638 9.81666 9.81693 9.81721 9.81748 9.81776 9.81803 9.81831 9.81858 9.81886 9.81913 9.81941 9.81968 9.81996 9.82023 9.82051 9.82078 9.82106 9.82133 9.82161 9.82188 9.82215 9.82243 9.82270 9.82298 9.82325 9.82352 9.82380 9.82407 9.82435 9.82462 9.82489 9.82517 9.82544 9.82571 9.82599 9.82626 9.82653 9.82681 9.82708 9.82735 9.82762 9.82790 9.82817 9.82844 9.82871 9.82899 28 2.8 3.3 3.7 4.2 4.7 9.3 14.0 18.7 23.3 27 2.7 3.2 3.6 4.1 4.5 9.0 13.5 18.0 22.5 20 2.0 2.3 2.7 3.0 3.3 6.7 10.0 13.3 16.7 19 1.9 2.2 2.5 2.9 3.2 6.3 9.5 12.7 15.8 18 1.8 2.1 2.4 2.7 3.0 6.0 9.0 12.0 15.0 8 0.8 0.9 1.1 1.2 1.3 2.7 4.0 5.3 6.7 d. L. Cotg. d. c. P.P. 56 ° 526 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 34 ° f L. Sin. 0 9.74756 1 9.74775 2 9.74794 3 9.74812 4 9.74831 5 9.74850 6 9.74868 7 9.74887 8 9.74906 9 9.74924 10 9.74943 11 9.74961 12 9.74980 13 9.74999 14 9.75017 15 9.75036 16 9.75054 17 9.75073 18 9.75091 19 9.75110 20 9.75128 21 9.75147 22 9.75165 23 9.75184 24 9.75202 25 9.75221 26 9.75239 27 9.75258 28 9.75276 29 9.75294 30 9.75313 31 9.75331 32 9.75350 33 9.75368 34 9.75386 35 9.75405 36 9.75423 37 9.75441 38 9.75459 39 9.75478 40 9.75496 41 9.75514 42 9.75533 43 9.75551 44 9.75569 45 9.75587 46 9.75605 47 9.75624 48 9.75642 49 9.75660 50 9.75678 51 9.75696 52 9.75714 53 9.75733 54 9.75751 55 9.75769 56 9.75787 57 9.75805 58 9.75823 59 9.75841 60 9.75859 L. Cos. L. Cotg. L. Cos. d. 0.17101 9.91857 60 0.17074 9.91849 8 59 0.17047 9.91840 9 58 0.17020 9.91832 8 57 0.16992 9.91823 9 Q 56 0.16965 9.91815 O 55 0.16938 9.91806 9 54 0.16911 9.91798 8 53 0.16883 9.91789 9 52 0.16856 9.91781 8 Q 51 0.16829 9.91772 a 50 0.16802 9.91763 9 49 0.16775 9.91755 8 48 0.16748 9.91746 9 47 0.16720 9.91738 8 9 46 0.16693 9.91729 45 0.16666 9.91720 9 44 0.16639 9.91712 8 43 0.16612 9.91703 9 42 0.16585 9.91695 8 41 Q 0.16558 9.91686 O 40 0.16530 9.91677 9 39 0.16503 9.91669 8 38 0.16476 9.91660 9 37 0.16449 9.91651 9 g 36 0.16422 9.91643 35 0.16395 9.91634 9 34 0.16368 9.91625 9 33 0.16341 9.91617 8 32 0.16314 9.91608 9 9 31 0.16287 9.91599 30 0.16260 9.91591 8 29 0.16232 9.91582 9 28 0.16205 9.91573 9 27 0.16178 9.91565 8 9 26 0.16151 9.91556 25 0.16124 9.91547 9 24 0.16097 9.91538 9 23 0.16070 9.91530 8 22 0.16043 9.91521 9 9 21 0.16016 9.91512 20 0.15989 9.91504 8 19 0.15962 9.91495 9 18 0.15935 9.91486 9 17 0.15908 9.91477 9 8 16 0.15881 9.91469 15 0.15854 9.91460 9 14 0.15827 9.91451 9 13 0.15800 9.91442 9 12 0.15773 9.91433 9 8 11 0.15746 9.91425 10 0.15720 9.91416 9 9 0.15693 9.91407 9 8 0.15666 9.91398 9 . 7 0.15639 9.91389 9 8 6 0.15612 9.91381 5 0.15585 9.91372 9 4 0.15558 9.91363 9 3 0.15531 9.91354 9 2 0.15504 9.91345 9 9 1 0.15477 9.91336 0 L.Tang. L. Sin. d. / d. L.Tang. 9.82899 9.82926 9.82953 9.82980 9.83008 9.83035 9.83062 9.83089 9.83117 9.83144 d. c. 9.83171 9.83198 9.83225 9.83252 9.83280 9.83307 9.83334 9.83361 9.83388 9.83415 9.83713 9.83740 9.83768 9.83795 9.83822 9.83849 9.83876 9.83903 9.83930 9.83957 9.83984 9.84011 9.84038 9.84065 9.84092 9.84119 9.84146 9.84173 9.84200 9.84227 9.84254 9.84280 9.84307 9.84334 9.84361 9.84388 9.84415 9.84442 9.84469 9.84496 9.84523 L. Cotg. 27 27 27 28 27 27 27 28 27 27 27 27 27 28 27 27 27 ■ 27 27 27 28 27 27 27 27 27 27 27 27 27 27 28 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 27 26 27 27 27 27 27 27 27 27 27 d. c. P. P. 28 2.8 3.3 3.7 4.2 4.7 9.3 14.0 18.7 23.3 27 2.7 3.2 3.6 4.1 4.5 9.0 13.5 18.0 22.5 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 19 1.9 2.2 2.5 2.9 3.2 6.3 9.5 12.7 15.8 18 1.8 2.1 2.4 2.7 3.0 6.0 9.0 12.0 15.0 9 8 6 0.9 0.8 7 1.1 0.9 8 1.2 1.1 9 1.4 1.2 10 1.5 1.3 20 3.0 2.7 30 4.5 4.0 40 6.0 5.3 50 7.5 6.7 P. P. 55 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 527 35 ° f L. Sin. d. L.Tang.j d. c. L. Cotg. L. Cos. d. P. P. 0 1 2 3 4 9.75859 9.75877 9.75895 9.75913 9.75931 18 18 . 18 18 18 18 18 18 18 18 18 18 18 18 18 17 18 18 18 18 18 17 18 18 18 17 18 18 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 17 18 17 18 17 18 17 18 17 18 17 18 17 18 17 17 18 9.84523 9.84550 9.84576 9.84603 9.84630 27 26 27 27 27 27 27 '27 26 27 27 27 27 27 26 27 27 27 27 26 27 27 27 26 27 27 27 26 27 27 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 26 27 27 26 27 26 27 27 26 0.15477 0.15450 0.15424 0.15397 0.15370 9.91336 9.91328 9.91319 9.91310 9.91301 8 9 9 9 9 9 ‘9 8 9 9 9 9 9 9 9 9 9 9 9 9 9 8 9 9 9 9 9 9 9 9 9 9 9 9 10 9 9 9 9 9 9 9 9 9 9 9 9 9 10 9 9 9 9 9 9 10 9 9 9 9 60 59 58 57 56 27 26 6 2.7 2.6 7 3.2 3.0 8 3.6 3.5 9 4.1 3.9 10 4.5 4.3 20 9.0 8.7 30 13.5 13.0 40 18.0 17.3 50 22.5 21.7 18 6 1.8 7 2.1 8 2.4 9 2.7 10 3.0 20 6.0 30 9.0 40 12.0 50 15.0 17 6 1.7 7 2.0 8 2.3 9 2.6 10 2.8 20 5.7 30 8.5 40 11.3 50 14.2 10 6 1.0 7 1.2 8 1.3 9 1.5 10 1.7 20 3.3 30 5.0 40 6.7 50 8.3 6 1 0^9 0% 7 1.1 0.9 8 1 1.2 1.1 9 1 1.4 1.2 10 1.5 1.3 20 3.0 2.7 30 4.5 4.0 40 6.0 5.3 50 i 7.5- 6.7 5 6 7 8 9 9.75949 9.75967 9.75985 9.76003 9.76021 9.84657 9.84684 9.84711 9.84738 9.84764 0.15343 0.15316 0.15289 0.15262 0.15236 9.91292 9.91283 9.91274 9.91266 9.91257 55 54 53 52 51 10 11 12 13 14 9.76039 9.76057 9.76075 9.76093 9.76111 9.84791 9.84818 9.84845 9.84872 9.84899 0.15209 0.15182 0.15155 0.15128 0.15101 9.91248 9.91239 9.91230 9.91221 9.91212 50 49 48 47 46 15 16 17 18 19 9.76129 9.76146 9.76164 9.76182 9.76200 9.84925 9.84952 9.84979 9.85006 9.85033 0.15075 0.15048 0.15021 0.14994 0.14967 9.91203 9.91194 9.91185 9.91176 9.91167 45 44 43 42 41 40 39 38 37 36 20 21 22 23 24 9.76218 9.76236 9.76253 9.76271 9.76289 9.85059 9.85086 9.85113 9.85140 9.85166 0.14941 0.14914 0.14887 0.14860 0.14834 9.91158 9.91149 9.91141 9.91132 9.91123 25 26 27 28 29 9.76307 9.76324 9.76342 9.76360 9.76378 9.85193 9.85220 9.85247 9.85273 9.85300 0.14807 0.14780 0.14753 0.14727 0.14700 9.91114 9.91105 9.91096 9.91087 9.91078 35 34 33 32 31 30 31 32 33 34 9.76395 9.76413 9.76431 9.76448 9.76466 9.85327 9.85354 9.85380 9.85407 9.85434 0.14673 0.14646 0.14620 0.14593 0.14566 9.91069 9.91060 9.91051 9.91042 9.91033 30 29 28 27 26 25 24 23 22 21 35 36 37 38 39 9.76484 9.76501 9.76519 9.76537 9.76554 9.85460 9.85487 9.85514 9.85540 9.85567 0.14540 0.14513 0.14486 0.14460 0.14433 9.91023 9.91014 9.91005 9.90996 9.90987 40 41 42 43 44 9.76572 9.76590 9.76607 9.76625 9.76642 9.85594 9.85620 9.85647 9.85674 9.85700 0.14406 0.14380 0.14353 0.14326 0.14300 9.90978 9.90969 9.90960 9.90951 9.90942 20 19 18 17 16 45 46 47 48 49 9.76660 9.76677 9.76695 9.76712 9.76730 9.85727 9.85754 9.85780 9.85807 9.85834 0.14273 0.14246 0.14220 0.14193 0.14166 9.90933 9.90924 9.90915 9.90906 9.90896 15 14 13 12 11 10 9 8 7 6 50 51 52 53 54 9.76747 9.76765 9.76782 9.76800 9.76817 9.85860 9.85887 9.85913 9.85940 9.85967 0.14140 0.14113 0.14087 0.14060 0.14033 9.90887 9.90878 9.90869 9.90860 9.90851 55 56 57 58 59 9.76835 9.76852 9.76870 9.76887 9.76904 9.85993 9.86020 9.86046 9.86073 9.86100 0.14007 0.13980 0.13954 0.13927 0.13900 9.90842 9.90832 9.90823 9.90814 9.90805 5 4 3 2 1 60 9.76922 9.86126 0.13874 9.90796 0 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. “dr / P. P. 54 ^ 528 LOGARimuS OF TRIGONOMETRIC FUNCTIONS, 36 ° / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. 0 9.76922 17 9.86126 '■ 27 0.13874 9.90796 1 9.76939 9.86153 0.13847 9.90787 2 9.76957 18 9.86179 26 0.13821 9.90777 3 9.76974 17 9.86206 27 0.13794 9.90768 4 9.76991 17 18 17 9.86232 26 27 26 0.13768 9.90759 5 6 9.77009 9.77026 9.86259 9.86285 0.13741 0.13715 9.90750 9.90741 7 9.77043 17 9.86312 27 0.13688 9.90731 8 9.77061 18 9.86338 26 0.13662 9.90722 9 9.77078 17 17 17 9.86365 27 27 26 0.13635 9.90713 0 11 9.77095 9.77112 9.86392 9.86418 0.13608 0.13582 9.90704 9.90694 12 9.77130 18 9.86445 27 0.13555 9.90685 13 9.77147 17 9.86471 26 0.13529 9.90676 14 9.77164 17 17 18 9.86498 27 26 27 0.13502 9.90667 15 16 9.77181 9.77199 9.86524 9.86551 0.13476 0.13449 9.90657 9.90648 17 9.77216 17 9.86577 26 0.13423 9.90639 18 9.77233 17 9.86603 26 0.13397 9.90630 19 9.77250 17 18 17 9.86630 27 26 27 0.13370 9.90620 20 21 9.77268 9.77285 9.86656 9.86683 0.13344 0.13317 9.90611 9.90602 22 9.77302 17 9.86709 26 0.13291 9.90592 23 9.77319 17 9.86736 27 0.13264 9.90583 24 9.77336 17 17 17 9.86762 26 27 26 0.13238 9.90574 25 26 9.77353 9.77370 9.86789 9.86815 0.13211 0.13185 9.90565 9.90555 27 9.77387 17 9.86842 27 0.13158 9.90546 28 9.77405 18 9.86868 26 0.13132 9.90537 29 9.77422 17 17 . 17 9.86894 26 27 26 0.13106 9.90527 30 31 9.77439 9.77456 9.86921 9.86947 0.13079 0.13053 9.90518 9.90509 32 9.77473 17 9.86974 27 0.13026 9.90499 33 9.77490 17 9.87000 26 0.13000 9.90490 34 9 77507 17 17 17 9.87027 27 26 26 0.12973 9.90480 35' 36 9.77524 9.77541 9.87053 9.87079 0.12947 0.12921 9.90471 9.90462 37 9.77558 17 9.87106 27 /0. 12894 9.90452 38 9.77575 17 9.87132 26 0.12868 9.90443 39 9.77592 17 17 17 9.87158 26 27 26 0.12842 9.90434 40 41 9.77609 9.77626 9.87185 9.87211 0.12815 0.12789 9.90424 9.90415 42 9.77643 17 9.87238 27 0.12762 9.90405 43 9.77660 17 9.87264 26 0.12736 9.90396 44 9.77677 17 17 17 9.87290 26 27 26 0.12710 9.90386 45 46 9.77694 9.77711 9.87317 9.87343 0.12683 0.12657 9.90377 9.90368 47 9.77728 17 9.87369 26 0.12631 9.90358 48 9.77744 16 9.87396 27 0.12604 ^.90349 49 9.77761 17 17 17 9.87422 26 26 27 0.12578 9.90339 50 51 9.77778 9.77795 9.87448 9.87475 0.12552 0.12525 9.90330 9.90320 52 9.77812 17 9.87501 26 0.12499 9.90311 53 9.77829 17 9.87527 26 0.12473 9.90301 54 9.77846 17 16 17 9.87554 27 26 26 0.12446 9.90292 55 56 9.77862 9.77879 9.87580 9.87606 0.12420 0.12394 9.90282 9.90273 57 9.77896 17 9.87633 27 0.12367 9.90263 58 9.77913 17 9.87659 26 0.12341 9.90254 59 9.77930 17 16 9.87685 26 26 0.12315 9.90244 60 9.77946 9.87711 0.12289 9.90235 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin 1 P. P. 27 2.7 3.2 3.6 4.1 4.5 9.0 13.5 18.0 22.5 26 2.6 3.0 3.5 3.9 4.3 8.7 13.0 17.3 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 1.1 1.2 1.4 1.5 3.0 4.5 6.0 7.5 P. P. 53 ‘ LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 37 ° 529 L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P.P. 0 1 2 3 ' 4 9.77946 9.77963 9.77980 9.77997 9.78013 17 17 17 16 17 17 16 17 17 16 17 17 16 17 17 16 17 16 17 17 16 17 16 17 16 17 16 17 16 17 16 17 16 16 17 16 17 16 16 17 16 17 16 16 17 16 16 16 17 16 16 17 16 16 16 16 17 16 16 16 9.87711 9.87738 9.87764 9.87790 9.87817 27 26 26 27 26 26 26 27 26 26 26 27 26 26 26 26' 27 26 26 26 26 27 26 26 26 26 27 26 26 26 26 26 27 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 26 26 26 27 26 26 26 26 26 26 26 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 9 10 9 10 10 9 10 9 10 10 9 10 9 10 10 9 10 10 9 10 10 9 10 10 9 10 10 9 10 10 10 9 10 10 10 9 10 10 10 9 10 10 10 10 9 10 10 10 10 10 9 10 10 10 10 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 27 6 2.7 7 3.2 8 3.6 9 4.1 10 4.5 20 9.0 30 13.5 40 18.0 50 22.5 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 60 21.7 17 6 1.7 . 7 2.0 8 2.3 9 2.6 10 2.8 20 5.7 30 8.5 40 11.3 50 14.2 16 6 1.6 7 1.9 8 2.1 9 2.4 10 2.7 20 5.3 30 8.0 40 10.7 50 13.3 10 9 6 1 1.0 0.9 7 1.2 1.1 8 1.3 1.2 9 1.5 1.4 10 1.7 1.5 20 3.3 3.0 30 5.0 4.5 40 6.7 6.0 50 8.3 7.5 5 6 7 8 9 9.78030 9.78047 9.78063 9.78080 9.78097 9.87843 9.87869 9.87895 9.87922 9.87948 0.12157 0.12131 0.12105 0.12078 0.12052 9.90187 9.90178 9.90168 9.90159 9.90149 10 11 12 13 14 9.78113 9.78130 9.78147 9.78163 9.78180 9.87974 9.88000 9.88027 9.88053 9.88079 0.12026 0.12000 0.11973 0.11947 0.11921 9.90139 9.90130 9.90120 9.90111 9.90101 15 16 17 18 19 9.78197 9.78213 9.78230 9.78246 9.78263 9.88105 9.88131 9.88158 ■9.88184 9.88210 0.11895 0.11869 0.11842 0.11816 0.11790 9.90091 9.90082 9.90072 9.90063 9.90053 20 21 22 23 24 9.78280 9.78296 9.78313 9.78329 9.78346 9.88236 9.88262 9.88289 9.88315 9.88341 0.11764 0.11738 0.11711 0.11685 0.11659 9.90043 9.90034 9.90024 9.90014 9.90005 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 26 27 28 29 9.78362 9.78379 9.78395 9.78412 9.78428 9.88367 9.88393 9.88420 9.88446 9.88472 0.11633 0.11607 0.11580 0.11554 0.11528 9.89995 9.89985 9.89976 9.89966 9.89956 30 31 32 33 34 9.78445 9.78461 9.78478 9.78494 9.78510 9.88498 9.88524 9.88550 9.88577 9.88603 0.11502 0.11476 0.11450 0.11423 0.11397 9.89947 9.89937 9.89927 9.89918 9.89908 35 36 37 38 39 9.78527 9.78543 9.78560 9.78576 9.78592 9.88629 9.88655 9.88681 9.88707 9.88733 0.11371 0.11345 0.11319 0.11293 0.11267 9.89898 9.89888 9.89879 9.89869 9.89859 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 40 41 42 43 44 9.78609 9.78625 9.78642 9.78658 9.78674 9.88759 9.88786 9.88812 9.88838 9.88864 0.11241 0.11214 0.11188 0.11162 0.11136 9.89849 9.89840 9.89830 9.89820 9.89810 45 46 47 48 49 9.78691 9.78707 9.78723 9.78739 9.78756 9.88890 9.88916 9.88942 9.88968 9.88994 0.11110 0.11084 0.11058 0.11032 0.11006 9.89801 9.89791 9.89781 9.89771 9.89761 50 51 52 53 54 9.78772 9.78788 9.78805 9.78821 9.78837 9.89020 9.89046 9.89073 9.89099 9.89125 0.10980 0.10954 0.10927 0.10901 0.10875 9.89752 9.89742 9.89732 9.89722 9.89712 55 56 57 58 59 9.78853 9.78869 9.78886 9.78902 9.78918 9.89151 9.89177 9.89203 9.89229 9.89255 0.10849 0.10823 0.10797, 0.10771 0.10745 9.89702 9.89693 9.89683 9.89673 9.89663 60 9.78934 9.89281 0.10719 9.89653 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. ~~dr ' P. P. 530 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS, 38 ° / L. Sin. 0 9.78934 1 9.78950 2 9.78967 3 9.78983 4 9.78999 5 9.79015 6 9.79031 7 9.79047 8 9.79063 9 9.79079 10 9.79095 11 9.79111 12 9.79128 13 9.79144 14 9.79160 15 9.79176 16 9.79192 17 9.79208 18 9.79224 19 9.79240 20 9.79256 21 9.79272 22 9.79288 23 9.79304 24 9.79319 25 9.79335 26 9.79351 27 9.79367 28 9.79383 29 9.79399 30 9.79415 31 9.79431 32 9.79447 33 9.79463 34 9.79478 35 9.79494 36 9.79510 37 9.79526 38 9.79542 39 9.79558 40 9.79573 41 9.79589 42 9.79605 43 9.79621 44 9.79636 45 9.79652 46 9.79668 47 9.79684 48 9.79699 49 9.79715 50 9.79731 51 9.79746 52 9.79762 53 9.79778 54 9.79793 55 9.79809 56 9.79825 57 9.79840 58 9.79856 59 9.79872 60 9.79887 L. Cos. L. Cotg. L. Cos. 0.10719 9.89653 0.10693 9.89643 0.10667 9.89633 0.10641 9.89624 0.10615 9.89614 0.10589 9.89604 0.10563 9.89594 0.10537 9.89584 0.10511 9.89574 0.10485 9.89564 0.10459 9.89554 0.10433 9.89544 0.10407 9.89534 0.10381 9.89524 0.10355 9.89514 0.10329 9.89504 0.10303 9.89495 0.10277 9.89485 0.10251 9.89475 0.10225 9.89465 0.10199 9.89455 0.10173 9.89445 0.10147 9.89435 0.10121 9.89425 0.10095 9.89415 0.10069 9.89405 0.10043 9.89395 0.10017 9.89385 0.09991 9.89375 0.09965 9.89364 0.09939 9.89354 0.09914 9.89344 0.09888 9.89334 0.09862 9.89324 0.09836 9.89314 0.09810 9.89304 0.09784 9.89294 0.09758 9.89284 0.09732 9.89274 0.09706 9.89264 0.09680 9.89254 0.09654 9.89244 0.09629 9.89233 0.09603 9.89223 0.09577 9.89213 0.09551 9.89203 0.09525 9.89193 0.09499 9.89183 0.09473 9.89173 0.09447 9.89162 0.09422 9.89152 0.09396 9.89142 0.09370 9.89132 0.09344 9.89122 0.09318 9.89112 0.09292 9.89101 0.09266 9.89091 0.09241 9.89081 0.09215 9.89071 0.09189 9.89060 0.09163 9.890.50 L.Tang. L. Sin. L.Tang. d. c. P. P. 9.89281 9.89307 9.89333 9.89359 9.89385 9.89411 9.89437 9.89463 9.89489 9.89515 9.89541 9.89567 9.89593 9.89619 9.89645 9.89671 9.89697 9.89723 9.89749 9.897 75 9.89801 9.89827 9.89853 9.89879 9.89905 9.89931 9.89957 9.89983 9.90009 9.9003 5 9.90061 9.90086 9.90112 9.90138 9.90164 9.90190 9.90216 9.90242 9.90268 9.90294 9.90320 9.90346 9.90371 9.90397 9.90423 9.90449 9.90475 9.90501 9.90527 9.90553 9.90578 9.90604 9.90630 9.90656 9.90682 9.90708 9.90734 9.90759 9.90785 9.90811 9.90837 L. Cotg, 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 26 25 26 26 26 26 26 26 26 26 26 26 25 26 26 26 26 26 26 26 25 26 26 26 26 26 26 25 26 26 26 ~d. c. 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 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 15 1.5 1.8 2.0 2.3 2.5 5.0 7.5 10.0 12.5 II 1.1 1.3 1.5 1.7 1.8 3.7 5.5 7.3 9.2 9 0.9 1.1 1.2 1.4 1.5 3.0 4.5 6.0 7.5 P. P. 51 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 531 39 ° L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 0 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 60 59 58 57 56 55 54 53 52 51 50 49 48 47 46 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 25 6 2.5 7 2.9 8 3.3 9 3.8 10 4.2 20 8.3 30 12.5 40 16.7 50 20.8 16 6 1.6 7 1.9 8 2.1 9 2.4 10 2.7 20 5.3 30 8.0 40 10.7 50 13.3 15 6 1.5 7 1.8 8 2.0 9 2.3 10 2.5 20 5.0 30 7.5 40 10.0 50 12.5 II 10 6 1.1 1.0 7 1.3 1.2 8 1.5 1.3 9 1.7 1.5 10 1.8 1.7 20 3.7 3.3 30 5.5 5.0 40 7.3 6.7 50 9.2 8.3 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 9.88999 9.88989 9.88978 9.88968 9.88958 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 9.80043 9.80058 9.80074 9.80089 9.80105 9.91095 9.91121 9.91147 9.91172 9.91198 0.08905 0.08879 0.08853 0.08828 0.08802 9.88948 9.88937 9.88927 9.88917 9.88906 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 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 29 28 27 26 25 24 23 22 21 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 35 36 37 38 39 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 40 41 42 43 44 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 45 46 47 48 49 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 10 9 8 7 6 5 4 3 2 1 0 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 9.88531 9.88521 9.88510 9.88499 9.88489 55 56 57 58 59 9.80731 9.80746 9.80762 9.80777 9.80792 9.92253 9.92279 9.92304 9.92330 9.92356 0.07747 0.07721 0.07696 0.07670 0.07644 9.88478 9.88468 9.88457 9.88447 9.88436 60 9.80807 9.92381 0.07619 9.88425 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. ' P. P. 50 ^ 532 LOGAUimMS OF miGONOMETRIC FUNCTIONS. 40 ° ' L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 0 1 2 3 4 9.80807 9.80822 9.80837 9.80852 9.80867 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 14 15 15 15 15 15 15 15 14 15 15 15 15 14 15 15 15 15 14 15 15 14 15 15 15 14 15 15 14 15 15 14 15 15 14 15 14 15 15* 14 15 14 15 14 9.92381 9.92407 9.92433 9.92458 9.92484 26 26 25 26 26 25 26 26 25 26 25 26 26 25 26 26 25 26 25 26 26 25 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 26 25 26 25 26 25 26 25 26 25 26 25 0.07619 0.07593 0.07567 0.07542 0.07516 9.88425 9.88415 9.88404 9.88394 9.88383 10 11 10 11 11 10 11 11 10 11 11 10 11 11 10 11 11 10 11 11 11 10 11 11 11 10 11 11 11 10 11 11 11 11 10 11 11 11 11 11 11 10 11 11 11 11 11 11 11 11 10 11 11 11 11 11 11 11 11 11 60 59 58 57 56 55 54 53 52 51 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 25 6 2.5 7 2.9 8 3.3 9 3.8 10 4.2 20 8.3 30 12.5 40 16.7 60 20.8 15 6 1.5 7 1.8 8 2.0 9 2.3 10 2.5 20 5.0 30 • 7.5 40 10.0 50 12.5 14 6 1.4 7 1.6 8 1.9 9 2.1 10 2.3 20 4.7 30 7.0 40 9.3 50 11.7 II 10 6 1.1 1.0 7 1.3 1.2 8 1.5 1.3 9 1.7 1.5 10 1.8 1.7 20 3.7 3.3 30 5.5 5.0 40 7.3 6.7 50 9.2 8.3 5 6 7 8 9 9.80882 9.80897 9.80912 9.80927 9.80942 9.92510 9.92535 9.92561 9.92587 9.92612 0.07490 0.07465 0.07439 0.07413 0.07388 9.88372 9.88362 9.88351 9.88340 9.88330 10 11 12 13 14 9.80957 9.80972 9.80987 9.81002 9.81017 9.92638 9.92663 9.92689 9.92715 9.92740 0.07362 0.07337 0.07311 0.07285 0.07260 9.88319 9.88308 9.88298 9.88287 9.88276 50 49 48 47 46 15 16 17 18 19 9.81032 9.81047 9.81061 9.81076 9.81091 9.92766 9.92792 9.92817 9.92843 9.92868 0.07234 0.07208 0.07183 0.07157 0.07132 9.88266 9.88255 9.88244 9.88234 9.88223 45 44 43 42 41 20 21 22 23 24 9.81106 9.81121 9.81136 9.81151 9.81166 9.92894 9.92920 9.92945 9.92971 9.92996 0.07106 0.07080 0.07055 0.07029 0.07004 9.88212 9.88201 9.88191 9.88180 9.88169 40 39 38 37 36 25 26 27 28 29 9.81180 9.81195 9.81210 9.81225 9.81240 9.93022 9.93048 9.93073 9.93099 9.93124 0.06978 0.06952 0.06927 0.06901 0.06876 9.88158 9.88148 9.88137 9.88126 9.88115 35 34 33 32 31 30 31 32 33 34 9.81254 9.81269 9.81284 9.81299 9.81314 9.93150 9.93175 9.93201 9.93227 9.93252 0.06850 0.06825 0.06799 0.06773 0.06748 9.88105 9.88094 9.88083 9.88072 9.88061 30 29 28 27 26 35 36 37 38 39 9.81328 9.81343 9.81358 9.81372 9.81387 9.93278 9.93303 9.93329 9.93354 9.93380 0.06722 0.06697 0.06671 0.06646 0.06620 9.88051 9.88040 9.88029 9.88018 9.88007 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 40 41 42 43 44 9.81402 9.81417 9.81431 9.81446 9.81461 9.93406 9.93431 9.93457 9.93482 9.93508 0.06594 0.06569 0.06543 0.06518 0.06492 9.87996 9.87985 9.87975 9.87964 9.87953 45 46 47 48 49 9.81475 9.81490 9.81505 9.81519 9.81534 9.93533 9.93559 9.93584 9.93610 9.93636 0.06467 0.06441 0.06416 0.06390 0.06364 9.87942 9.87931 9.87920 9.87909 9.87898 50 51 52 53 54 9.81549 9.81563 9.81578 9.81592 9.81607 9.93661 9.93687 9.93712 9.93738 9.93763 0.06339 0.06313 0.06288 0.06262 0.06237 9.87887 9.87877 9.87866 9.87855 9.87844 10 9 8 7 6 55 56 57 58 59 9.81622 9.81636 9.81651 9.81665 9.81680 9.93789 9.93814 9.93840 9.93865 9.93891 0.06211 0.06186 0.06160 0.06135 0.06109 9.87833 9.87822 9.87811 9.87800 9.87789 5 4 3 2 1 60 9.81694 9.93916 0.06084 9.87778 0 L. Cos. d. L. Cotg. ”d.~c. L.Tang. L. Sin. ^d7 / P. P. 49 * LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 533 . 41 ° L. Sin. d . L.Tang. d . c . L. Cotg. L. Cos. d . P . P . 0 9.81694 9.93916 0.06084 9.87778 60 1 9.81709 15 9.93942 26 0.06058 9.87767 11 59 2 9.81723 14 9.93967 0.06033 9.87756 11 58 3 9.81738 15 9.93993 26 0.06007 9.87745 11 57 CQ o a. 4 9.81752 14 9.94018 25 26 0.05982 9.87734 11 11 56 6 7 Z.o 3.0 5 9.81767 9.94044 0.05956 9.87723 55 8 3.5 6 9.81781 14 9.94069 Zly 0.05931 9.87712 11 54 9 3.9 7 9.81796 15 9.94095 26 0.05905 9.87701 11 53 10 4.3 8 9.81810 14 9.94120 25 0.05880 9.87690 11 52 20 8.7 9 9.81825 15 14 9.94146 26 25 0.05854 9.87679 11 11 51 30 13.0 10 9.81839 9.94171 0.05829 9.87668 50 40 17.3 11 9.81854 15 9.94197 26 0.05803 9.87657 11 49 50 21.7 12 9.81868 14 9.94222 0.05778 9.87646 11 48 13 9.81882 M 9.94248 26 0.05752 9.87635 11 47 14 9.81897 15 14 9.94273 25 26 0.05727 9.87624 11 11 46 25 15 9.81911 9.94299 0.05701 9.87613 45 6 1 2.5 16 9.81926 15 9.94324 25 0.05676 9.87601 12 44 7 2.9 17 9.81940 14 9.94350 26 0.05650 9.87590 11 43 8 3.3 18 9.81955 15 9.94375 0.05625 9.87579 11 42 9 3.8 19 9.81969 14 14 9.94401 26 25 0.65599 9.87568 11 11 41 10 4.2 20 9.81983 9.94426 0.05574 9.87557 40 20 8.3 21 9.81998 15 9.94452 26 0.05548 9.87546 11 39 30 12.5 22 9.82012 14 9.94477 0.05523 9.87535 11 38 40 16.7 23 9.82026 14 9.94503 26 0.05497 9.87524 11 37 50 20.8 24 9.82041 15 14 9.94528 ^5 26 0.05472 9.87513 11 12 36 25 9.82055 9.94554 0.05446 9.87501 35 26 9.82069 14 9.94579 0.05421 9.87490 11 34 15 27 9.82084 45 9.94604 jiS 0.05396 9.87479 11 33 6 1.5 28 9.82098 14 9.94630 26 0.05370 9.87468 11 32 7 1.8 29 9.82112 14 14 9.94655 25 26 0.05345 9.87457 11 11 31 8 2.0 30 9.82126 9.94681 0.05319 9.87446 30 in 2.3 31 9.82141 15 9.94706 25 0.05294 9.87434 12 29 lU on z«o 32 9.82155 14 9.94732 26 0.05268 9.87423 11 28 Qn O.U 33 9.82169 14 5.94757 25 0.05243 9.87412 11 27 oU /in /.D in A 34 9.82184 15 14 9.94783 26 25 0.05217 9.87401 11 11 26 .'sn lU.U I9 35 9.82198 9.94808 0.05192 9.87390 25 36 9.82212 14 9.94834 26 0.05166 9.87378 12 24 37 9.82226 14 9.94859 25 0.05141 9.87367 11 23 38 9.82240 14 9.94884 25 0.05116 9.87356 11 22 I4 39 9.82255 15 14 9.94910 26 25 0.05090 9.87345 11 11 21 6 >7 1.4 1 fi 40 9.82269 9.94935 0.05065 9.87334 20 8 1.0 1.9 41 9.82283 14 9.94961 26 0.05039 9.87322 12 19 Q 2!i 42 9.82297 14 9.94986 25 0.05014 9.87311 11 18 10 2^3 43 9.82311 14 9.95012 26 0.04988 9.87300 11 17 20 4 7 44 9.82326 15 14 9.95037 25 25 0.04963 9.87288 12 11 16 30 7.0 45 9.82340 9.95062 0.04938 9.87277 15 40 9.3 46 9.82354 14 9.95088 26 0.04912 9.87266 11 14 50 11.7 47 9.82368 14 9.95113 25 0.04887 9.87255 11 13 48 9.82382 14 9.95139 26 0.04861 9.87243 12 12 49 9.82396 14 14 9.95164 25 26 0.04836 9.87232 11 11 11 II 50 9.82410 9.95190 0.04810 9.87221 10 6 1.2 1.1 51 9.82424 14 9.95215 25 0.04785 9.87209 12 9 7 1.4 1.3 52 9.82439 15 9.95240 25 0.04760 9.87198 11 8 8 1.6 1.5 53 9.82453 14 9.95266 26 0.04734 9.87187 11 7 9 1.8 1.7 54 9.82467 14 14 9.95291 25 26 0.04709 9.87175 12 11 6 10 2.0 1.8 55 9.82481 9.95317 0.04683 9.87164 5 20 4.0 3.7 56 9.82495 14 9.95342 25 0.04658 9.87153 11 4 30 6.0 5.5 57 9.82509 14 9.95368 26 0.04632 9.87141 12 3 40 8.0 7.3 58 9.82523 14 9.95393 25 0.04607 9.87130 11 2 50 10.0 9.2 59 9.82537 14 14 9.95418 25 26 0.04582 9.87119 11 12 1 60 9.82551 9.95444 0.04556 9.87107 0 L. Cos. d . L. Cotg. d . c . L.Tang. L. Sin. d . / P . P . 49 ’ 534 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 420 / L. Sin. 0 9.82551 1 9.82565 2 9.82579 3 9.82593 4 9.82607 5 9.82621 6 9.82635 7 9.82649 8 9.82663 9 9.82677 10 9.82691 11 9.82705 12 9.82719 13 9.82733 14 9.82747 15 9.82761 : 16 9.82775 ^ 17 9.82788 18 9.82802 19 9.82816 20 9.82830 21 9.82M4 22 9.82858 23 9.82872 24 9.82885 25 9.82899 26 9.82913 27 9.82927 28 9.82941 29 9.82955 30 9.82968 31 9.82982 32 9.82996 33 9.83010 34 9.83023 35 9.83037 36 9.83051 37 9.83065 38 9.83078 39 9.83092 40 9.83106 41 9.83120 42 9.83133 43 9.83147 44 9.83161 45 9.83174 46 9.83188 47 9.83202 48 9.83215 49 9.83229 50 9.83242 51 9.83256 52 9.83270 53 9.83283 54 9.83297 55 9.83310 56 9.83324 1 57 9.83338 i 58 9.83351 i 59 9.83365 1 60 " 9.83378 l:cos. L.Tang. d. c. L. Cotg. L. Cos. d. 9.95444 0.04556 9.87107 60 9.9^69 25 0.04531 9.87096 11 59 9.95495 26 0.04505 9.87085 11 58 9.95520 25 0.04480 9.87073 12 57 9.95545 25 26 0.04455 9.87062 11 12 56 9.95571 0.04429 9.87050 55 9.95596 25 0.04404 9.87039 11 54 9.95622 26 0.04378 9.87028 11 53 9.95647 25 0.04353 9.87016 12 52 9.95672 25 26 0.04328 9.87005 11 12 51 9.95698 0.04302 9.86993 50 9.95723 25 0.04277 9.86982 11 49 9.95748 25 0.04252 9.86970 12 48 9.95774 26 0.04226 9.86959 11 47 9.95799 25 26 0.04201 9.86947 12 11 46 9.95825 0.04175 9.86936 45 9.95850 25 0.04150 9.86924 12 44 9.95875 25 0.04125 9.86913 11 43 9.95901 26 0.04099 9.86902 11 42 9.95926 25 26 0.04074 9.86890 12 11 41 9.95952 0.04048 9.86879 40 9.95977 25 0.04023 9.86867 12 39 9.96002 25 0.03998 9.86855 12 38 9.96028 26 0.03972 9.86844 11 37 9.96053 25 25 0.03947 9.86832 12 11 36 9.96078 0.03922 9.86821 35 9.96104 26 0.03896 9.86809 12 34 9.96129 25 0.03871 9.86798 11 33 9.96155 26 0.03845 9.86786 12 32 9.96180 25 25 0.03820 9.86775 11 12 31 9.96205 0.03795 9.86763 30 9.96231 26 0.03769 9.86752 11 29 9.96256 25 0.03744 9.86740 12 28 9.96281 25 0.03719 9.86728 12 27 9.96307 26 25 0.03693 9.86717 11 1 0 26 9.96332 0.03668 9.86705 25 9.96357 25 0.03043 9.86694 11 24 9.96383 .26 0.03617 9.86682 12 23 9.90408 25 0.03592 9.86670 12 22 9.96433 25 26 0.03567 9.86659 11 io 21 9.90459 0.03041 9.86647 iz 20 9.96404 25 0.03516 9.86635 12 19 9.96510 26 0.03490 9.86624 11 18 9.96535 25 0.03465 9.86612 12 17 9.96560 25 26 0.03440 9.86600 12 11 16 9.96586 0.03414 9.86589 15 9.96611 25 0.03389 9.86577 12 14 9.96636 25 0.03304 9.86565 12 13 9.96662 26 0.03338 9.86554 11 12 9.96687 25 25 0.03313 9.86642 12 12 11 9.96712 0.03288 9.86530 10 9.96738 26 0.03262 9.86518 12 9 9.96763 25 0.03237 9.86507 11 8 9.96788 25 0.03212 9.86495 12 7 9.96814 26 25 0.03186 9.86483 12 11 6 9.96839 0.03161 9.86472 5 9.96804 2d 0.03136 9.86460 12 4 9.90890 26 0.03110 9.86448 12 3 9.96915 25 0.03085 9.86436 12 2 9.96940 25 26 0.03060 9.86425 11 12 1 9.96966 0.03004 9.86413 _0 P . P. 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 25 6 2.5 7 2.9 8 3.3 9 3.8 10 4.2 20 8.3 30 12.5 40 16.7 50 20.8 (4 6 1.4 7 1.6 8 1.9 9 2.1 10 2.3 20 4.7 30 7.0 40 9.3 50 11.7 6 1.3 7 1.5 8 1.7 9 2.0 10 2.2 20 , 4.3 30 6.5 40 i 8.7 50 i 10.8 12 II 6 1.2 1.1 7 1.4 1.3 8 1.6 1.5 9 1.8 1.7 10 2.0 1.8 20 4.0 3.7 30 6.0 5.5 40 8.0 7.3 50 10.0 9.2 L. Cotg. d. c. L.Tang. L. Sin. ! d. P. P. 47 ° LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 585 43 ° / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 0 1 2 3 4 9.83378 9.83392 9.83405 9.83419 9.83432 14 13 14 13 14 13 14 . 13 14 13 14 13 14 13 14 13 14 13 13 14 13 13 14 13 14 13 13 14 13 13 14 13 13 13 . 14 13 13 13 14 13 13 13 14 13 13 13 13 14 13 13 13 13 13 13 14 13 13 13 13 13 9.96966 9.96991 9.97016 9.97042 9.97067 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 26 25 25 25 26 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 12 12 12 12 11 12 12 12 12 12 12 12 11 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 12 12 12 12 12 12 13 12 12 12 12 12 13 60 59 58 57 56 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 25 6 2.5 7 2.9 8 3.3 9 3.8 10 4.2 20 8.3 30 12.5 40 16.7 50 20.8 14 6 1.4 7 1.6 8 1.9 9 2.1 10 2.3 20 4.7 30 7.0 40 9.3 50 11.7 13 6 1.3 7 1.5 8 1.7 9 2.0 10 2.2 20 4.3 30 6.5 40 8.7 50 10.8 12 II 6 1.2 1.1 7 1.4 1.3 8 1.6 1.5 9 1.8 1.7 10 2.0 1.8 20 4.0 3.7 30 6.0 5.5 40 8.0 7.3 50 10.0 9.2 5 6 7 8 9 9.83446 9.83459 9.83473 9.83486 9.83500 9.97092 9.97118 9.97143 9.97168 9.97193 0.02908 0.02882 0.02857 0.02832 0.02807 9.86354 9.86342 9.86330 9.86318 9.86306 55 54 53 52 51 10 11 12 13 14 9.83513 9.83527 9.83540 9.83554 9.83567 9.97219 9.97244 9.97269 9.97295 9.97320 0.02781 0.02756 0.02731 0.02705 0.02680 9.86295 9.86283 9.86271 9.86259 9.86247 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 15 16 17 18 19 9.83581 9.83594 9.83608 9.83621 9.83634 9.97345 9.97371 9.97396 9.97421 9.97447 0.02655 0.02629 0.02604 0.02579 0.02553 9.86235 9.86223 9.86211 9.86200 9.86188 20 21 22 23 24 9.83648 9.83661 9.83674 9.83688 9.83701 9.97472 9.97497 9.97523 9.97548 9.97573 0.02528 0.02503 0.02477 0.02452 0.02427 9.86176 9.86164 9.86152 9.86140 9.86128 25 26 27 28 29 9.83715 9.83728 9.83741 9.83755 9.83768 9.97598 9.97624 9.97649 9.97674 9.97700 0.02402 0.02376 0.02351 0.02326 0.02300 9.86116 9.86104 9.86092 9.86080 9.86068 30 31 32 33 34 9.83781 9.83795 9.83808 9.83821 9.83834 9.97725 9.97750 9.97776 9.97801 9.97826 0.02275 0.02250 0.02224 0.02199 0.02174 9.86056 9.86044 9.86032 9.86020 9.86008 35 36 37 38 39 9.83848 9.83861 9.83874 9.83887 9.83901 9.97851 9.97877 9.97902 9.97927 9.97953 0.02149 0.02123 0.02098 0.02073 0.02047 9.85996 9.85984 9.85972 9.85960 9.85948 25 24 23 22 21 40 41 42 43 44 9.83914 9.83927 9.83940 9.83954 9.83967 9.97978 9.98003 9.98029 9.98054 9.98079 0.02022 0.01997 0.01971 0.01946 0.01921 9.85936 9.85924 9.85912 9.85900 9.85888 20 19 18 17 16 15 14 13 12 11 45 46 47 48 49 9.83980 9.83993 9.84006 9.84020 9.84033 9.98104 9.98130 9.98155 9.98180 9.98206 0.01896 0.01870 0.01845 0.01820 0.01794 9.85876 9.85864 9.85851 9.85839 9.85827 50 51 52 53 54 9.84046 9.84059 9.84072 9.84085 9.84098 9.98231 9.98256 9.98281 9.98307 9.98332 0.01769 0.01744 0.01719 0.01693 0.01668 9.85815 9.85803 9.85791 9.85779 9.85766 10 9 8 7 6 55 56 57 58 59 9.84112 9.84125 9.84138 9.84151 9.84164 9.98357 9.98383 9.98408 9.98433 9.98458 0.01643 0.01617 0.01592 0.01567 0.01542 ^9.85754 9.85742 9.85730 9.85718 9.85706 5 4 3 2 1 0 60 9.84177 9.98484 0.01516 9.85693 L. Cos. d. L. Cotg. d. G. L.Tang. L. Sin. “dT ' P. P. 46 ° 536 LOGARITHMS OF TRIGONOMETRIC FUNCTIONS. 440 / L. Sin. d. L.Tang. d. c. L. Cotg. L. Cos. d. P. P. 0 1 2 3 4 9.84177 9.84190 9.84203 9.84216 9.84229 13 13 13 13 13 13 14 13 13 13 13 13 13 13 13 12 13 13 13 13 13 13 13 13 13 13 13 12 13 13 13 13 13 13 12 13 13 13 13 12 13 13 13 12 13 13 13 12 13 13 13 12 13 13 12 13 13 12 13 13 9.98484 9.98509 9.98534 9.98560 9.98585 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25 25 26 25 25 25 26 25 25 25 26 25 25 25 26 25 0.01516 0.01491 0.01466 0.01440 0.01415 9.85693 9.85681 9.85669 9.85657 9.85645 12 12 12 12 13 12 12 12 13 12 12 12 13 12 12 13 12 12 13 12 12 . 13 12 12 13 12 13 12 12 13 12 13 12 13 12 12 13 12 13 12 13 12 13 12 13 12 13 12 13 13 12 13 12 13 12 13 13 12 13 12 60 59 58 57 56 26 6 2.6 7 3.0 8 3.5 9 3.9 10 4.3 20 8.7 30 13.0 40 17.3 50 21.7 25 6 2.5 7 2.9 8 3.3 9 3.8 10 4.2 20 8.3 30 12.5 40 16.7 50 20.8 14 6 1.4 7 1.6 8 1.9 9 2.1 10 2.3 20 4.7 30 7.0 40 9.3 50 11.7 13 6 1.3 7 1.5 8 1.7 9 2.0 10 2.2 20 4.3 30 6.5 40 8.7 50 10.8 12 6 1.2 7 1.4 8 1.6 9 1.8 10 2.0 20 4.0 30 6.0 40 8.0 50 10.0 5 6 7 8 9 9.84242 9.84255 9.84269 9.84282 9.84295 9.98610 9.98635 9.98661 9.98686 9.98711 0.01390 0.01365 0.01339 0.01314 0.01289 9.85632 9.85620 9.85608 9.85596 9.85583 55 54 53 52 51 10 11 12 13 14 9.84308 9.84321 9.84334 9.84347 9.84360 9.98737 9.98762 9.98787 9.98812 9.98838 0.01263 0.01238 0.01213 0.01188 0.01162 9.85571 9.85559 9.85547 9.85534 9.85522 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 15 16 17 18 19 9.84373 9.84385 9.84398 9.84411 9.84424 9.98863 9.98888 9.98913 9.98939 9.98964 0.01137 0.01112 0.01087 0.01061 0.01036 9.85510 9.85497 9.85485 9.85473 9.85460 20 21 22 23 24 9.84437 9.84450 9.84463 9.84476 9.84489 9.98989 9.99015 9.99040 9.99065 9.99090 0.01011 0.00985 0.00960 0.00935 0.00910 9.85448 9.85436 9.85423 9.85411 9.85399 25 26 27 28 29 9.84502 9.84515 9.84528 9.84540 9.84553 9.99116 9.99141 9.99166 9.99191 9.99217 0.00884 0.00859 0.00834 0.00809 0.00783 9.85386 9.85374 9.85361 9.85349 9.85337 35 34 33 32 31 30 31 32 33 34 9.84566 9.84579 9.84592 9.84605 9.84618 9.99242 9.99267 9.99293 9.99318 9.99343 0.00758 0.00733 0.00707 0.00682 0.00657 9.85324 9.85312 9.85299 9.85287 9.85274 30 29 28 27 26 35 36 37 38 39 9.84630 9.84643 9.84656 9.84669 9.84682 9.99368 9.99394 9.99419 9.99444 9.99469 0.00632 0.00606 0.00581 0.00556 0.00531 9.85262 9.85250 9.85237 9.85225 9.85212 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 40 41 42 43 44 9.84694 9.84707 9.84720 9.84733 9.84745 9.99495 9.99520 9.99545 9.99570 9.99596 0.00505 0.00480 0.00455 0.00430 0.00404 9.85200 9.85187 9.85175 9.85162 9.85150 45 46 47 48 49 9.84758 9.84771 9.84784 9.84796 9.84809 9.99621 9.99646 9.99672 9.99697 9.99722 0.00379 0.00354 0.00328 0.00303 0.00278 9.85137 9.85125 9.85112 9.85100 9.85087 50 51 52 53 54 9.84822 9.84835 9.84847 9.84860 9.84873 9.99747 9.99773 9.99798 9.99823 9.99848 0.00253 0.00227 0.00202 0.00177 0.00152 9.85074 9.85062 9.85049 9.85037 9.85024 10 9 8 7 6 5 4 3 2 1 0 55 56 57 58 59 9.84885 9.84898 9.84911 9.84923 9.84936 9.99874 9.99899 9.99924 9.99949 9.99975 0.00126 0.00101 0.00076 0.00051 0.00025 9.85012 9.84999 9.84986 9.84974 9.84961 60 9.84949 0.00000 0.00000 9.84949 L. Cos. d. L. Cotg. d. c. L.Tang. L. Sin. d. / P. P. 45 ‘ 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 0 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 337 1 7 6490 2622 907 8 4 0.9 9 0 3 3 9.7 2 2 Here the place of 0 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. 538 LATITUDES AND DEPARTURES. tkO c 1 2 3 4 5 txo c €Q CO 0> CQ Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. fiO 0 ° 1.000 0.000 2.000 0.000 3.000 1 i 0.000 4.000 0.000 5.000 90® Oi 1.000 0.004 2.000 0.009 3.000 1 0.013 4.000 0.017 5.000 89^ Oh 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 |0 1.000 0.017 2.000 0.035 3.000 0.052 3.999 0.070 4.999 89® li 1.000 0.022 2.000 0.044 2.999 0.065 3.999 0.087 4.999 m u 1.000 0.026 1.999 0.052 2.999 0.079 3.999 0.105 4.998 88h u 1.000 0.031 1.999 0.061 2.999 0.092 3.998 0.122 4.998 88i 20 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 87f 2i 0.999 0.044 1.998 0.087 2.997 0.131 3.996 0.174 4.995 87i 2^ 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® 3i 0.998 0.057 1.997 0.113 2.995 0.170 3.994 0.227 4.992 86f 3i 0.998 0.061 1.996 0.122 2.994 0.183 3.993 0.244 4.991 86h 3^ 0.998 0.065 1.996 0.131 2.994 0.196 3.991 0.262 4.989 867 40 0.998 0.070 1.995 0.140 2.993 0.209 3.990 0.279 4.988 86 ® 41- 0.997 0.074 1.995 0.148 2.992 0.222 3.989 0.296 4.986 85^ 4i 0.997 0.078 1.994 0.157 2.991 0.235 3.988 0.314 4.985 85i 4J 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® 5i 0.996 0.092 1.992 0.183 2.987 0.275 3.983 0.366 4.979 84^ 0.995 0.096 1.991 0.192 2.986 0.288 3.982 0.383 4.977 84h 5f 0.995 0.100 1.990 0.200 2.985 0.301 3.980 0.401 4.975 84i 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 83i 6i 0.994 0.113 1.987 0.226 2.981 0.340 3.974 0.453 4.968 8Sh 6^ 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® 0.992 0.126 1.984 0.252 2.976 0.379 3.968 0.505 4.960 82^ 0.991 0.131 1.983 0.261 2.974 0.392 3.966 0.522 4.957 82h 7# 0.991 0.135 1.982 0.270 2.973 0.405 3.963 0.539 4.954 82i 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 8ii 81 0.989 0.148 1.978 0.296 2.967 0.443 3.956 0.591 4.945 8H 8i 0.988 0.152 1.977 0.304 2.965 0.456 3.953 0.608 4.942 81i 90 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 80i 9i 0.986 0.165 1.973 0.330 2.959 0.495 3.945 0.660 4.931 80h 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® lOi 0.984 0.178 1.968 0.356 2.952 0.534 3.936 0.712 4.920 79^ lOi 0.983 0.182 1.967 0.364 2.950 0.547 3.933 0.729 4.916 79h 10^ 0.982 0.187 1.965 0.373 2.947 0.560 3.9.30 0.746 4.912 79i II® 0.982 0.191 1.963 0.382 2.945 0.572 3.927 0.763 4.908 79® Hi 0.981 0.195 1.962 0.390 2.942 0.585 3.923 0.780 4.904 78i lU 0.980 0.199 1.960 0.399 2.940 0.598 3.920 0.797 4.900 78i lU 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 4.886 771 12i 0.976 0.216 1.953 0.433 2.929 0.649 3.905 0.866 4.881 77h m 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 1 1 0.900 4.872 77® b 0 Dep. Lati Dep. Lat. Dep. Lat. Dep. 1 Lat. Dep. bc c <0 a> flO 1 2 3 4 5 CD V CD LATITUDES AND DEPARTURES. 539 Bearing. 5 6 7 8 9 Bearing. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 0° 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 89f Oi 0.044 6.000 0.052 7.000 0.061 8.000 0.070 9.000 0.079 89i Of 0.065 5.999 0.079 6.999 0.092 7.999 0.105 8.999 0.118 89i |0 0.087 5.999 0.105 6.999 0.122 7.999 0.140 8.999 0.157 89° If 0.109 5.999 0.131 6.998 0.153 7.998 0.175 8.998 0.196 88f 0.131 5.998 0.157 6.998 0.183 7.997 0.209 8.997 0.236 88i If 0.153 5.997 0.183 6.997 0.214 7.996 0.244 8.996 0.275 88i 20 0.174 5.996 0.209 6.996 0.244 7.995 0.279 8.995 0.314 88° 2i 0.196 5.995 0.236 6.995 0.275 7.994 0.314 8.993 0.353 87f 2f 0.218 5.994 0.262 6.993 0.305 7.992 0.349 8.991 0.393 87i 2f 0.240 5.993 0.288 6.992 0.336 7.991 0.384 8.990 0.432 87i 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 86f 3i 0.305 5.989 0.366 6.987 0.427 7.985 0.488 8.983 0.549 86i 3f 0.327 5.987 0.392 6.985 0.458 7.983 0.523 8.981 0.589 86i 40 0.349 5.985 0.419 6.983 0.488 7.981 0.558 8.978 0.628 86° 4f 0.371 5.984 0.445 6.981 0.519 7.978 0.593 8.975 0.667 85f 4i 0.392 5.982 0.471 6.978 0.549 7.975 0.628 8.972 0.706 85i 4f 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 0.784 85° 5f 0.458 5.975 0.549 6.971 0.641 7.966 0.732 8.962 0.824 84f 5f 0.479 5.972 0.575 6.968 0.671 7.963 0.767 8.959 0.863 84i 5f 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° Of 0.544 5.964 0.653 6.958 0.762 7.952 0.871 8.947 0.980 83f 6i 0.566 5.961 0.679 6.955 0.792 7.949 0.906 8.942 1.019 83i 6f 0.588 5.958 0.705 6.951 0.823 7.945 0.940 8.938 1.058 83i 70 0.609 5.955 0.731 6.948 0.853 7.940 0.975 8.933 1.097 83° 7f 0.631 5.952 0.757 6.944 0.883 7.936 1.010 8.928 1.136 82f 7i 0.653 5.949 0.783 6.940 0.914 7.932 1.044 8.923 1.175 82i 7f 0.674 5.945 0.809 6.936 0.9H 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° 8f 0.717 5.938 0.861 6.928 1.004 7.917 1.148 8.907 1.291 81f 8i 0.739 5.934 0.887 6.923 1.035 7.912 1.182 8.901 1.330 81i 8f 0.761 5.930 0.913 6.919 1.065 7.907 1.217 8.895 1.369 81i 9° 0.782 5.926 0.939 6.914 1.095 7.902 1.251 8.889 1.408 81° 9f 0.804 5.922 0.964 6.909 1.125 7.896 1.286 8.883 1.447 80f 9f 0.825 5.918 0.990 6.904 1.155 7.890 1.320 8.877 1.485 80i 9f 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° lOf 0.890 5.904 1.068 6.888 1.246 7.872 1.424 8.856 1.601 79f lOf 0.911 5.900 1.093 6.883 1.276 7.866 1.458 8.849 1.640 79i lOf 0.933 5.895 1.119 6.877 1.306 7.860 1.492 8.842 1.679 79i IP 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 78f Hi 0.997 5.880. 1.196 6.859 1.396 7.839 1.595 8.819 1.794 78i Hf 1.018 5.874 1.222 6.853 1.425 7.832 1.629 8.811 1.833 78i (20 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 77f 12i 1.082 5.858 1.299 6.834 1.515 7.810 1.732 8.787 1.948 77i 12f 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° bi> c Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. tai> a to 0> CD 5 6 7 8 9 «D a> CQ 540 LATITUDES AND DEPARTURES. i 2 3 4 5 £ Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. £ 13° 0.974 0.225 1.949 0.450 2.923 0.675 3.897 0.900 4.872 77° 13 i 0.973 0.229 1.947 0.458 2.920 0.688 3.894 0.917 4.867 761 13 i 0.972 0.233 1.945 0.467 2.917 0.700 3.889 0.934 4.862 76 i 13 ^ 0.971 0.238 1.943 0.475 2.914 0.713 3.885 0.951 4.857 761 140 0.970 0.242 1.941 0.484 2.911 0.726 3.881 0.968 4.851 76® 14 i 0.969 0.246 1.938 0.492 2.908 0.738 3.877 0.985 4.846 75 f 14 i 0.968 0.250 1.936 0.501 2.904 0.751 3.873 1.002 4.841 751 751 14 ^ 0.967 0.255 1.934 0.509 2.901 0.764 3.868 1.018 4.835 15® 0.966 0.259 1.932 0.518 2.898 0.776 3.864 1.035 4.830 75® 15 i 0.965 0.263 1.930 0.526 2.894 0.789 3.859 1.052 4.824 741 15 i 0.964 0.267 1.927 0.534 2.891 0.802 3.855 1.069 4.818 741 15 ^ 0.962 0.271 1.925 0.543 2.887 0.814 3.850 1.086 4.812 741 16® 0.961 0.276 1.923 0.551 2.884 0.827 3.845 1.103 4.806 74® 16 i 0.960 0.280 1.920 0.560 2.880 0.839 3.840 1.119 4.800 731 16 i 0.959 0.284 1.918 0.568 2.876 0.852 3.835 1.136 4.794 731 16 f 0.958 0.288 1.915 0.576 2.873 0.865 3.830 1.153 4.788 731 17® 0.956 0.292 1.913 0.585 2.869 0.877 3.825 1.169 4.782 73® 17 i 0.955 0.297 1.910 0.593 2.865 0.890 3.820 1.186 4.775 721 17 i 0.954 0.301 1.907 0.601 2.861 0.902 3.815 1.203 4.769 721 17 ^ 0.952 0.305 1.905 0.610 2.857 0.915 3.810 1.220 4.762 721 18® 0.951 0.309 1.902 0.618 2.853 0.927 3.804 1.236 4.755 72® m 0.950 0.313 1.899 0.626 2.849 0.939 3.799 1.253 4.748 711 18 ^- 0.948 0.317 1.897 0.635 2.845 0.952 3.793 1.269 4.742 711 m 0.947 0.321 1.894 0.643 2.841 0.964 3.788 1.286 4.735 711 (9® 0.946 0.326 1.891 0.651 2.837 0.977 3.782 1.302 4.728 71° 19 i 0.944 0.330 1.888 0.659 2.832 0.989 3.776 1.319 4.720 701 19 i 0.943 0.334 1.885 0.668 2.828 1.001 3.771 1.335 4.713 701 m 0.941 0.338 1.882 0.676 2.824 1.014 3.765 1.352 4.706 701 20 ® 0.940 0.342 1.879 0.684 2.819 1.026 3.759 1.368 4.698 70® 20 i 0.938 0.346 1.876 0.692 2.815 1.038 3.753 1.384 4.691 691 20 i 0.937 0.350 1.873 0.700 2.810 1.051 3.747 1.401 4.683 691 201 0.935 0.354 1.870 0.709 2.805 1.063 3.741 1.417 4.676 691 21 ® 0.934 0.358 1.867 0.717 2.801 1.075 3.734 1.433 4.668 69® 21 i 0.932 0.362 1.864 0.725 2.796 1.087 3.728 1.450 4.660 681 21 i 0.930 0.367 1.861 0.733 2.791 1.100 3.722 1.466 4.652 681 21 ^ 0.929 0.371 1.858 0.741 2.786 1.112 3.715 1.482 4.644 681 22 ® 0.927 0.375 1.854 0.749 2.782 1.124 3.709 1.498 4.636 68 ® 22 i 0.926 0.379 1.851 0.757 2.777 1.136 3.702 1.515 4.628 671 22 i 0.924 0.383 1.848 0.765 2.772 1.148 3.696 1.531 4.619 671 221 0.922 0.387 1.844 0.773 2.767 1.160 3.689 1.547 4.611 671 23® 0.921 0.391 1.841 0.781 2.762 1.172 3.682 1.563 4.603 67® 23 i 0.919 0.395 1.838 0.789 2.756 1.184 3.675 1.579 4.594 661 23 i 0.917 0.399 1.834 0.797 2.751 1.196 3.668 1.595 4.585 661 23 ^ 0.915 0.403 1.831 0.805 2.746 1.208 3.661 1.611 4.577 661 24® 0.914 0.407 1.827 0.813 2.741 1.220 3.654 1.627 4.568 66 ® 24 i 0.912 0.411 1.824 0.821 2.735 1.232 3.647 1.643 4.559 651 24 i 0.910 0.415 1.820 0.829 2.730 1.244 3.640 1.659 4.550 651 651 24 f 0.908 0.419 1.816 0.837 2.724 1.256 3.633 1.675 4.541 25® 0.906 0.423 1.813 0.845 2.719 1.268 3.625 1.690 4.532 65® 25 i 0.904 0.427 1.809 0.853 2.713 1.280 3.618 1.706 4.522 641 25 i 0.903 0.431 1.805 0.861 2.708 1.292 3.610 1.722 4.513 641 25 J 0.901 0.434 1.801 0.869 2.702 1.303 3.603 1.738 4.503 641 26® 0.899 0.438 1.798 0.877 2.696 1.315 3.595 1.753 4.494 64® C Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. CO «> 00 1 2 3 4 5 £ LATITUDES AND DEPARTUKES. 541 Bearing. 5 6 7 8 9 Bearing. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. 130 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 m 1.188 5.828 1.426 6.799 1.664 7.771 1.902 8.742 2.139 76i 140 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^ m 1.252 5.809 1.502 6.777 1.753 7.745 2.003 8.713 2.253 75^ m 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 2.367 741 15i 1.336 5.782 1.603 6.745 1.871 7.709 2.138 8.673 2.405 74i 15^ 1.357 5.775 1.629 6.737 1.900 7.700 2.172 8.662 2.443 741 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 m 16i 1.420 5.753 1.704 6.712 1.988 7.671 2.272 8.629 2.556 73i 161 1.441 5.745 1.729 6.703 2.017 7.661 2.306 8.618 2.594 73i 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 72f 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° I8i 1.566 5.698 1.879 6.648 2.192 7.598 2.505 8.547 2.818 m 1.587 5.690 1.904 6.638 2.221 7.587 2.538 8.535 2.856 7U 18f 1.607 5.682 1.929 6.629 2.250 7.575 2.572 8.522 2.893 71i 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 70f m 1.669 5.656 2.003 6.598 2.337 7.541 2.670 8.484 3.004 70i m 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 20i 1.771 5.611 2.126 6.546 2.480 7.481 2.834 8.416 3.189 691 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 3.262 681 2H 1.833 5.582 2.199 6.513 2.566 7.443 2.932 8.374 3.299 681 21^ 1.853 5.573 2.223 6.502 2.594 7.430 2.964 8.359 3.335 681 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 3.408 671 22i 1.913 5.543 2.296 6.467 2.679 7.391 3.061 8.315 3.444 671 22^ 1.934 5.533 2.320 6.455 2.707 7.378 3.094 8.300 3.480 671 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 3.553 661 23i 1.994 5.502 2.392 6.419 2.791 7.336 3.190 8.254 3.589 661 23f 2.014 5.492 2.416 6.407 2.819 7.322 3.222 8.238 3.625 661 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 3.696 651 24i 2.073 5.460 2.488 6.370 2.903 7.280 3.318 8.190 3.732 651 24^ 2.093 5.449 2.512 6.357 2.931 7.265 3.349 8.173 3.768 651 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 3.839 641 25i 2.153 5.416 2.583 6.318 3.014 7.221 3.444 8.123 3.875 641 25^ 2.172 5.404 2.607 6.305 3.041 7.206 3.476 8.106 3.910 641 26° 2.192 5.393 2.630 6.292 3.069 7.190 3.507 8.089 3.945 64° c XiSit. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. bio <0 tt OQ 5 6 7 8 9 €0 a> OQ 542 LATITUDES AND DEPARTURES, bib c «o OO 1 2 3 4 5 Bearing. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 26® 0.899 0.438 1.798 0.877 2.696 1.315 3.595 1.753 4.494 64® 26i 0.897 0.442 1.794 0.885 2.691 1.327 3.587 1.769 4.484 63i 26i 0.895 0.446 1.790 0.892 2.685 1.339 3.580 1.785 4.475 63i 26f 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 m 27^ 0.885 0.466 1.770 0.931 2.655 1.397 3.540 1.862 4.425 62i 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 6U 28i 0.879 0.477 1.758 0.954 2.636 1.431 3.515 1.909 4.394 61i 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 60f 29i 0.820 0.492 1.741 0.985 2.611 1.477 3.481 1.970 4.352 601 29i 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 59i 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 59i 31® 0.857 0.515 1.714 1.030 2.572 1.545 3.429 2.060 4.286 59® 31i 0.855 0.519 1.710 1.038 2.565 1.556 3.420 2.075 4.275 58i 31'j 0.853 0.522 1.705 1.045 2.558 1.567 3.411 2.090 4.263 58i 3U 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 57i 32i 0.843 0.537 1.687 1.075 2.530 1.612 3.374 2.149 4.217 57i m 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 33f 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 55j 34i 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 54i 35i 0.814 0.581 1.628 1.161 2.442 1.742 3.257 2.323 4.071 54i 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 53J 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 53i 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 2 388 1.816 3.184 2.421 3.980 52f 37i 0.793 0.609 1.587 1.218 2.380 1.826 3.173 2.435 3.967 52i 37J 0.791 0.612 1.581 1.224 2.372 L837 3.163 2.449 3.953 524 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 5U 38i 0.783 0.623 1.565 1.245 2.348 1.868 3.130 2.490 3.913 5U • 38^ 0.780 0.626 1.560 1.252 2.340 1.878 3.120 2.504 3.899 5U 39® 0.777 0.629 1.554 1.259 2.331 1.888 3.109 2.517 3.886 51® bb c Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. bb c 00 ' 2 3 4 5 CO CQ LATITUDES AND DEPARTURES. 543 bib c 5 6 7 8 9 tu> _IC n a> QQ Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. CO flO 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^ 26i 2.231 5.370 2.677 6.265 3.123 7.160 3.570 8.054 4.016 63i 26J 2.250 5.358 2.701 6.251 3.151 7.144 3.601 8.037 4.051 63i 270 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} 27i 2.309 5.322 2.770 6.209 3.232 7.096 3.694 7.983 4.156 62i 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} 28i 2.386 5.273 2.863 6.152 3.340 7.031 3.817 7.909 4.294 6U 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 60f 29i 2.462 5.222 2.955 6.093 3.447 6.963 3.939 7.833 4.432 60i 29f 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° 30i 2.519 5.183 3.023 6.047 3.526 6.911 4.030 7.775 4.534 59} 30i '2.538 5.170 3.045 6.031 3.553 6.893 4.060 7.755 4.568 591 30^ 2.556 5.156 3.068 6.016 3.579 6.875 4.090 7.735 4.602 59i 31° 2.575 5.143 3.090 6.000 3.605 6.857 4.120 7.715 4.635 59° 31i 2.594 5.129 3.113 5.984 3.631 6.839 4.150 7.694 4.669 58f 31i 2.612 5.116 3.135 5.968 3.657 6.821 4.180 7.674 4.702 58i 31^ 2.631 5.102 3.157 5.952 3.683 6.803 4.210 7.653 4.736 581 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} 32i 2.686 5.060 3.224 5.904 3.761 6.747 4.298 7.591 4.836 57i 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^ 33^ 2.760 5.003 3.312 5.837 3.864 6.671 4.416 7.505 4.967 56i 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} 34i 2.832 4.945 3.398 5.769 3.965 6.593 4.531 7.417 5.098 55i 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^ 35i 2.904 4.885 3.484 5.699 4.065 6.513 4.646 7.327 5.226 54i 35J 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} 36i 2.974 4.823 3.569 5.627 4.164 6.431 4.759 7.235 5.353 53i 36^ 2.992 4.808 3.590 5.609 4.188 6.410 4.787 7.211 5.385 53i 37° 3.009 4.792 3.611 5.590 4.213 6.389 4.815 7.188 5.416 53° 37i 3.026 4.776 3.632 5.572 4.237 6.368 4.842 7.164 5.448 52} 37i 3.044 4.760 3.653 5.554 4.261 6.347 4.870 7.140 5.479 52i 371 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} 38i 3.113 4.696 3.735 5.478 4.358 6.261 4.980 7.043 5.603 5U 38f 3.130 4.679 3.756 5.459 4.381 6.239 5.007 7.019 5.633 51} 39° 3.147 4.663 3.776 5.440 4.405 6.217 5.035 6.994 5.664 51° txb c Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. c <0 V CO 5 6 7 8 9 <0 03 CQ 544 LATITUDES AND DEPARTURES. C 1 2 3 4 5 to ca 0> OQ Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. 0} OQ 39° 0.777 0.629 1.554 1.259 2.331 1.888 3.109 2.517 3.886 51° 39i 0.774 0.633 1.549 1.265 2.323 1.898 3.098 2.531 3.872 50f 39i 0.772 0.636 1.543 1.272 2.315 1.908 3.086 2.544 3.858 50i 39^ 0.769 0.639 1.538 1.279 2.307 1.918 3.075 2.558 3.844 50i 40° 0.766 0.643 1.532 1.286 2.298 1.928 3.064 2.571 3.830 50° 40i 0.763 0.646 1.526 1.292 2.290 1.938 3.053 2.584 3.816 49^ 40i 0.760 0.649 1.521 1.299 2.281 1.948 3.042 2.598 3.802 40^ 0.758 0.653 1.515 1.306 2.273 1.958 3.030 2.611 3.788 491 41° 0.755 0.656 1.509 1.312 2.264 1.968 3.019 2.624 3.774 49° 41i- 0.752 0.659 1.504 1.319 2.256 1.978 3.007 2.637 3.759 481 4H 0.749 0.663 1.498 1..325 2.247 1.988 2.996 2.650 3.745 481 41^ 0.746 0.666 1.492 1.332 2.238 1.998 2.984 2.664 3.730 481 42° 0.743 0.669 1.486 1.338 2.229 2.007 2.973 2.677 3.716 48° 42i 0.740 0.672 1.480 1.345 2.221 2.017 2.961 2.689 3.701 471 m 0.737 0.676 1.475 1.351 2.212 2.027 2.949 2.702 3.686 471 m 0.734 0.679 1.469 1.358 2.203 2.036 2.937 2.715 3.672 471 43° 0.731 0.682 1.463 1.364 2.194 2.046 2.925 2.728 3.657 47° 43i 0.728 0.685 1.457 1.370 2.185 2.056 2.913 2.741 3.642 461 43i 0.725 0.688 1.451 1.377 2.176 2.065 2.901 2.753 3.627 461 43f 0.722 0.692 1.445 1.383 2.167 2.075 2.889 2.766 3.612 461 44° 0.719 0.695 1.439 1.389 2.158 2.084 2.877 2.779 3.597 46° 44i 0.716 0.698 1.433 1.396 2.149 2.093 2.865 2.791 3 582' 451 44i 0.713 0.701 1.427 1.402 2.140 2.103 2.853 2.804 3.566 451 44f 0.710 0.704 1.420 1.408 2.131 2.112 2.841 2.816 3.551 451 45° 0.707 0.707 1.414 1.414 2.121 2.121 2.828 2.828 3.536 45° Bear- ing. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. Bear- ing. fZ 5 6 7 8 9 bi> c CO CO 0} CO Dep. Lat. Dep. Lat. Dep. Lat. Dep. Lat. Dep. SQ 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 5.694 501 39i 3.180 4.630 3.816 5.401 4.453 6.173 5.089 6.945 5.725 501 39f 3.197 4.613 3.837 5.382 4.476 6.151 5.116 6.920 5.755 501 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 5.815 491 40i 3.247 4.562 3.897 5.323 4.546 6.083 5.196 6.844 5.845 491 40^ 3.264 4.545 3.917 5.303 4.569 6.061 5.222 6.818 5.875 491 41° 3.280 4.528 3.936 5.283 4.592 6.038 5.2^18 6.792 5.905 49° 41i 3.297 4.511 3.956 5.263 4.615 6.015 5.275 6.767 5.934 481 41i 3.313 4.494 3.976 5.243 4.638 5.992 5.301 6.741 5.964 481 41f 3.329 4.476 3.995 5.222 4.661 5.968 5.327 6.715 5.993 481 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 6.051 471 42i 3.378 4.424 4.054 5.161 4.729 5.898 5.405 6.635 6.080 471 42^ 3.394 4.406 4.073 5.140 4.752 5.875 5.430 6.609 6.109 471 43° 3.410 4.388 4.092 5.119 4.774 5.851 5.456 6.582 6.138 47° 43i 3.426 4.370 4.111 5.099 4.796 5.827 5.481 6.555 6.167 461 43i 3.442 4.352 4.130 5.078 4.818 5.803 5.507 6.528 6.195 461 43f 3.458 4.334 4.149 5.057 4.841 5.779 5.532 6.501 6.224 461 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 6.280 451 44i 3.505 4.280 4.206 4.993 4.906 5.706 5.607 6.419 6.308 451 44f 3.520 4.261 4.224 4.971 4.928 5.681 5.632 6.392 6.336 451 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. CIRCVMFERENCES, AND AREAS. 545 SQUARES, CUBES, SQUARE AND CUBE ROOTS, CIRCUMFERENCES, AND AREAS. No. Square. Cube. 1 Sq. Root. Cu. Root. Reciprocal. Circum. Area. 1 1 1 1.0000 1.0000 1.000000000 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 7.068G 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 69,319 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 166.50 2,206.18 54 2,916 157,464 7.3485 3.7798 .018518519 169.65 2,290.22 55 3,025 166,375 7.4162 3.8030 .018181818 172.79 2,375.83 54G SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 56 3,136 175,616 7.4833 3.8259 .017&57143 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 .011494253 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 28.5.88 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 .0096153^5 326.73 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 9,852.03 113 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 .0087719.30 358.14 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 5.0528 .007751938 405.27 13,069.81 130 16,900 2,197,000 11.4018 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 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 M3.50 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 563.63 25,730.43 548 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square, Cube. 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 14.456: 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 ^,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 6.0277 .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 6.2403 .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 No. 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 .008412969 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 74,022.99 550 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 94,864 95,481 96,100 96,721 97,344 97,969 98,596 99,225 99,856 100,489 101,124 101,761 102,400 103,041 103,684 104,329 104,976 105,625 106,276 106,929 107,584 108,241 108.900 109,561 110.224 110,889 111,556 112.225 112,896 113,569 114,244 114,921 115.600 116,281 116,964 117,649 118,336 119.025 119,716 • 120,409 121,104 121,801 122,500 123,201 123,904 124,609 125,316 126.025 126,736 127,449 128,164 128,881 129.600 130,321 131,044 131,769 132,496 133.225 133,956 134,689 135,424 136,161 136.900 29,218,112 29,503,629 29.791.000 30,080,231 30,371,328 30,664,297 30,959,144 31.255.875 31,554,496 31,855,013 32,157,432 32,461,759 32.768.000 33,076,161 33,386,248 33,698,267 34,012,224 34.328.125 34.645.976 34,965,783 35,287,552 35,611,289 35.937.000 36,264,691 36,594,368 36,926,037 37,259,704 37,595,375 37,933,056 38,272,753 38,614,472 38,958,219 39.304.000 39,651,821 40,001,688 40,353,607 40,707,584 41,063,625 41,421,736 41,781,923 42,144,192 42,508,549 42.875.000 43,243,551 43,614,208 43.986.977 44,361,864 44.738.875 45,118,016 45,499,293 45,882,712 46,268,279 46.656.000 47,045,881 47,437,928 47,832,147 48.228,544 48.627.125 49,027,896 49,430,863 49,836,032 50,243,409 50.653.000 17.5499 17.5784 17.6068 17.6352 17.6635 17.6918 17.7200 17.7482 17.7764 17.8045 17.8326 17.8606 17.8885 17.9165 17.9444 17.9722 18.0000 18.0278 18.0555 18.0831 18.1108 18.1384 18.1659 18.1934 18.2209 18.2483 18.2757 18.3030 18.3303 18.3576 18.3848 18.4120 18.4391 18.4662 18.4932 18.5203 18.5472 18.5742 18.6011 18.6279 18.6548 18.6815 18.7083 18.7350 18.7617 18.7883 18.8149 18.8414 18.8680 18.8944 18.9209 18.9473 18.9737 19.0000 19.0263 19.0526 19.0788 19.1050 19.1311 19.1572 19.1833 19.2094 19.2354 6.7533 6.7606 6.7679 6.7752 6.7824 6.7897 6:7969 6.8041 6.8113 6.8185 6.8256 6.8328 6.8399 6.8470 6.8541 6.8612 6.8683 6.8753 6.8824 6.8894 6.8964 6.9034 6.9104 6.9174 6.9244 6.9313 6.9382 6.9451 6.9521 6.9589 6.9658 6.9727 6.9795 6.9864 6.9932 7.0000 7.0068 7.0136 7.0203 7.0271 7.0338 7.0406 7.0473 7.0540 7.0607 7.0674 7.0740 7.0807 7.0873 7.0940 7.1006 7.1072 7.1138 7.1204 7.1269 7.1335 7.1400 7.1466 7.1531 7.1596 7.1661 7.1726 7.1791 .003246753 .003236246 .003225806 .003215434 .003205128 .003194888 .003184713 .003174603 .003164557 .003154574 .003144654 .003134796 .003125000 .003115265 .003105590 .003095975 .003086420 .003076923 .003067485 .003058104 .003048780 .003039514 .003030303 .003021148 .003012048 .003003003 .002994012 .002985075 .002976190 .002967359 .002958580 .002949853 .002941176 .002932551 .002923977 .002915452 .002906977 .002898551 .002890173 .002881844 .002873563 .002865330 .002857143 .002849003 .002840909 .002832861 .002824859 .002816901 .002808989 .002801120 .002793296 .002785515 .002777778 .002770083 .002762431 .002754821 .002747253 .002739726 .002732240 .002721796 .002717391 .002710027 .002702703 967.61 970.75 973.89 977.04 980.18 983.32 986.46 989.60 992.74 995.88 999.03 1,002.17 1,005.31 1,008.45 1,011.59 1.014.73 1,017.88 1,021.02 1,024.16 1,027.30 1,030.44 1.033.58 1.036.73 1,039.87 1,043.01 1,046.15 1,049.29 1,052.43 1.055.58 1,058.72 1,061.86 1,065.00 1,068.14 1,071.28 1.074.42 1,077.57 1,080.71 1,083.85 1,086.99 1,090.13 1.093.27 1.096.42 1,099.56 1,102.70 1,105.84 1,108.98 1,112.12 1.115.27 1,118.41 1,121.55 1,124.69 1,127.83 1,130.97 1.134.11 1,137.26 1,140.40 1,143.54 1,146.68 1,149.82 1,152.96 1.156.11 1,159.25 1,162.39 j 74.506.01 74,990.60 75,476.76 75,964.50 76.453.80 76.944.67 77.437.12 77.931.13 78.426.72 78.923.88 1 79,422.60 1 79,922.90 ! 80,424.77 i 80,928.21 81.433.22 81.939.80 82.447.96 82.957.68 83,468.98 83.981.84 84.496.28 85.012.28 85.529.86 86.049.01 86.569.73 87.092.02 87.615.88 88.141.31 88.668.31 89.196.88 89.727.03 90.258.74 90.792.03 91.326.88 91.863.31 92.401.31 92.940.88 93,482.02 94,024.73 94,569.01 95.114.86 95.662.28 96.211.28 96.761.84 97.313.97 97.867.68 98,422.96 98.979.80 99.538.22 100,098.21 100,659.77 101,222.90 101.787.60 102,353.87 102,921.72 103,491.13 104,062.12 104,634.67 105,208.80 105,7&4.49 106,361.76 106.940.60 107,521.01 CIRCUMFERENCES, AND AREAS. 551 No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 371 ,372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 137.641 138,384 139.129 139,876 140.625 141,376 142.129 142,884 143.641 144,400 145,161 145,924 146,689 147,456 148.225 148,996 149,769 150,544 151,321 152.100 152,881 153,664 154,449 155,236 156,025 156,816 157,609 158,404 159,201 160,000 160,801 161,604 162,409 163,216 164,-625 164,836 165,649 166,464 167,281 168.100 168,921 169,744 170,569 171,396 172.225 173,056 173,889 174,724 175,561 -176,400 177,241 178,084 178,929 179,776 180.625 181,476 182,329 183,184 184,041 184,900 185,761 186,624 187,489 51,064,811 51,478,848 51,895,117 52.313.624 52.734.375 53.157.376 53,582,633 54,010,152 54,439,939 54.872.000 55,306,341 55,742,968 56,181,887 56,623,104 57.066.625 57.512.456 57,960,603 58,411,072 58,863,869 59.319.000 59,776,471 60,236,288 60.698.457 61,162,984 61,629,875 62,099,136 62,570,773 63,044,792 63,521,199 64,000,000 64,481,201 64,964,808 65,450,827 65,939,264 66,430,125 66,923,416 67,419,143 67,917,312 68,417,929 68.921.000 69,426,531 69,934,528 70,444,997 70,957,944 71,473,375 71,991,296 72,511,713 73,034,632 73,560,059 74.088.000 74,618,461 75,151,448 75,686,967 76,225,024 76.765.625 77,308,776 77,854,483 78,402,752 78,953,589 79.507.000 80,062,991 80,621,568 81,182,737 19.2614 19.2873 19.3132 19.3391 19.3649 19.3907 19.4165 19.4422 19.4679 19.4936 19.5192 19.5448 19.5704 19.5959 19.6214 19.6469 19.6723 19.6977 19.7231 19.7484 19.7737 19.7990 19.8242 19.8494 19.8746 19.8997 19.9249 19.9499 19.9750 20.0000 20.0250 20.0499 20.0749 20.0998 20.1246 20.1494 20.1742 20.1990 20.2237 20.2485 20.2731 20.2978 20.3224 20.3470 20.3715 20.3961 20.4206 20.4450 20.4695 20.4939 20.5183 20.5426 20.5670 20.5913 20.6155 20.6398 20.6640 20.6882 20.7123 20.7364 20.7605 20.7846 20.8087 7.1855 7.1920 7.1984 7.2048 7.2112 7.2177 7.2240 7.2304 7.2368 7.2432 7.2495 7.2558 7.2622 7.2685 7.2748 7.2811 7.2874 7.2936 7.2999 7.3061 7.3124 7.3186 7.3248 7.3310 7.3372 7.3434 7.3496 7.3558 7.3619 7.3681 7.3742 7.3803 7.3864 7.3925 7.3986 7.4047 7.4108 7.4169 7.4229 7.4290 7.4350 7.4410 7.4470 7.4530 7.4590 7.4650 7.4710 7.4770 7.4829 7.4889 7.4948 7.5007 7.5067 7.5126 7.5185 7.5244 7.5302 7.5361 7.5420 7.5478 7.5537 7.5595 7.5654 .002695418 .002688172 .002680965 .002673797 .002666667 .002659574 .002652520 .002645503 .002638521 .002631579 .002624672 .002617801 .002610966 .002604167 .002597403 .002590674 .002583979 .002577320 .002570694 .002564103 .002557545 .002551020 .002544529 .002538071 .002531646 .002525253 .002518892 .002512563 .002506266 .002500000 .002493766 .002487562 .002481390 .002475248 .002469136 .002463054 .002457002 .002450980 .002444988 .002439024 .002433090 .002427184 .002421308 .002415459 .002409639 .002406846 .002398082 .002392344 .002386635 .002380952 .002375297 .002369668 .002364066 .002358491 .002352941 .002347418 .002341920 .002336449 .002331002 .002325581 .002320186 .002314815 .002309469 1,165.53 1,168.67 1.171.81 1,174.96 1,178.10 1,181.24 1,184.38 1,187.52 1,190.66 1.193.81 1,196.95 1,200.09 1,203.23 1,206.37 1,209.51 1.212.65 1,215.80 1,218.94 1,222.08 1,225.22 1,228.36 1.231.50 1.234.65 1,237.79 1,240.93 1,244.07 1,247.21 1.250.35 1.253.50 1,256.64 1,259.78 1,262.92 1,266.06 1,269.20 1.272.35 1,275.49 1,278.63 1,281.77 1,284.91 1,288.05 1.291.19 1,294.34 1,297.48 1,300.62 1,303.76 1,306.90 1.310.04 1.313.19 1,316.33 1,319.47 1,322.61 1,325.75 1,328.89 1.332.04 1,335.18 1,338.32 1,341.46 1,344.60 1,347.74 1,350.88 1,354.03 1,357.17 1,360.31 108,102.99 108.686.54 109.271.66 109.858.35 110.446.62 111.036.45 111.627.86 112,220.83 112.815.38 113,411.49 114.009.18 114,608.44 115,209.27 115.811.67 116,415.64 117.021.18 117,628.30 118,236.98 118.847.24 119.459.06 120.072.46 120.687.42 121,303.96 121.922.07 122.541.75 123,163.00 123,785.82 124,410.21 125,036.17 125,663.71 126,292.81 126,923.48 127.555.73 128.189.55 128,824.93 129,461.89 130.100.42 130,740.52 131.382.19 132.025.43 132.670.24 133.316.63 133,964.58 134.614.10 135.265.20 135.917.86 136.572.10 137.227.91 137,885.29 138.544.24 139.204.76 139.866.85 140.530.51 141.195.74 141,862.54 142.530.92 143.200.86 143.872.38 144.545.46 145,220.12 145.896.35 146,574.15 147.253.52 552 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. *' Circum. Area. 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 171 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 188,356 189.225 190,096 190,969 191,844 192,721 193.600 194,481 195,364 196,249 197,136 198.025 198,916 199,809 200,704 201.601 202,500 203,401 204,304 205,209 206,116 207.025 207,936 208,849 209,764 210,681 211,600 212,521 213,444 214,369 215,296 216.225 217,156 218,089 219.024 219,961 220,900 221,841 222,784 223,729 224,676 225,625 226,576 227,529 228,484 229,441 230,400 231,361 232,324 233,289 234,256 235.225 236,196 237,169 238,144 239,121 240,100 241,081 242,064 243,049 244.036 245.025 246,016 81,746,504 82,312,875 82,881,856 83,453,453 84,027,672 84,604,519 85.184.000 85,766,121 86,350,888 86,938,307 87,528,384 88,121,125 88,716,536 89,314,623 89,915,392 90,518,849 91.125.000 91,733,851 92,345,408 92,959,677 93,576,664 94,196,375 94,818,816 95,443,993 96,071,912 96,702,579 97.336.000 97,972,181 98,611,128 99,252.847 99,897,344 100,544,625 101,194,696 101,847,563 102,503,232 103,161,709 103.823.000 104,487,111 105,154,048 105,823,817 106,496,424 107,171,875 107,850,176 108,531,333 109,215,352 109,902,239 110.592.000 111,284,641 111.980.168 112,678,587 113,379,904 114,084,125 114,791,256 115,501,303 116,214,272 116.930.169 117.649.000 118,370,771 119,095,488 119,823,157 120,553,784 121,287,375 122,023,936 20.8327 20.8567 20.8806 20.9045 20.9284 20.9523 20.9762 21.0000 21.0238 21.0476 21.0713 21.0950 21.1187 21.1424 21.1660 21.1896 21.2132 21.2368 21.2603 21.2838 21.3073 21.3307 21.3542 21.3776 21.4009 21.4243 21.4476 21.4709 21.4942 21.5174 21.5407 21.5639 21.5870 21.6102 21.6333 21.6564 21.6795 21.7025 21.7256 21.7486 21.7715 21.7945 21.8174 21.8403 21.8632 21.8861 21.9089 21.9317 21.9545 21.9775 22.0000 22.0227 22.0454 22.0681 22.0907 22.1133 22.1359 22.1585 22.1811 22.2036 22.2261 22.2486 22.2711 7.5712 7.5770 7.5828 7.5886 7.5944 7.6001 7.6059 7.6117 7.6174 7.6232 7.6289 7.6346 7.6403 7.6460 7.6517 7.6574 7.6631 7.6688 7.6744 7.6801 7.6857 7.6914 7.6970 7.7026 7.7082 7.7188 7.7194 7.7250 7.7306 7.7362 7.7418 7.7473 7.7529 7.7584 7.7639 7.7695 7.7750 7.7805 7.7860 7.7915 7.7970 7.8025 7.8079 7.8134 7.8188 7.8243 7.8297 7.8352 7.8406 7.8460 7.8514 7.8568 7.8622 7.8676 7.8730 7.8784 7.8837 7.8891 7.8944 7.8998 7.9051 7.9105 7.9158 .002304147 .002298851 .002293578 .002288330 .002283105 .002277904 .002272727 .002267574 .002262443 .002257336 .002252252 .002247191 .002242152 .002237136 .002232143 .002227171 .002222222 .002217295 .002212389 .002207506 .002202643 .002197802 .002192982 .002188184 .002183406 .002178649 .002173913 .002169197 .002164502 .002159827 .002155172 .002150538 .002145923 .002141328 .002136752 .002132196 .002127660 .002123142 .002118644 .002114165 .002109705 .002105263 .002100840 .002096486 .002092050 .002087683 .002083333 .002079002 .002074689 .002070393 .002066116 .002061856 .002057613 .002053388 .002049180 .002044990 .002040816 .002036660 .002032520 .002028398 .002024291 .002020292 .002016129 1,363.45 1,366.59 1.369.73 1,372.88 1,376.02 1,379.16 1,382.30 1,385.44 1.388.58 1.391.73 1,394.87 1,398.01 1,401.15 1,404.29 1,407.43 1.410.58 1,413.72 1,416.86 1,420.00 1,423.14 1,426.28 1.429.42 1,432.57 1,435.71 1,438.85 1,441.99 1,445.13 1.448.27 1.451.42 1,454.56 1,457.70 1,460.84 1,463.98 1,467.12 1.470.27 1,473.41 1,476.55 1,479.69 1,482.83 1,485.97 1.489.11 1,492.26 1,495.40 1,498.54 1,501.68 1,504.82 1.507.96 1.511.11 1,514.25 1.517.39 1,520.53 1,523.67 1.526.81 1.529.96 1,533.10 1,536.24 1,539.38 1,542.52 1,545.66 1.548.81 1,551.95 1,555.09 1,558.23 147.934.46 148.616.97 149.301.05 149.986.70 150,673.93 151.362.72 152.053.08 152.745.02 153.438.53 154.133.60 154.830.25 155.528.47 156.228.26 156.929.62 157.632.55 158.337.06 159.043.13 159.750.77 160,459.99 161.170.77 161.883.13 162.597.05 163.312.55 164.029.62 164.748.26 165.468.47 166,190.25 166.913.60 167.638.53 168.365.02 169.093.08 169.822.72 170,553.92 171.286.70 172.021.05 172.756.97 173.494.45 174,233.51 174.974.14 175,716.35 176,460.12 177.205.46 177,952.37 178.700.86 179,450.91 180.202.54 180.955.74 181.710.50 182,466.84 183.224.75 183.984.23 184,745.28 185,507.90 186.272.10 187.037.86 187,805.19 188.574.10 189,344.57 190.116.62 190.890.24 191,665.43 192,442.18 193.220.51 CIRCUMFERENCES, AND AREAS. 553 No. Square. * Cube . Sq. Root. Cu. Root. Reciprocal. Circum . Area. 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 5^5 556 557 558 559 247.009 248.004 249,001 250.000 251.001 252.004 253.009 254,016 255,025 256,036 257,049 258,064 259,081 260,100 261,121 262,144 263,169 264,196 265.225 266,256 267,289 268,324 269,361 270.400 271,411 272,484 273,529 274,576 275,625 276,676 277,729 278,784 279,841 280,900 281,961 283.024 284,089 285,156 286.225 287,296 288,369 289,444 290,521 291.600 292,681 293,764 294,849 295,936 297.025 298,116 299,209 300,304 301.401 302,500 303.601 304,704 305,809 306,916 308.025 309,136 310,249 311,364 312,481 122 , 763,473 123 , 505,992 124 , 251,499 125 , 000,000 125 , 751,501 126 , 506,008 127 , 263,527 128 , 024,064 128 . 787.625 1 ^ 9 , 554,216 130 , 323,843 131 , 096,512 131 , 872.229 132 . 651.000 133 . 432.831 134 , 217,728 135 , 005,697 135 , 796,744 136 . 590.875 137 , 388,096 138 , 188,413 138 . 991.832 139 , 798,359 140 . 608.000 141 , 420,761 142 , 236,648 143 , 055,667 143 , 877,824 144 , 703,125 145 , 531,576 146 . 363.183 147 , 197,952 148 , 035,889 148 . 877.001 149 , 721,291 150 , 568,768 151 , 419,437 152 , 273,304 153 , 130,375 153 , 990,656 154 , 854,153 155 , 720,872 156 , 590,819 157 . 464.000 158 , 340,421 159 , 220,088 160 , 103,007 160 . 989.184 161 . 878.625 162 , 771,336 163 , 667,323 164 , 566,592 165 , 469,149 166 . 375.000 167 , 284,151 168 , 196,608 169 , 112,377 170 , 031,464 170 . 953.875 171 , 879,616 172 , 808,693 173 , 741,112 174 , 676,879 22.2935 22.3159 22.3383 22.3607 22.3830 22.4054 22.4277 22.4499 22.4722 22.4944 22.5167 22.5389 22.5610 22.5832 22.6053 22.6274 22.6495 22.6716 22.6936 22.7156 22.7376 22.7596 22.7816 22.8035 22.8254 22.8473 22.8692 22.8910 22.9129 22.9347 22.9565 22.9783 23.0000 23.0217 23.0434 23.0651 23.0868 23.1084 23.1301 23.1517 23.1733 23.1948 23.2164 23.2379 23.2594 23.2809 23.3024 23.3238 23.3452 23.3666 23.3880 23.4094 23.4307 23.4521 23.4734 23.4947 23.5160 23.5372 23.5584 23.5797 23.6008 23.6220 23.6432 7.9211 7.9264 7.9317 7.9370 7.9423 7.9476 7.9528 7.9581 7.9634 7.9686 7.9739 7.9791 7.9843 7.9895 7.9948 8.0000 8.0052 8.0104 8.0156 8.0208 8.0260 8.0311 8.0363 8.0415 8.0466 8.0517 8.0569 8.0620 8.0671 8.0723 8.0774 8.0825 8.0876 8.0927 8.0978 8.1028 8.1079 8.1130 8.1180 8.1231 8.1281 8.1332 8.1382 8.1433 8.1483 8.1533 8.1583 8.1633 8.1683 8.1733 8.1783 8.1833 8.1882 8.1932 8.1982 8.2031 8.2081 8.2130 8.2180 8.2229 8.2278 8.2327 8.2377 .002012072 .002008032 .002004008 .002000000 .001996008 .001992032 .001988072 .001984127 .001980198 .001976285 .001972387 .001968504 .001964637 .001960785 . 00 L 956947 .001953125 .001949318 .001945525 .001941748 .001937984 .001934236 .001930502 .001926782 .001923077 .001919386 .001915709 .001912046 .001908397 .001904762 .001901141 .001897533 .001893939 .001890359 .001886792 .001883239 .001879699 .001876173 .001872659 .001869159 .001865672 .001862197 .001858736 .001855288 .001851852 .001848429 .001845018 .001841621 .001838235 .001834862 .001831502 .001828154 .001824818 .001821494 .001818182 .001814882 .001811594 .001808318 .001805054 .001801802 .001798561 .001795332 .001792115 .001788909 1 , 561.37 1 , 564.51 1 . 567.65 1 , 570.80 1 , 573.94 1 , 577.08 1 , 580.22 1 , 583.36 1 . 586.50 1 . 589.65 1 , 592.79 1 , 595.93 1 , 599.07 1 , 602.21 1 , 605.35 1 . 608.50 1 , 611.64 1 , 614.78 1 , 617.92 1 , 621.06 1 , 624.20 1 . 627.34 1 , 630.49 1 , 633.63 1 , 636.77 1 , 639.91 1 , 643.05 1 . 646.19 1 . 649.34 1 , 652.48 1 , 655.62 1 , 658.76 1 , 661.90 1 . 665.04 1 . 668.19 1 , 671.33 1 , 674.47 ], 677.61 1 , 680.75 1 , 683.89 1 . 687.04 1 , 690.18 1 , 693.32 1 , 696.46 1 , 699.60 1 , 702.74 1 . 705.88 1 , 709.03 1 , 712.17 1 , 715.31 1 , 718.45 1 , 721.59 1 . 724.73 1 . 727.88 1 , 731.02 1 , 734.16 1 , 737.30 1 , 740.44 1 , 743.58 1 . 746.73 1 , 749.87 1 , 753.01 1 , 756.15 194 , 000.41 194 . 781.89 195 . 564.93 196 , 349.54 197 , 135.72 197 . 923.48 198 . 712.80 199 . 503.70 200 . 296.17 201 . 090.20 201 . 885.81 202 , 682.99 203 . 481.74 204 , 282.06 205 . 083.95 205 . 887.42 206 , 692.45 207 , 499.05 208 , 307.23 209 . 116.97 209 , 928.29 210 . 741.18 211 , 555.63 212 , 371.66 213 . 189.26 214 . 008.43 214 , 829.17 215 . 651.49 216 , 475.37 217 . 300.82 218 . 127.85 218 . 956.44 219 , 786.61 220 , 618.34 221 . 451.65 222 , 286.53 223 . 122.98 223 . 961.00 224 . 800.59 225 . 641.75 226 , 484.48 227 . 328.79 228 . 174.66 229 , 022.10 229 , 871.12 230 . 721.71 231 . 573.86 232 . 427.59 233 . 282.89 234 . 139.76 234 . 998.20 235 . 858.21 236 . 719.79 237 . 582.94 238 . 447.67 239 . 313.96 240 . 181.83 241 . 051.26 241 . 922.27 242 , 794.85 243 . 668.99 244 . 544.71 245 . 422.00 554 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root . Cu. Root Reciprocal. Circum. Area. 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 .578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 313,600 314,721 315,844 316,969 318,096 319.225 320,356 321,489 322.624 323,761 324,900 326,041 327,184 328,329 329,476 330.625 331,776 332,929 334,084 335,241 336.400 337,561 338,724 339,889 341,056 342.225 343,396 344,569 345,744 346,921 348.100 349,281 350,464 351,649 352,836 354.025 355,216 356,409 357,604 358,801 360,000 361,201 362,404 363,609 364,816 366.025 367,236 368,449 369,664 370,881 372.100 373,321 374,544 375,769 376,996 378.225 379,456 380,689 381,924 383,161 384.400 385,641 386,884 175.616.000 176,558,481 177,504,328 178,453,547 179,406,144 180,362,125 181,321,496 182,284,263 183,250,432 184,220,009 185.193.000 186,169,411 187,149,248 188,132,517 189,119,224 190,109,375 191,102,976 192,100,033 193,100,552 194,104,539 195.112.000 196,122,941 197,137,368 198,155,287 199,176,704 200,201,625 201,230,056 202,262,003 203,297,472 204,336,469 205.379.000 206,425,071 207,474,688 208,527,857 209,584,584 210,644,875 211,708,736 212,776,173 213,847,192 214,921,799 216,000,000 217,081,801 218,167,208 219,256,227 220,348,864 221,44.5,125 222,545,016 223.648.543 224,755,712 225,866,529 226.981.000 228,099,131 229,220,928 230,346,397. 231.475.544 232,608,375 233,744,896 234,885,113 236,029,032 237,176,659 238.328.000 239,483,061 240,641,848 23.6643 23.6854 23.7065 23.7276 23.7487 23.7697 23.7908 23.8118 23.8328 23.8537 23.8747 23.8956 23.9165 23.9374 23.9583 23.9792 24.0000 24.0208 24.0416 24.0624 24.0832 24.1039 24.1247 24.1454 24.1661 24.1868 24.2074 24.2281 24.2487 24.2693 24.2899 24.3105 24.3311 24.3516 24.3721 24.3926 24.4131 24.4336 24.4540 24.4745 24.4949 24.5153 24.5357 24.5561 24.5764 24.5968 24.6171 24.6374 24.6577 24.6779 24.6982 24.7184 24.7386 24.7588 24.7790 24.7992 24.8193 24.8395 24.8596 24.8797 24.8998 24.9199 24.9399 8.2426 8.2475 8.2524 8.2573 8.2621 8.2670 8.2719 8.2768 8.2816 8.2865 8.2913 8.2962 8.3010 8.3059 8.3107 8.3155 8.3203 8.3251 8.3300 8.3348 8.3396 8.3443 8.3491 8.3539 8.3587 8.3634 8.3682 8.3730 8.3777 8.3825 8.3872 8.3919 8.3967 8.4014 8.4061 8.4108 8.4155 8.4202 8.4249 8.4296 8.4343 8.4390 8.4437 8.4484 8.4530 8.4577 8.4623 8.4670 8.4716 8.4763 8.4809 8.4856 8.4902 8.4948 8.4994 8.5040 8.5086 8.5132 8.5178 8.5224 8.5270 8.5316 8.5362 .001785714 .001782531 .001779359 .001776199 .001773050 .001769912 .001766784 .001763668 .001760563 .001757469 .001754386 .001751313 .001748252 .001745201 .001742164 .001739130 .001736111 .001733102 .001730104 .001727116 .001724138 .001721170 .001718213 .001715266 .001712329 .001709402 .001706485 .001703578 .001700680 .001697793 .001694915 .001692047 .001689189 .001686341 .001683502 .001680672 .001677852 .001675042 .001672241 .001669449 .001666667 .001663894 .001661130 .001658375 .001655629 .001652893 .001650165 .001047446 .001644737 .001642036 .001639344 .001636661 .001633987 .001631321 : .001628664 : .001626016 ; .001623377 ; .001620746 : .001618123 : .001615509 : .001612903 ] .001610306 ] .001607717 ] 1 1,759.29 246,300.86 1,762.43 247,181.30 1,765.58 248,063.30 1,768.72 248,946.87 1,771.86 249,832.01 1,775.00 250,718.73 1,778.14 251,607.01 1,781.28 252,496.87 1.784.42 253,388.30 1,787.57 254,281.29 1,790.71 255,175.86 1,793.85 256,072.00 1,796.99 256,969.71 1,800.13 257,868.99 1.803.27 258,769.85 1.806.42 259,672.27 1,809.56 260,576.26 1,812.70 261,481.83 1,815.84 262,388.96 1,818.98 263,297.67 1,822.12 264,207.94 1.825.27 265,119.79 1,828.41 266,033.21 1,831.55 266.948.20 1,834.69 267,864.76 1,837.83 268,782.89 1,840.97 269,702.59 1.844.11 270,623.86 1,847,26 271,546.70 1,850.40 272,471.12 1,853.54 273,397.10 1,856.68 274,324.66 1,859.82 275,253.78 1.862.96 276,184.48 1.866.11 277,116.75 1,869.25 278,050.58 1,872.39 278,985.99 1,875.53 279.922.97 1,878.67 280,861.52 1.881.81 1281,801.65 1.884.96 282,743.34 1,888.10 283,686.60 1,891.24 284,631.44 1,894.38 1285,577.84 1,897.52 286,525.82 1,900.66 '287,475.36 1.903.81 1288,426.48 1,906.95 ,289,379.17 1,910.09 290,333.43 1,913.23 291,289.26 1,916.37 1292,246.66 1,919.51 293,205.63 1.922.65 294,166.17 1,925.80 295,128.28 1,928.94 296,091.97 1,932.08 297,057.22 1,935.22 298,024.05 1,938.36 298,992.44 1,941.50 299,962.41 1.944.65 300.933.95 L ,947.79 301,907.05 L ,950.93 302,881.73 L ,954.07 |303,857.98 CIRCUMFERENCES, AND AREAS. 555 No. Square. Cube. Sq. Root, . Cu. Root, Reciprocal. Circum. Area. 623 ,624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 842 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 388.129 389,376 390,625 391,876 393.129 394,384 395,641 396,900 398,161 399,424 400,689 401,956 403.225 404,496 405,769 407,044 408,321 409.600 410,881 412,164 413,449 414,736 416,125 417,316 418,609 419,904 421,201 422,500 423,801 425,104 426,409 427,716 429,025 430,336 431,639 432,964 434,281 435.600 436,921 438,244 439,569 440,896 442.225 443,556 444.899 446.224 447,561 448.900 450,241 451,584 452,929 454,276 455,625 456,976 458,329 459,684 461,041 462,400 463,761 465,124 466,489 467,856 469.225 241,804,367 242.970.624 244.140.625 245,314,376 246,491,883 247,673,152 248,858,189 250.047.000 251,239,591 252,435,968 253,636,137 254,840,104 256.047.875 257,259,456 258,474,853 259,694,072 260,917,119 262.144.000 263,374,721 264,609,288 265,847,707 267,089,984 268.336.125 269,585,136 270.840.023 272,097,792 273,359,449 274.625.000 275,894,451 277,167,808 278,445,077 279,726,264 281,011,375 282,300,416 283,593,393 284,890,312 286,191,179 287.496.000 288,804,781 290,117,528 291,434,247 292,754,944 294,079,625 295,408,296 296,740,963 298,077,632 299,418,309 300.763.000 302,111,711 303,464,448 304,821,217 306.182.024 307.546.875 308.915,776 310,288,733 311,665,752 313,046,839 314.432.000 315,821,241 317,214,568 318,611,987 320,013,504 321.419.125 24.9600 24.9800 25.0000 25.0200 25.0400 25.0599 25.0799 25.0998 25.1197 25.1396 25.1595 25.1794 25.1992 25.2190 25.2389 25.2587 25.2784 25.2982 25.3180 25.3377 25.3574 25.3772 25.3969 25.4165 25.4362 25.4558 25.4755 25.4951 25.5147 25.5343 25.5539 25.5734 25.5930 25.6125 25.6320 25.6515 25.6710 25.6905 25.7099 25.7294 25.7488 25.7682 25.7876 25.8070 25.8263 25.8457 25.8650 25.8844 25.9037 25.9230 25.9422 25.9615 25.9808 26.0000 26.0192 26.0384 26.0576 26.0768 26.0960 26.1151 26.1343 26.1534 26.1725 8.5408 8.5453 8.5499 8.5544 8.5589 8.5635 8.5681 8.5726 S .5772 8.5817 8.5862 8.5907 8.5952 8.5997 8.6043 8.6088 8.6132 8.6177 8.6222 8.6267 8.6312 8.6357 8.6401 8.6446 8.6490 8.6535 8.6579 8.6624 8.6668 8.6713 8.6757 8.6801 8.6845 8.6890 8.6934 8.6978 8.7022 8.7066 8.7110 8.7154 8.7198 8.7241 8.7285 8.7329 8.7373 8.7416 8.7460 8.7503 8.7547 8.7590 8.7634 8.7677 8.7721 8.7764 8.7807 8.7850 8.7893 8.7937 8.7980 8.8023 8.8066 8.8109 8.8152 .001605136 .001602564 .001600000 .001597444 .001594896 .001592357 .001589825 .001587302 .001584786 .001582278 .001579779 .001577287 .001574803 .001572327 .001569859 .001567398 .001564945 .001562500 .001560062 .001557632 .001555210 .001552795 .001550388 .001547988 .001545595 .001543210 .001540832 .001538462 .001536098 .001533742 .001531394 .001529052 .001526718 .001524390 .001522070 .001519751 .001517451 .001515152 .001512859 .001510574 .001508296 .001506024 .001503759 .001501502 .001499250 .001497006 .001494768 .001492537 .001490313 .001488095 .001485884 .001483680 .001481481 .001479290 .001477105 .001474926 .001472754 .001470588 : .001468429 : .001466276 ! .001464129 ; .001461988 : .001459854 : 1,957.21 1.960.35 1,963.50 1,966.64 1,969.78 1,972.92 1,976.06 1,979.20 1.982.35 1,985.49 1,988.63 1,991.77 1,994.91 1,998.05 2.001.19 2,004.34 2,007.48 2,010.62 2,013.76 2,016.90 2.020.04 2.023.19 2,026.33 2,029.47 2,032.61 2,035.75 2,038.89 2.042.04 2,045.18 2,048.32 2,051.46 2,054.60 2,057.74 2,060.88 2,064.03 2,067.17 2,070.31 2,073.45 2,076.59 2.079.73 2,082.88 2,086.02 2,089.16 2,092.30 2,095.44 2.098.58 2.101.73 2,104.87 2,108.01 2,111.15 2,114.29 2,117.43 2.120.58 2,123.72 2,126.86 : 2,130.00 : 2,133.14 : 2,136.28 : 2,139.42 ; 2,142.57 ; 2,145.71 : 2,148.85 : 2,151.99 : 304,835.80 305,815.20 306.796.16 307,778.69 308,762.79 309,748.47 310.735.71 311.724.53 312,714.92 313.706.88 314,700.40 315,695.50 316.692.17 317,690.42 318.690.23 319,691.61 320,694.56 321.699.09 322.705.18 323.712.85 324.722.09 325.732.89 326,745.27 327,759.22 328.774.74 329,791.83 330.810.49 331.830.72 332.852.53 333.875.90 334.900.85 335,927.36 336,955.45 337.985.10 339,016.33 340,049.13 341.083.50 342.119.44 343,156.95 344.196.03 345.236.69 346.278.91 347.322.70 348,368.07 349,415.00 350.463.51 351.513.59 352.565.24 353.618.45 354.673.24 355.729.60 356.787.54 357.847.04 358.908.11 359.970.75 361,034,97 362.100.75 363.168.11 364.237.04 365.307.54 366.379.60 367.453.24 368.528.45 556 SQUARES, CVBES, 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 8.8280 .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 2,346.77 438,259.24 748 559,504 418,50^,992 27.3496 9.0775 .001336898 2,349.91 439,433.41 CmCVMFERENCES, AND AREAS. 557 No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 '809 810 811 561.001 562,500 564.001 565,504 567.009 568,516 570.025 571,536 573,049 574,564 576,081 577.600 579,121 580,644 582,169 583,696 585.225 586,756 588,289 589,824 591,361 592,900 594,441 595,984 597,529 599,076 600,625 602,176 603,729 605,284 606,841 608.400 609,961 611,524 613,089 614,656 616.225 617,796 619,369 620,944 622,521 624.100 625,681 627,264 628,849 630,436 632.025 633,616 635,209 636,804 638.401 640,000 641.601 643,204 644,809 646,416 648.025 649,636 651,249 652,864 654,481 656.100 657,721 420,189,749 421.875.000 423,564,751 425,259,008 426,957,777 428,661,064 430.368.875 432,081,216 433,798,093 435,519,512 437,245,479 438.976.000 440,711,081 442,450,728 444,194,947 445,943,744 447.697.125 449,455,096 451,217,663 452,984,832 454,756,609 456.533.000 458,314,011 460,099.648 461,88£ 917 463,684,824 465,484,375 467,288,576 469,097,433 470,910,952 472,729,139 474.552.000 476,379,541 478,211,768 480,048,687 481,890,304 483,736,625 485,587,656 487,443,403 489,303,872 491,169,069 493.039.000 494,913,671 496,793,088 498,677,257 500,566,184 502.459.875 504,358,336 506,261,573 508,169,592 510,082,399 512,000,000 513,922,401 515,849,608 517,781,627 519,718,464 521.660.125 523,606,616 525,557,943 527,514,112 529,475,129 531.441.000 533,411,731 27.3679 27.3861 27.4044 27.4226 27.4408 27.4591 27.4773 27.4955 27.5136 27.5318 27.5500 27.5681 27.5862 27.6043 27.6225 27.6405 27.6586 27.6767 27.6948 27.7128 27.7308 27.7489 27.7669 27.7849 27.8029 27.8209 27.8388 27.8568 27.8747 27.8927 27.9106 27.9285 27.9464 27.9643 27.9821 28.0000 28.0179 28.0357 28.0535 28.0713 28.0891 28.1069 28.1247 28.1425 28.1603 28.1780 28.1957 28.2135 28.2312 28.2489 28.2666 28.2843 28.3019 28.3196 28.3373 28.3549 28.3725 28.3901 28.4077 28.4253 28.4429 28.4605 28.4781 9.0816 9.0856 9.0896 9.0937 9.0977 9.1017 9.1057 9.1098 9.1138 9.1178 9.1218 9.1258 9.1298 9.1338 9.1378 9.1418 9.1458 9.1498 9.1537 9.1577 9.1617 9.1657 9.1696 9.1736 9.1775 9.1815 9.1855 9.1894 9.1933 9.1973 9.2012 9.2052 9.2091 9.2130 9.2170 9.2209 9.2248 9.2287 9.2326 9.2365 9.2404 9.2443 9.2482 9.2521 9.2560 9.2599 9.2638 9.2677 9.2716 9.2754 9.2793 9.2832 9.2870 9.2909 9.2948 8.2986 9.3025 9.3063 9.3102 9.3140 9.3179 9.3217 9.3255 .001335113 .001333333 .001331558 .001329787 .001328021 .001326260 .001324503 .001322751 .001321004 .001319261 .001317523 .001315789 .001314060 .001312336 .001310616 .001308901 .001307190 .001305483 .001303781 .001302083 .001300390 .001298701 .001297017 .001295337 .001293661 .001291990 .001290323 .001288660 .001287001 .001285347 .001283697 .001282051 .001280410 .001278772 .001277139 .001275510 .001273885 .001272265 .001270648 .001269036 .001267427 .001265823 .001264223 .001262626 .001261034 .001259446 .001257862 .001256281 .001254705 .001253133 .001251364 .001250000 .001248439 .001246883 .001245330 .001243781 .001242236 .001240695 .001239157 .001237624 .001236094 .001234568 .001233046 2,353.05 2.356.19 2,359.34 2,362.48 2,365.62 2,368.76 2,371.90 2.375.04 2.378.19 2,381.33 2,384.47 2,387.61 2,390.75 2,393.89 2.397.04 2,400.18 2,403.32 2,406.46 2,409.60 2,412.74 2.415.88 2,419.03 2,422.17 2,425.31 2,428.45 2,431.59 2.434.73 2.437.88 2,441.02 2,444.16 2,447.30 2,450.44 2.453.58 2.456.73 2,459.87 2,463.01 2,466.15 2,469.29 2,472.43 2.475.58 2,478.72 2,481.86 2,485.00 2,488.14 2,491.28 2.494.42 2,497.57 2,500.71 2,503.85 2,506.99 2,510.13 2.513.27 2.516.42 2,519.56 2,522.70 2,525.84 2,528.98 2,532.12 2.535.27 2,538.41 2,541.55 2,544.69 2,547.83 440,609.16 441,786.47 442,965.35 444.145.80 445.327.83 446,511.42 447,696.59 448.883.32 450.071.63 451,261.51 452.452.96 453.645.98 454.840.57 456.036.73 457,234.46 458.433.77 459.634.64 460,837.08 462,041.10 463.246.69 464.453.84 465.662.57 466.872.87 468.084.74 469.298.18 470.513.19 471.729.77 472.947.92 474.167.65 475.388.94 476.611.81 477.836.24 479.062.25 480.289.83 481.518.97 482.749.69 483.981.98 485.215.84 486.451.28 487.688.28 488.926.85 490.166.99 491,408.71 492.651.99 493.896.85 495.143.28 496,391.27 497,640.84 498.891.98 500.144.69 501,398.97 502.654.82 503.912.25 505,171.24 506,431.80 507.693.94 508,957.64 510.222.92 511.489.77 512.758.19 514,028.18 515.299.74 516.572.87 558 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq. Root. Cu. Root. Reciprocal. Circum. Area. 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 .846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 659,344 660,969 662,596 664,225 665,856 667,489 669,124 670,761 672,400 674,041 675.584 677,329 678,976 680,625 682,276 683,929 685.584 687,241 688.900 690,561 692.224 693,889 695,556 697.225 698,896 700.569 702; 244 703,921 705.600 707,281 708,964 710,649 712,336 714.025 715,716 717,409 719,104 720,801 722,500 724,201 725,904 727,609 729,316 731.025 732,736 734,449 736,164 737,881 739.600 741,321 743,044 744,769 746,496 748.225 749,956 751,689 753,424 755,161 756.900 758,641 760,384 762,129 763,876 535,387,328 537,367,797 539,353,144 541.343.375 543,338,496 545,338,513 547,343,432 549,353,259 551.368.000 553,387,661 555,412,248 557,441,767 559,476,224 561.515.625 563,559,976 565,609,283 567,663,552 569,722,789 571.787.000 573.856.191 575,930,368 578,009,537 580,093,704 582,182,875 584,277,056 586,376,253 588,480,472 590,589,719 592.704.000 594,823,321 596,947,688 599,077,107 601,211,584 603,351,125 605,495,736 607,645,423 609.800.192 611,960,049 614.125.000 616,295,051 618,470,208 620,650,477 622,835,864 625.026.375 627,222,016 629,422,793 631,628,712 633,839,779 636.056.000 638,277,381 640,503,928 642,735,647 644,972,541 647.214.625 649,461,896 651,714,363 653,972,032 656,234,909 658.503.000 660,776,311 663,054,848 665,338,617 667,627,624 28.4956 28.5132 28.5307 28.5482 28.5657 28.5832 28.6007 28.6182 28.6356 28.6531 28.6705 28.6880 28.7054 28.7228 28.7402 28.7576 28.7750 28.7924 28.8097 28.8271 28.8444 28.8617 28.8791 28.8964 28.9137 28.9310 28.9482 28.9655 28.9828 29.0000 29.0172 29.0345 29.0517 29.0689 29.0861 29.1033 29.1204 29.1376 29.1548 29.1719 29.1890 29.2062 29.2233 29.2404 29.2575 29.2746 29.2916 29.3087 29.3258 29.3428 29.3598 29.3769 29.3939 29.4109 29.4279 29.4449 29.4618 29.4788 29.4958 29.5127 29.5296 29.5466 29.5635 9.3294 9.3332 9.3370 9.3408 9.3447 9.3485 9.3523 9.3561 9.3599 9.3637 9.3675 9.3713 9.3751 9.3789 9.3827 9.3865 9 3902 9.3940 9.3978 9.4016 9.4053 9.4091 9.4129 9.4166 9.4204 9.42^11 9.4279 9.4316 9.4354 9.4391 9.4429 9.4466 9.4503 9.4541 9.4578 9.4615 9.4652 9.4690 9.4727 9.4764 9.4801 9.4838 9.4875 9.4912 9.4949 9.4986 9.5023 9.5060 9.5097 9.5135 9.5171 9.5207 9.5244 9.5281 9.5317 9.5354 9.5391 9.5427 9.5464 9.5501 9.5537 9.5574 9.5610 .001231527 .001230012 .001228501 .001226994 .001225490 .001223990 .001222494 .001221001 .001219512 .001218027 .001216545 .001215067 .001213592 .001212121 .001210654 .001209190 .001207729 .001206273 .001204819 .001203369 .001201923 .001200480 .001199041 .001197605 .001196172 .001194743 .001193317 .001191895 .001190476 .001189061 .001187648 .001186240 .001184834 .001183432 .001182033 .001180638 .001179245 .001177856 .001176471 .001175088 .001173709 .001172333 .001170960 .001169591 .001168224 .001166861 .001165501 .001164144 .001162791 .001161440 .001160093 .001158749 .001157407 .001156069 .001154734 .001153403 .001152074 .001150748 .001149425 .001148106 .001146789 .001145475 .001144165 2,550.97 2,554:11 2,557.26 2,560.40 2,563.54 2,566.68 2,569.82 2.572.96 2,576.11 2,579.25 2,582.39 2,585.53 2,588.67 2.591.81 2.594.96 2,598.10 2,601.24 2,604.38 2,607.52 2,610.66 2.613.81 2,616.95 2,620.09 2,623.23 2,626.37 2,629.51 2.632.65 2,635.80 2,638.94 2,642.08 2,645.22 2,648.36 2.651.50 2.654.65 2,657.79 2,660.93 2,664.07 2,667.21 2,670.35 2.673.50 2,676.64 2,679.78 2,682.92 2,686.06 2,689.20 2.692.34 2,695.49 2,698.63 2,701.77 2,704.91 2,708.05 2.711.19 2.714.34 2,717.48 2,720.62 2,723.76 2,726.90 2,730.04 2.733.19 2,736.33 2,739.47 2,742.61 2,745.75 517.847.57 519.123.84 520.401.68 521,681.10 522,962.08 524,244.63 525.528.76 526.814.46 528,101.73 529,390.56 530,680.97 531.972.95 533.266.50 534.561.62 535,858.32 537.156.58 538.456.41 539.757.82 541,060.79 542,365.34 543.671.46 544.979.15 546,288.40 547,599.23 548.911.63 550,225.61 551.541.15 552,858.26 554,176.94 555.497.20 556.819.02 558.142.42 559,467.39 560,793.92 562.122.03 563.451.71 564.782.96 566; 115.78 567,450.17 568.786.14 570,123.67 571.462.77 572,803.45 574.145.69 575.489.51 576,834.90 578.181.85 579.530.38 580,880.48 582.232.15 583.585.39 584.940.20 586.296.59 587,654.54 589,014.07 590.375.16 591.737.83 593,102.06 594,467.87 595,835.25 597.204.20 598.574.72 599,946.81 CIRCVMFERENCES, AND AREAS. 559 No. Square. Cube. Sq. Boot. Cu. Root. Reciprocal. Circum. Area. 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 765.625 767,376 769,129 770,884 772,641 774.400 776,161 777,924 779,689 781,456 783.225 784,996 786,769 788,544 790,321 792.100 793,881 795,664 797,449 799,236 801.025 802,816 804,609 806,404 808,201 810,000 811,801 813,604 815,409 817,216 819.025 820,836 822,649 824,464 826,281 828.100 829,921 831,744 833,569 835,396 837.225 839,056 840,889 842,724 844,561 846.400 848,241 850,084 851,929 853,776 855.625 857,476 859,329 861,184 863,041 864,900 866,761 868,624 870,489 872,356 874.225 876,096 877,969 669.921.875 672,221,376 674,526,133 676,836,152 679,151,439 681.472.000 683,797.841 686,128,968 688,465,387 690,807,104 693.154.125 695,506,456 697,864,103 700,227,072 702,595,369 704.969.000 707,347,971 707,932,288 712,121,957 714,516,984 716.917.375 719,323,136 721,734,273 724,150,792 726,572,699 729,000,000 731,432,701 733,870,808 736,314,327 738,763,264 741,217,625 743,677,416 746,142,643 748,613,312 751,089,429 753.571.000 756,058,031 758,550,825 761,048,497 763,551,944 766.060.875 768,575,296 771,095,213 773,620,632 776,151,559 778.688.000 781,229,961 783.777,448 786;330,467 788,889,024 791.453.125 794,022,776 796,597,983 799,178,752 801,765,089 804.357.000 806,954,491 809,557,568 812,166,237 814,780,504 817.400.375 820,025,856 822,656,953 29.5804 29.5973 29.6142 29.6311 29.6479 29.6648 29.6816 29.6985 29.7153 29.7321 29.7489 29.7658 29.7825 29.7993 29.8161 29.8329 29.8496 29.8664 29.8831 29.8998 29.9166 29.9333 29.9500 29.9666 29.9833 30.0000 30.0167 30.0333 30.0500 30.0666 30.0832 30.0998 30.1164 30.1330 30.1496 30.1662 30.1828 30.1993 30.2159 30.2324 30.2490 30.2655 30.2820 30.2985 30.3150 30.3315 30.3480 30.3645 30.3809 30.3974 30.4138 30.4302 30.4467 30.4631 30.4795 30.4959 30.5123 30.5287 30.5450 30.5614 30.5778 30.5941 30.6105 9.5647 9.5683 9.5719 9.5756 9.5792 9.5828 9.5865 9.5901 9.5937 9.5973 9.6010 9.6046 9.6082 9.6118 9.6154 9.6190 9.6226 9.6262 9.6298 9.6334 9.6370 9.6406 9.6442 9.6477 9.6513 9.6549 9.6585 9.6620 9.6656 9.6692 9.6727 9.6763 9.6799 9.6834 9.6870 9.6905 9.6941 9.6976 9.7012 9.7047 9.7082 9.7118 9.7153 9.7188 9.7224 9.7259 9.7294 9.7329 9.7364 9.7400 9.7435 9.7470 9.7505 9.7540 9.7575 9.7610 9.7645 9.7680 9.7715 9.7750 9.7785 9.7829 9.7854 .001142857 .001141553 .001140251 .001138952 .001137656 .001136364 .001135074 .001133787 .001132503 .001131222 .001129944 .001128668 .001127396 .001126126 .001124859 .001123596 .001122334 .001121076 .001119821 .001118568 .001117818 .001116071 .001114827 .001113586 .001112347 .001111111 .001109878 .001108647 .001107420 .001106195 .001104972 .001103753 .001102536 .001101322 .001100110 .001098901 .001091695 .001096491 .001095290 .001094092 .001092896 .001091703 .001090513 .001089325 .001088139 .001086957 .001085776 .001084599 .001083423 .001082251 .001081081 .001079914 .001078749 .001077586 .001076426 .001075269 .001074114 .001072961 .001071811 .001070664 .001069519 .001068376 .001067236 2,748.89 2,752.04 2,755.18 2,758.32 2,761.46 2,764.60 2,767.74 2.770.88 2,774.03 2,777.17 2,780.31 2,783.45 2,786.59 2.789.73 2.792.88 2,796.02 2,799.16 2,802.30 2,805.44 2.808.58 2.811.73 2,814.87 2,818.01 2,821.15 2,824.29 2,827.43 2.830.58 2,833.72 2,836.86 2,840.00 2,843.14 2,846.28 2.849.42 2,852.57 2,855.71 2,858.85 2,861.99 2,865.13 2.868.27 2.871.42 2,874.56 2,877.70 2,880.84 2,883.98 2.887.12 2.890.27 2,893.41 2,896.55 2,899.69 2,902.83 2,905.97 2.909.11 2,912.26 2,915.40 2,918.54 2,921.68 2,924.82 2,927.96 2.931.11 2,934.25 2,937.39 2,940.53 2,943.67 601.320.47 602.695.70 604.072.50 605.450.88 606.830.82 608,212.34 609.595.42 610.980.08 612,366.31 613,754.11 615.143.48 616.534.42 617,926.93 619.321.01 620.716.66 622.113.89 623.512.68 624.913.04 626.314.98 627.718.49 629.123.56 630.530.21 631.938.43 633.348.22 634.759.58 636.172.51 637.587.01 639.003.09 640.420.73 641,839.95 643.260.73 644.683.09 646.107.01 647.532.51 648.959.58 650.388.22 651.818.43 653,250.21 654.683.56 656,118.48 657.554.98 658.993.04 660.432.68 661,873.88 663.316.66 664.761.01 666,206.92 667.654.41 669,103.47 670.554.10 672,006.30 673,460.08 674.915.42 676,372.33 677.830.82 679,290.87 680.752.50 682.215.69 683,680.46 685,146.80 686.614.71 688,084.19 689,555.24 560 SQUARES, CUBES, SQUARE AND CUBE ROOTS, No. Square. Cube. Sq . Root. Cu. Root. Reciprocal. Circum. Area. 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 879,844 881,721 883.600 885,481 887,364 889,249 891,136 893.025 894,916 896;808 898,704 900.601 902,500 904,401 906,304 908,209 910,116 912.025 913,936 915,849 917,764 919,681 921,600 923,521 925,444 927,369 929,296 931.225 933,156 935,089 937.024 938,961 940,900 942,841 944,784 946,729 948,676 950,625 952,576 954,529 956,484 958,441 960,400 962,361 964,324 966,289 968,256 970.225 972,196 974,169 976,144 978,121 980,100 982,081 984,064 986,049 988,036 990.025 992,016 994,009 996,004 998,001 1,000,000 825,293,672 827,936,019 830.584.000 833,237,621 835,896,888 838,561,807 841,232,384 843.908.625 846,590,536 849,278,123 851,971,392 854,670,349 857.375.000 860.085.351 862,801,408 865,523,177 868,250,664 870.983.875 873,722,816 876,467,493 879,217,912 881,974,079 884.736.000 887,503,681 890,277,128 893,056,347 895,841,344 898,632,125 901,428,696 904,231,063 907,039,232 909,853,209 912.673.000 915,498,611 918,330,048 921,167,317 924,010,424 926,859,375 929,714,176 932,574,833 935.441.352 938,313,739 941.192.000 944,076,141 946,966,168 949,862,087 952,763,904 955.671.625 958,585,256 961,504,803 964,430,272 967,361,669 970.299.000 973,242,271 976,191,488 979,146,657 982,107,784 985.074.875 988,047,936 991,026,973 994,011,992 997,002,999 1,000,000,000 30.6268 30.6431 30.6594 30.6757 30.6920 30.7083 30.7246 30.7409 30.7571 30.7734 30.7896 30.8058 30.8221 30.8383 30.8545 30.8707 30.8869 30.9031 30.9192 30.9354 30.9516 30.9677 30.9839 31.0000 31.0161 31.0322 31.0483 31.0644 31.0805 31.0966 31.1127 31.1288 31.1448 31.1609 31.1769 31.1929 31.2090 31.2250 31.2410 31.2570 31.2730 31.2890 31.3050 31.3209 31.3369 31.3528 31.3688 31.3847 31.4006 31.4166 31.4325 31.4484 31.4643 31.4802 31.4960 31.5119 31.5278 31.5436 31.5595 31.5753 31.5911 31.6070 31.6228 9.7889 9.7924 9.7959 9.7993 9.8028 9.8063 9.8097 9.8132 9.8167 9.8201 9.8236 9.8270 9.8305 9.8339 9.8374 9.8408 9.8443 9.8477 9.8511 9.8546 9.8580 9.8614 9.8648 9.8683 9.8717 9.8751 9.8785 9.8819 9.8854 9.8888 9.8922 9.8956 9.8990 9.9024 9.9058 9.9092 9.9126 9.9160 9.9194 9.9228 9.9261 9.9295 9.9329 9.9363 9.9396 9.9430 9.9464 9.9497 9.9531 9.9565 9.9598 9.9632 9.9666 9.9699 9.9733 9.9766 9.9800 9.9833 9.9866 9.9900 9.9933 9.996r 10.0000 .001066098 .001064963 .001063830 .001062699 .001061571 .001060445 .001059322 .001058201 .001057082 .001055966 .001054852 .001053741 .001052632 .001051525 .001050420 .001049318 .001048218 .001047120 .001046025 .001044932 .001043841 .001042753 .001041667 .001040583 .001039501 .001038422 .001037344 .001036269 .001035197 .001034126 .001033058 .001031992 .001030928 .001029866 .001028807 .001027749 .001026694 .001025641 .001024590 .001023541 .001022495 .001021450 .001020408 .001019168 .001018330 .001017294 .001016260 .001015228 .001014199 .001013171 .001012146 .001011122 .001010101 .001009082 .001008065 .001007049 .001006036 .001005025 .001004016 .001003009 .001002004 .001001001 .001000000 2.946.81 2,949.96 2,953.10 2,956.24 2,959.38 2,962.52 2,965.66 2.968.81 2,971.95 2,975.09 2,978.23 2,981.37 2,984.51 2.987.65 2,990.80 2,993.94 2,997.08 3,000.22 3,003.36 3.006.50 3.009.65 3,012.79 3,015.93 3,019.07 3,022.21 3,025.35 3.028.50 3,031.64 3,034.78 3,037.92 3,041.06 3,044.20 3.047.34 3,050.49 3,053.63 3,056.77 3,059.91 3,063.05 3.066.19 3.069.34 3,072.48 3,075.62 3,078.76 3,081.90 3.085.04 3.088.19 3,091.33 3,094.47 3,097.61 3,100.75 3,103.89 3.107.04 3,110.18 3,113.32 3,116.46 3,119.60 3,122.74 3,125.88 3,129.03 3,132.17 3,135.31 3,138.45 3,141.59 691,027.86 692.502.05 693.977.82 695.455.15 696.934.06 698.414.53 699.896.58 701,380.19 702.865.38 704.352.14 705.840.47 707.330.37 708.821.84 710,314.88 711,809.50 713,305.68 714.803.43 716.302.76 717.803.66 719.306.12 720.810.16 722.315.77 723.822.95 725.331.70 726,842.02 728,353.91 729.867.37 731,382.40 732,899.01 734,417.18 735.936.93 737,458.24 738.981.13 740.505.59 742,031.62 743,559.22 745.088.39 746.619.13 748.151.44 749,685.32 751.220.78 752,757.80 754.296.40 755,836.56 757,378.30 758.921.61 760.466.48 762.012.93 763.560.95 765.110.54 766.661.70 768.214.44 769,768.74 771.324.61 772.882.06 774.441.07 776.001.66 777.563.82 779.127.54 780.692.84 782.259.71 783.828.15 785.398.16 CIRCUMFERENCES AND AREAS OF CIRCLES. 561 CIRCUMFERENCES AND AREAS OF CIRCLES FROM 1-64 TO 100. Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. Bi .0491 .0002 6 18.8496 28.2744 13f 41.2335 135.297 35 .0982 .0008 6f 19.2423 29.4648 13i 41.6262 137.887 TB .1963 .0031 6f 19.CC30 30.6797 13| 42.0189 140.501 h .3927 .0123 6f 20.02V7 31.9191 13i 42.4116 143.139 .5890 .0276 6i 20.4204 33.1831 13t 42.8043 145.802 .7854 .0491 6f 20.8131 34.4717 13f 43.1970 148.490 .9817 .0767 6f 21.2058 35.7848 13f 43.5897 151.202 1.1781 .1104 6f 21.5985 37.1224 14 43.9824 153.938 TB 1.3744 .1503 7 21.9912 38.4846 14f 44.3751 156.700 h 1.5708 .1963 7f 22.3839 39.8713 14i 44.7678 159.485 1.7671 .2485 Vi 22.7766 41.2826 14f 45.1605 162.296 1 1.9635 .3068 Vf 23.1693 42.7184 14i 45.5532 165.130 H 2.1598 .3712 Vf 23.5620 44.1787 14f 45.9459 167.990 i 2.3562 .4418 Vf 23.9547 45.6636 14f 46.3386 170.874 H 2.5525 .5185 Vf 24.3474 47.1731 14f 46.7313 173.782 i 2.7489 .6013 Vf 24.7401 48.7071 15 47.1240 176.715 11 2.9452 .6903 8 25.1328 50.2656 15i 47.5167 179.673 1 3.1416 .7854 8f 25.5255 51.8487 15i 47.9094 182.655 n 3.5343 .9940 8i 25.9182 53.4563 15t 48.3021 185.661 li 3.9270 1.2272 8f 26.3109 55.0884 15f 48.6948 188.692 If 4.3197 1.4849 8i 26.7036 56.7451 151 49.0875 191.748 H 4.7124 1.7671 8f 27.0963 58.4264 15f 49.4802 194.828 If 5.1051 2.0739 8f 27.4890 60.1322 15f 49.8729 197.933 If 5.4978 2.4053 8f 27.8817 61.8625 16 50.2656 201.062 If 5.8905 2.7612 9 28.2744 63.6174 16i 50.6583 204.216 2 6.2832 3.1416 9f 28.6671 65.3968 16i 51.0510 207.395 2f 6.6759 3.5466 9i 29.0598 67.2008 161 51.4437 210.598 2i 7.0686 3.9761 9f 29.4525 69.0293 16i 51.8364 213.825 2f 7.4613 4.4301 9i 29.8452 70.8823 16f 52.2291 217.077 21 7.8540 4.9087 9f 30.2379 72.7599 16f 52.6218 220.354 2f 8.2467 5.4119 9f 30.6306 74.6621 16f 53.0145 223.655 2f 8.6394 5.9396 9f 31.0233 76.589 17 53.4072 226.981 2f 9.0321 6.4918 10 31.4160 78.540 IVf 53.7999 230.331 3 9.4248 7.0686 lOf 31.8087 80.516 17i 54.1926 233.706 3f 9.8175 7.6699 lOi 32.2014 82.516 17f 54.5853 237.105 3i 10.2102 8.2958 lOf 32.5941 84.541 17i 54.9780 240.529 3f 10.6029 8.9462 lOi 32.9868 86.590 171 55.3707 243.977 31 10.9956 9.6211 lOf 33.3795 88.664 17f 65.7634 247.450 3f 11.3883 10.3206 lOf 33.7722 90.763 17| 56.1561 250.948 3f 11.7810 11.0447 lOf 34.1649 92.886 18 56.5488 254.470 3f 12.1737 11.7933 11 34.5576 95.033 18f 56.9415 258.016 4 12.5664 12.5664 Ilf 34.9503 97.205 18i 57.3342 261.587 41 12.9591 13.3641 Ilf 35.3430 99.402 18f 57.7269 265.183 41 13.3518 14.1863 Ilf 35.7357 101.623 18i 58.1196 268.803 4f 13.7445 15.0330 Ilf 36.1284 103.869 181 58.5123 272.448 41 14.1372 15.9043 Ilf 36.5211 106.139 18f 58.9050 276.117 4f 14.5299 16.8002 Ilf 36.9138 108.434 18f 59.2977 -279.811 4f 14.9226 17.7206 Ilf 37.3065 110.754 19 59.6904 283.529 4f 15.3153 18.6555 12 37.6992 113.098 19f 60.0831 287.272 5 15.7080 19.6350 12f 38.0919 115.466 19i 60.4758 291.040 5f 16.1007 20.6290 12i 38.4846 117.859 19| 60.8685 294.832 51 16.4934 21.6476 12f 38.8773 120.277 19i 61.2612 298.648 5f 16.8861 22.6907 12i 39.2700 122.719 19f 61.6539 302.489 51 17.2788 23.7583 12f 39.6627 125.185 19f 62.0466 306.355 5f 17.6715 24.8505 12f 40.0554 127.677 19f 62.4393 310.245 5f 18.0642 25.9673 12f 40.4481 130.192 20 62.8320 314.160 5f 18.4569 27.1086 13 40.8408 132.733 20i 63.2247 318.099 562 CIRCUMFERENCES AND AREAS OF CIRCLES. Diam. Circum. Area. Diam. 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 28i 88.7502 626.798 36} 113.490 1,024.960 20i 64.4028 330.064 28f 39.1429 632.357 36} 113.883 1,032.065 201 64.7955 334.102 28i 89.5356 637.941 36} 114.276 1,039.195 20^ 65.1882 338.164 281 89.9283 643.549 36} 114.668 1,046.349 20| 65.5809 342.250 28f 90.3210 649.182 36} 115.061 1,053.528 21 65.9736 346.361 28^ 90.7137 654.840 36} 115.454 1,060.732 2ii 66.3663 350.497 29 91.1064 660.521 36} 115.846 1,067.960 21i 66.7590 354.657 29} 91,4991 666.228 37 116.239 1,075.213 21f 67.1517 358.842 29} 91,8918 671.959 37} 116.632 1,082.490 21i 67.5444 363.051 291 92.2845 677.714 37} 117.025 1,089.792 2H 67.9371 367.285 29} 92.6772 683.494 37} 117.417 1,097.118 21| 68.3298 371.543 291 93.0699 689.299 37} 117.810 1,104.469 21i 68.7225 375.826 29} 93.4626 695.128 37} 118.203 1,111.844 22 69.1152 380.134 29} 93.8553 700.982 37} 118.595 1,119.244 22f 69.5079 384.466 30 94.2480 706.860 37} 118.988 1,126.669 22i 69.9006 388.822 30} 94.6407 712.763 38 119.381 1,134.118 22i 70.2933 393.203 30} 95.0334 718.690 38} 119.773 1,141.591 22i 70.6860 397.609 30| 95.4261 724.642 38} 120.166 1,149.089 22f 71.0787 402.038 30} 95.8188 730.618 38} 120.559 1,156.612 22f 71.4714 406.494 301 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 25 72.2568 415.477 30} 96.9969 748.695 38} 121.737 1,179.327 23i 72.6495 420.004 31 97.3896 754.769 38} 122.130 1,186.948 23i 73.0422 424.558 31} 97.7823 760.869 39 122.522 1,194.593 23f 73.4349 429.135 31} 98.1750 766.992 39} 122.915 1,202.263 23i 73.8276 433.737 31f 98.5677 773.140 39} 123.308 1,209.958 23f 74.2203 438.364 31} 98.9604 779.313 39} 123.700 1,217.677 23f 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 31} 100.1385 797.979 39} 124.879 1,240.981 24} 75.7911 457.115 32 100.5312 804.250 39} 125.271 1,248.798 24i 76.1838 461.864 32} 100.9239 810.545 40 125.664 1,256.640 241 76.5765 466.638 32} 101.3166 816.865 40} 126.057 1,264.510 241 76.9692 471.436 32} 101.7093 823.210 40} 126.449 1,272.400 241 77.3619 476.259 32} 102.1020 829.579 40} 126.842 1,280.310 241 77.7546 481.107 32} 102.4947 835.972 40} 127.235 1,288.250 241 78.1473 485.979 32} 102.8874 842.391 40} 127.627 1,296.220 26 78.5400 490.875 32} 103.280 848.833 40} 128.020 1,304.210 251 78.9327 495.796 33 103.673 855.301 40} 128.413 1,312.220 251 79.3254 500.742 33} 104.065 861.792 41 128.806 1,320.260 251 79.7181 505.712 33} 104.458 868.309 41} 129.198 1,328.320 251 80.1108 510.706 33} 104.851 874.850 41} 129.591 1,336.410 251 80.5035 515.726 33} 105.244 881.415 41} 129.984 1,344.520 251 80.8962 520.769 33} 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 530.930 33} 106.422 901.259 41} 131.162 1,369.000 261 82.0743 536.048 34 106.814 907.922 41} 131.554 1,377.210 .261 82.4670 541.190 34} 107.207 914.611 42 131.947 1,385.450 261 82.8597 546.356 34} 107.600 921.323 42} 132.340 1,393.700 261 83.2524 551.547 34} 107.992 928.061 42} 132.733 1,401.990 261 83.6451 556.763 34} 108.385 934.822 42} 133.125 1,410.300 261 84.0378 562.003 34} 108.778 941.609 42} 133.518 1,418.630 261 84.4305 567.267 34} 109.171 948.420 42} 133.911 1,426.990 27 84.8232 572.557 34} 109.563 955.255 42} 134.303 1,435.370 271 85.2159 577.870 35 109.956 962.115 42} 134.696 1,443.770 271 85.6086 583.209 35} 110.349 969.000 43 135.089 1,452.200 271 86.0013 588.571 35} 110.741 975.909 43} 135.481 1,460.660 271 86.3940 593.959 35} 111.134 982.842 43} 135.874 1,469.140 271 86.7867 599.371 35} 111.527 989.800 43} 136.267 1,477.640 271 87.1794 604.807 35} 111.919 996.783 43} 136.660 1,486.170 271 87.5721 610.268 35} 112.312 1,003.790 43} 137.052 1,494.730 28 87.9648 615.754 35} 112.705 1,010.822 43} 137.445 1,503.300 CIRCVMFERENCES AND AREAS OE CIRCLES. 563 Diam. Circum. Area. Diam. Circum. Area. Diam. Circum. Area. 43| 137.838 1,511.910 51} 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 2,803.93 441- 138.623 1,529.190 52 163.363 2,123.72 59} 188.103 2,815.67 44i 139.016 1,537.860 52} 163.756 2,133.94 60 188.496 2,827.44 44f 139.408 1,546.56 52} 164.149 2,144.19 60} 188.889 2,839.23 44i 139.801 1,555.29 52} 164.541 2,154.46 60} 189.281 2,851.05 44f 140.194 1,564.04 52} 164.934 2,164.76 60} 189.674 2,862.89 44^ 140.587 1,572.81 52} 165.327 2,175.08 60} 190.067 2,874.76 44i 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 45} 142.157 1,608.16 53} 166.897 2,216.61 61 191.638 '2,922.47 451 142.550 1,617.05 53} 167.290 2,227.05 61} 192.030 2,934.46 45} 142.943 1,625.97 53} 167.683 2,237.52 61} 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 46} 144.906 1,670.95 54 169.646 2,290.23 61} 194.386 3,006.92 46} 145.299 1,680.02 54} 170.039 2,300.84 62 194.779 3,019.08 46} 145.692 1,689.11 54} 170.432 2,311.48 62} 195.172 3,031.26 46} 146.084 1,698.23 54} 170.824 2,322.15 62} 195.565 3,043.47 46} 146.477 1,707.37 54} 171.217 2,332.83 62} 195.957 3,055.71 46} 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} 148.048 1,744.19 55 172.788 2,375.83 62} 197.528 3,104.89 47} 148.441 1,753.45 55} 173.181 2,386.65 63 197.921 3,117.25 47} 148.833 1,762.74 55} 173.573 2,397.48 63} 198.313 3,129.64 47} 149.226 1,772.06 55} 173.966 2,408.34 63} 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 2,441.07 631 199.884 3,179.41 48 150.797 1,809.56 55} 175.537 2,452.03 63} 200.277 3,191.91 48} 151.189 1,819.00 56 175.930 2,463.01 63} 200.670 3,204.44 48} 151.582 1,828.46 56} 176.322 2,474.02 64 201.062 3,217.00 48} 151.975 1,837.95 56} 176.715 2,485.05 64} 201.455 3,229.58 48} 152.368 1,847.46 56} 177.108 2,496.11 64} 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 49} 154.331 1,895.38 57 179.071 2,551.76 64} 203.811 3,305.56 49} 154.724 1,905.04 57} 179.464 2,562.97 65 204.204 3,318.31 49} 155.116 1,914.72 57} 179.857 2,574.20 65} 204.597 3,331.09 49} 155.509 1,924.43 57} 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 65} 206.167 3,382.44 50 157.080 1,963.50 57} 181.820 2,630.71 65} 206.560 3,395.33 50} 157.473 1,973.33 58 182.213 2,642.09 65} 206 953 3,408.26 50} 157.865 1,983.18 58} 182.605 2,653.49 66 207.346 3,421.20 50} 158.258 1,993.06 58} 182.998 2,664.91 66} 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 51} 160.614 2,052.85 59 185.354 2,733.98 66} 210.094 3,512.52 51} 161.007 2,062.90 59} 185.747 2,745.57 67 210.487 3,525.66 51} 161.400 2,072.98 59} 186.140 2,757.20 67} 210.880 3,538.83 51} 161.792 2,083.08 59} 186.532 2,768.84 67} 211.273 3,552.02 51} 162.185 2,093.20 59} 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. 67i 212.058 3,578.48 75} 236.798 4,462.16 83} 261.538 5,443.26 67| 212.451 3,591.74 75} 237.191 4,476.98 83} 261.931 5,459.62 G7f 212.843 3,605.04 75} 237.583 4,491.81 83} 262.324 5,476.01 67 j 213.236 3,618.35 75} 237.976 4,506.67 83} 262.716 5,492.41 68 213.629 3,631.69 75} 238.369 4,521.56 83} 263.109 5,508.84 68i 214.021 3,645.05 76 238.762 4,536.47 83} 263.502 5,525.30 68i 214.414 3,658.44 76} 239.154 4,551.41 84 263,894 5,541.78 68i 214.807 3,671.86 76} 239.547 4,566.36 84} 264.287 5,558.29 68i 215.200 3,685.29 76} 239.940 4,581.35 84} 264.680 5,574.82 68f 215.592 3,698.76 76} 240.332 4,596.36 84} 265.072 5,591.37 68^ 215.985 3,712.24 76} 240.725 4,611.39 84} 265.465 5,607.95 681- 216.378 3,725.75 76} 241.118 4,626.45 84} 265.858 5,624.56 69 216.770 3,739.29 76} 241.510 4,641.53 84} 266.251 5,641.18 69} 217.163 3,752.85 77 241.903 4,656.64 84} 266.643 5,657.84 69i 217.556 3,766.43 m 242.296 4,671.77 85 267.036 5,674.51 691 217.948 3,780.04 77} 242.689 4,686.92 85} 267.429 5,691.22 69i 218.341 3,793.68 77f 243.081 4,702.10 85} 267.821 5,707.94 69i 218.734 3,807.34 77} 243.474 4,717.31 85} 268.214 5,724.69 69J 219.127 3,821.02 77} 243.867 4,732.54 85} 268.607 5,741.47 69f 219.519 3,834.73 111 244.259 4,747.79 85} 268.999 5,758.27 70 219.912 3,848.46 77} 244.652 4,763.07 85} 269.392 5,775.10 70i 220.305 3,862.22 78 245.045 4,778.37 85} 269.785 5,791.94 70^ 220.697 3,876.00 78} 245.437 4,793.70 86 270.178 5,808.82 70| 221.090 3,889.80 78} 245.830 4,809.05 86} 270.570 5,825.72 70i 221.483 3,903.63 78} 246.223 4,824.43 86} 270.963 5,842.64 70f 221.875 3,917.49 78} 246.616 4,839.83 86} 271.356 5,859.59 70^ 222.268 3,931.37 78} 247.008 4,855.26 86} 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 78} 247.794 4,886.18 86} 272.534 5,910.58 223.446 3,973.15 79 248.186 4,901.68 86} 272.926 5,927.62 71i 223.839 3,987.13 79} 248.579 4,917.21 87 273.319 5,944.69 71f 224.232 4,001.13 79} 248.972 4,932.75 87} 273.712 5,961.79 71i 224.624 4,015.16 79} 249.364 4,948.33 87} 274.105 5,978.91 71| 225.017 4,029.21 79} 249.757 4,963.92 87} 274.497 .5,996.05 7U 225.410 4,043.29 79} 250.150 4,979.55 87} 274.890 6,013.22 7H 225.802 4,057.39 79} 250.543 4,995.19 87} 275.283 6,030.41 72 226.195 4,071.51 79} 250.935 5,010.86 87} 275.675 6,047.63 72i 226.588 4,085.66 80 251.328 5,026.56 87} 276.068 6,064.87 72i 226.981 4,099.84 80} 251.721 5,042.28 88 276.461 6,082.14 72f 227.373 4,114.04 80} 252.113 5,058.03 88} 276.853 6,099.43 72i 227.766 4,128.26 80} 252.506 5,073.79 88} 277.246 6,116.74 72f 228.159 4,142.51 80} 252.899 5,089.59 88} 277.629 6,134.08 72f 228.551 4,156.78 80} 253.291 5,105.41 88} 278.032 6,151.45 72i 228.944 4,171.08 80} 253.684 5,121.25 88} 278.424 6,168.84 73 229.337 4,185.40 80} 254.077 5,137.12 00 00 278.817 6,186.25 73} 229.729 4,199.74 81 254.470 5,153.01 88} ■ 279.210 6,203.69 73} 230.122 4,214.11 81} 254.862 5,168.93 89 279.602 6,221.15 73| 230.515 4,228.51 81} 255.255 5,184.87 89} 279.995 6,238.64 73} 230.908 4,242.93 81} 255.648 5,200.83 89} 280.388 6,256.15 731 231.300 4,257.37 81} 256.040 5,216.82 89} 280.780 6,273.69 73^ 231.693 4,271.84 81} 256.433 5,232.84 89} 281.173 6,291.25 73} 232.086 4,286.33 81} 256.826 5,248.88 89} 281.566 6,308.84 74 232.478 4,300.85 81} 257.218 5,264.94 89} 281.959 6,326.45 74} 232.871 4,315.39 82 257.611 5,281.03 89} 282.351 6,344.08 74} 233.264 4,329.96 82} 258.004 5,297.14 90 282.744 6,361.74 74} 233.656 4,344.55 82} 258.397 5,313.28 90} 283.137 6,379.42 74} 234.049 4,359.17 82} 258.789 5,329.44 90} 283.529 6,397.13 74} 234.442 4,373.81 82} 259.182 5,345.63 90} 283.922 6,414.86 74} 234.835 4,388.47 82} 259.575 5,361.84 90} 284.315 6,432.62 74} 235.227 4,403.16 82} 259.967 5,378.08 90} 284.707 6,450.40 75 235.620 4,417.87 82} 260.360 5,394.34 90} 285.100 6,468.21 75} 236.013 4,432.61 83 250.753 5,410.62 90} 285.493 6,486.04 75} 236.405 4,447.38 83} 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. 91i 286.278 6,521.78 94i 295.703 6,958.26 97i 305.128 7,408.89 91i 286.671 6,539.68 94i 296.096 6,976.76 m 305.521 7,427.97 91| 287.064 6,557.61 94t 296.488 6,995.28 97f 305.913 7,447.08 91i 287.456 6,575.56 94i 296.881 7,013.82 97i 306.306 7,466.21 91| 287.849 6,593.54 94f 297.274 7,032.39 971 306.699 7,485.37 m 288.242 6,611.55 94^ 297.667 7,050.98 m 307.091 7,504.55 9H 288.634 6,629.57 94^ 298.059 7,069.59 97i 307.484 7,523.75 92 289.027 6,647.63 95 298.452 7,088.24 98 307.877 7,542.98 92i 289.420 6,665.70 95^ 298.845 7,106.90 98i 308.270 7,562.24 92i 289.813 6,683.80 95i 299.237 7,125.59 98i 308.662 7,581.52 92| 290.205 6,701.93 95| 299.630 7,144.31 98f 309.055 7,600.82 92i 290.598 6,720.08 95i 300.023 7,163.04 m 309.448 7,620.15 92| 290.991 6,738.25 95t 300.415 7,181.81 981 309.840 7,639.50 92^ 291.383 6,756.45 95f 300.808 7,200.60 98f 310.233 7,658.88 92i 291.776 6,774.68 95i 301.201 7,219.41 98| 310.626 7,678.28 93 292.169 6,792.92 96 301.594 7,238.25 99 311.018 7,697.71 93i 292.562 6,811.20 961- 301.986 7,257.11 99i 311.411 7,717.16 93i 292.954 6,829.49 96i 302.379 7,275.99 99i 311.804 7,736.63 93f 293.347 6,847.82 96f 302.772 7,294.91 99i 312.196 7,756.13 93i 293.740 6,866.16 96i 303.164 7,313.84 99i 312.589 7,775.66 931 294.132 6,884.53 96| 303.557 7,332.80 m 312.982 7,795.21 m 294.525 6,902.93 96^ 303.950 7,351.79 313.375 7,814.78 93i 294.918 6,921.35 96^ 304.342 7,370.79 m 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 95f 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; 11th 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. 566 Aba GLOSSARY, Air GLOSSARY. Abattis (Leicester).— Cross-packing of branches or rough wood, used to keep roads open for ventilation. Ahra (Spanish).— Fissure in a lode, unfilled or only partially filled. Ahronziado (Spanish).— Copper sulphides. Absolute Pressure— 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— Labor ers 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. Aerac/e (French).— Ventilation. Aerometers.— The air pistons of a Struve ventilator. Aerop/iore.— 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. A/terdamp.— 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-Cowrse.— 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).— Ventilation ways. Air Heading.— An airway. Air (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 long:wall 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.— K 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 SoUar.—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 6 r 0 ?d.— 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.— and down, or backward and forward motion. Alto (Mexican). — ^The hanging wall of a vein. See Respaldos. 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-sheiped. 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. Without water in its composition. Anneal.— To toughen metals, glass, etc. by first heating and then cooling very slowly. Anthracite.— Coa\ 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 A.r^s.— 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. Aparejo (Mexican).— A rigid pair of large stuffed pads connected over back of pack mule by an unpadded portion to protect body of mule when heavy or irregularly shaped loads are carried. 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.—lSlitnc acid. Aqua Regia.— A mixture of hydrochloric acid and nitric acid. Aqueduct.— An artificial elevated way for carrying water. 568 Ara GLOSSARY. AZO Araw (Mexican).— See Hatajo. Arch (Cornish).— Portion of lode left standing to support hanging wall, or because too poor. Archean.—An early period of geological time. ArcMTi^.— 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. Ar 5 'en^^/erons.— Silver-bearing. Argillaceous.— 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. Arroha (Mexican).— 25 lb. 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. Ashlar.— A facing of cut stone applied to a backing of rubble or rough masonry or brickwork. Aspirail (French).— Opening for ventilation. Assa?/.— The determination of the quality and quantity’ of any particular substance in a mineral. Assay er.— One who performs assays. Assessment Work.— The annual work necessary to hold a mining claim. Asfe^.— 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. A wgfef. —Priming tube. Aur (Wales).— Gold. Attn/eroas.- Gold-bearing. Ausscharen (German).— Junction of lodes. Auszimmern ( German) . — Timbering. 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.—Yree 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. — (1) 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.— D obX 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.-YYio 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. Bajf Ends . — Long wooden edges for adjusting linings in sinking shafts dur- ing the operation of fixing the lining. Baffle.— To brush out firedamp. Raif.— Provisions. Bajo (Mexican).— The footwall of a vein. See Respaldo. Bal (Cornish). — A mine. Balance. — (1) 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. Broken stone, gravel, sand, etc. used for keeping railroad ties ^tead 3 ^ 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. .BawM.— Auriferous conglomerate of South Africa. Bank Head. — The upper end of an inclined plane, next to the engine or drum, made nearly level. Bank Right (Australian). — Right to divert water to bank claim. Banksman.— 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 m. X 5 ft. are used. Bar I>iggmgs.—{1) 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.— Soo 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. Ran’ena (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 un worked 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.— {\) 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.— ^letai not classed with the precious metals, gold, silver, plat- inum, etc., that are not easily oxidized. Basin. — (1) 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 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. Batt (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.— YY iq inclination of a face of masonry or of any inclined portion of a frame or metal structure. Battery. — (1) 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 CowTifr?/.— (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 screen. Bean 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. — (1) 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 7?i.— 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 Bocfc.— The solid rock underlying the soil, drift, or alluvial deposits. Before-Breast— Bock 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. BeZZ.— 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. — (1) A natural terrace marking the outcrop of any stratum. (2) A stratum of coal forming a portion of the vein. Bench Diggings.— Bi\cv placers not subject to overfiow. Benching.— Yo 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 — made by the Bessemer process. Beton (English).— Concrete of hydraulic cement with broken stone, bricks, gravel, etc. Bevel .— slope formed by trimming away on edge. Bevel Gear . — A gear-wheel 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 Bmder.— Indurated argillaceous shales or clay, very commonly forming the roof of a coal seam and frequently containing clay iron- stone. See Batt. Binding.— Riring 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. BtocA:6a7id.— 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. ^tocfcdamp.— Carbonic-acid gas. Black Diamonds. — Coal. Black Ends.— Refuse coke. Black Flux.— ChavcooX 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 Tafttos.- Inclined planes covered with blankets, to catch the heavier minerals passing over them. .Btosf.— (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. J5tonde.— 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 Obscure bedding plane. Blind Lead, or Blind Lode.— A vein having no visible outcrop. Blind Level.— {!) 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 Coat— Coal that breaks in large rectangular lumps. Blocking^ Out.—{l) Working deep leads in blocks; somewhat like horizontal stoping. (2) (Australian) Washing gold gravel in sections. Block Re^s.— Reefs showing frequent contractions longitudinally. Blo GLOSSARY. Bon 573 Block Cast tin. Bloomary.— K forge for making wrought iron. Blossom.— YhQ decomposed outcrop, float, surface stain, or any indicating traces of a coal bed or mineral deposit. Blossom Rock. — (ij Colored veinstone detached from an outcrop. (2) The rock detached from a vein, but which has not been transported. Blow.—{l) 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.—Yo 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.—{l) 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 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 Jb/iTi.— 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. Ri^esto 7 ie.—( 1 ) 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.— B\\mt. 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 i 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. — (1) 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.— {!) 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, Bee JSoTise.— 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.” Bor^.— 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.—Gvaipe-like in appearance. Bottle Jack (English). — An appliance for lifting heavy weights. Bottom.— iX) 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. Bottomery 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.—{1) The deepest column of a pump. (2) The lowest or deepest lift or level of a mine. Bottom Pillars.— Largo 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. — (1) 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 a shaft on which miners stand to work the tackle. (3) (Cornish) Building at pit mouth. Brace Beads.— Wooden handles or bars for raising and rotating the rods when boring a deep hole. B?m 2 :e.— Charcoal dust. Brake Seive. — Hand jigger. Brances.—lron pyrites in coal. BrancTi.— 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. B?’asses (English).— Fitting of brass in plummer 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 CZof/i.-Du eking 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.—Y\iQ 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 .— 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. Freese.— Fine slack. J5ree2!e.— Small coke, probably same as braize or braise. Brettis (Derbyshire). — A timber crib filled with slack. Bridge.— {!) 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 haulageway and which can be raised out of the way of ascending and descending cars. (3) An air crossing. Bridle Chains.—SYioit 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 .— 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 CoaZ.— Anthracite coal that will pass through a mesh or bars 3i to 4i in., and over a mesh 2f in. square. (See page 434.) Bronce (Mexican). — In mining, copper or iron pyrites. Brooch (Cornish).— Mixed ores. Brooc/imgr.— 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 CoaZ.— Lignite. A fuel classed between peat and bituminous coal. Brown /Spar.— Dolomite containing carbonate of iron. Brownstone. — (1) 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 “6ras/i” 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. Bucket Sword.— 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 jigmng. 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 i in. and over a mesh i in. Buddie.— An inclined table, circular or oblong, on which ore is concentrated. Buddling.—W ashing. 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.— {!) A tight partition or stopping. (2) The end of a flume carry- ing water for hydraulicking. 576 GLOSSARY. Bul 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. Buller 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. Bull 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. Bull 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.— coal consumed on board ship. Bunney.—A nest of ore not lying in a regular vein. 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.— {!) 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.— TL q globule of metal, the result of an assay. Button Balance. — A small very delicate balance used for weighing assay buttons. Butty. — 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.— {!) 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 Omdcs.- 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. eager . — 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.— props or catches on which cages stand during caging or changing cars. Caking Coal. — Coal that agglomerates on the grate. Cal. — Wolfram. Cala (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.— K 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. Callys (Cornish).— Stratifled rocks traversed by lodes. Caw.— (1) A curved arm attached to a revolving shaft for raising stamps. (2) Carbonate of lime and 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.—{1) 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.— (1) 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. Capellina (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.—{l) A rich bunch of ore in the country rock connected with the lode by a mere thread of mineral. (2) ((’ornish) An irregular deposit of tin ore. Carbonaceous.— Coaiy, containing carbon or coal. Carbonate.— Caxhonic acid combined with a base. Carbonates.- Lead ore. The oxide and carbonic-acid compounds of lead; also applied to lead sulphate. Carbon?/erons.— 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.— Taper 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.— Tig 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 Cannier, or Cannier 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. Cawk. — Baryta sulphate. 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 wTOUght 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 reverberarory 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. Centrifngal Force.— A force drawing away from the center. Centripetal Force.— A force drawing toward the center. 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. C/iair.— Sometimes applied to keeps. Chamber. — See Breast. Char CO (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. Charqnear (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 C'oa?.— 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. CAeefc.— Wall. Chert— A silicious rock, often the gangue of lead and zinc. Chestnut CoaZ.- Anthracite coal that will pass through a mesh If in. square and over a mesh f 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.— {!) An ore shoot. (2) A furnace or air stack. Chinese Pump.— Lihe 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 fall. When worked by blows of a hammer or sledge, it is called a “ jumper.” Chute (also spelled Shute). — (1) 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 stoping. Cmr^abar.— 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 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. C'^as^^c.— 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.—¥ov molding clay in a wet bore hole. Clay J5and.— Argillaceous iron ore; common in many coal measures. Clean- Up. — Collecting the product of a period of work with battery or sluice. Clearance.— il) 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.— {1) 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. C/od.— 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.— ^ee Breaker. Coal Cutter. — A machine for holing or undercutting coal. Coal Dust.—Yerj 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 (Chose).— 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. Coh (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 ChcA:m.— 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.—K chock. Cohete (Mexican).— A rocket; applied to a blast within a mine or outside. Coil Brag— A tool for picking pebbles, etc. from drill holes. Coke— The fixed carbon and ash of coal sintered together. C'o^as (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. Co^or.— 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.— Ynion of different formations. Contact Load or Vein. — A vein lying between two differently constituted rocks. Contour.— {1) 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. Conteamwa (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. Co?'es.— 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 elsewbere. 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. Cro 581 Costean (Cornish).— To prospect a lode by sinking pits on its supposed course. Trenching for a lode. Cost Book (Cornish).— Mining accounts. Cotton Rock.— {1) Decomposed chert. (2) A variety of earthy limestone. Coulee.— {1) 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.— {1) A cross-vein. (2) (English) An apparatus for lecording the number of strokes made by the Cornish pumping engine. (3) A second- ary haulageway in a coal mine. Counterchute.^X chute down which coal is dumped to a lower level or gangway. Counter gangway. —X level or gangway driven at a higher level than the main one. Country.— TY iq formation traversed by a lode. Country i^ocA;.— 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.—X self-acting brake. Coyoting.— IrvQgyxlav mining by small pits. Crab.—X 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.— X box with a sieve mounted on rockers for washing auriferous alluvial. Cradle Dump.—X 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.— Fart 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 do not change their relative positions as they do in a derrick. There is also a rope drum with winding rope, etc. Create (Cornish).— (1) Tin ore collected in the middle of the huddle. (2) The middle of a huddle. 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.— X fissure. C revicing. —Fieking 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) X structure composed of horizontal timbers laid on one another, or a iramework 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.— X sieve. Crisol (Mexican).— A crucible of any kind. Crop. — See Outcrop. Crop Fall.—X 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.— FoTtions of a vein as seen exposed at the surface. Cropping Owi.— Appearing at the surface; outcropping. ; Cross- Course. —X vein lying more or less at right angles to the regular vein of the district. t.; : 582 Cro GLOSSARY. Deb Crosscut. — (1) A tunnel driven tlirough 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 ijy the discoverer of a lode to tempoiarily 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- Hole. — See Crosscut (2). Cross- Latches. — See Latches. Cross-Spur.— A vein of quartz that crosses the reef. Cross- rein.— 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. Cru^le.—{1) The bottom of a cupola furnace in which the molten materials collect. (2) Pots for smelting assays in. Crush. — See ^ueeze, 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. Cu^m.— Anthracite-coal dirt. Culm Bank, or Culm Dump. — Heaps of culm now generally kept separate from the rock and slate dumps. Cuha (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 snaft. (2) The heavy frame or sill at the top of a shaft. Curbing.— TRe 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 Dovm.—To cut down a shaft is to increase its sectional area. Dim.— 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 dro^vn out a mine fire. Damu. —Mine gases and gaseous mixtures are called dami)s. 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 se'en 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. — (1) Unproductive. (2) Unventilated. Dead Men's Graves (Australian). — Grave-like mounds in the basalt under- l 3 ring auriferous gravels. Dead Quartz. — Quartz canying no mineral. Dead Riches.— t^d carrying much bullion. Dead RoaM.— To completely drive off all volatile substances. Deads. — Waste or rubbish from a mine. Dead TUarfc.- Exploratory or prospecting work that is not directly productive. Brushing roof, lifting bottom, cleaning up falls, blowing roek, etc. Dean (Cornish). — The end of a level. D^rw.- 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. — (1) 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. — (1) A crane in which the rope or 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. Desaguador (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. 'Ohras 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. Despmsa (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 diagonal to the strike of the cleavage. Dial (English).— An instrument similar to a surveyor’s compass, with vernier attached. 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.— here gold and other minerals are dug out from shallow alluvials. Dike.—^ee also Dyke. Dillits, or Ginneys.— Short self-acting inclines where one or two tubs at a time are run. Dillueing (Cornish). — Dressing tin slimes in a fine sieve. Dip.—{i) 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. Dipping Needle.— A magnetic needle suspended in a vertical plane; for locating iron deposits. 584 Dir GLOSSARY, Dbe Dirt FauU.^A confusion in a seam of coal, the toj) and bottom of the seam being well defined, 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.— Sep&rsition by mechanical means, not by decomposition. Ditch.— {1) 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. Doles.— Small piles of assorted or concentrated ore. Dolly.— {!) 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. Z>oors.— 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.— Tvfo 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. Dradg'e (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.—{1) 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.— An 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, ^ee Robbed. Dresser (Staffordshire).— A large coal pick. Dre GLOSSARY. Egg 585 Preparing poor or mixed ores mechanically for metallurgical operations. Dressing Floors.— TY iq floors or places where ores are dressed. Drift.— \l) 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, driven from the surface in the seam. (3) Unstratified diluvium. Drifting.— Yfirming 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. Driwwsr.— 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 by 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 (Stafibrdshire).— A vessel for carrying fresh water into a mine. Drum.-TYie cylinder or pulley on which the winding ropes are coiled or wound. Drum Rings.— Q 2 i^i-iTon 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.— Yiaeers 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.—{\) 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.—Yieees, under 2 to 3 dwt. Duty.-TYie 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 Coo?.— Anthracite coal that will pass through a 2i" square mesh and over a 2" square mesh (see page 434). 586 Elb GLOSSARY. Pal Elbow— A sharp bend, as in a lode or pipe. Electric Instantaneous blasting of rock by means of electricity. Elevator Pump—Kn 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 race cleats. Endless Chain. — A system of haulage or pumping by the moving of an endless chain. Endless Rope. — 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. — (1) 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 manway. 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. Escoriai.— Slag pile. Esconficador (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 verj^ 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. Face.— (1) 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. Face-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.—{1) 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. Fal.se Bottom.— Ci) 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 GLOSS AEY. Fla 587 Famp (Northof 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 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— K 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. — (1) 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.— Fenemg 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- Of {English) .—A sort of bell-crank for turning a pump rod past the angle of a crooked shaft. Fierros (Mexican).— Iron matte. Fzeri/.— 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. — (1) A mixture of light carburetted hydrogen {CHf) 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 fiat 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 Fla GLOSSARY, Fre Flat Rod.— A horizontal rod for conveying power to a distance. Flats.— Narrow decomposed parts of limestones that are mineralized. Flat Sheet.— Qheei-iron flooring at landings and in the plats, chambers, and junctions of drives, to facilitate the turning and management of trucks. Flat Wall (Cornish).— Foot-wall. Flintshire Furnace . — A kind of reverberatory furnace used for smelting lead ores. 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 .— 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.— {1) 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 flne tin. Flour Gold.—Tlao flnest alluvial gold. Flouring.— Korcnry reduced to flne 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. F turning— lAiting a river out of its bed with wooden launders or pipes, in order to get at the bed for working. Flush.— il) 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. Fte.— 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.— FLolos, cut in the sides of shafts or winzes to enable miners to ascend and descend. Foot-Piece.— {!) 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.—^ee Blowdown Fan. Force P^ece.— Diagonal timbering to secure the ground. Force Pump.— A pump that forces water above its valves. Forebay.— PenstocL. The reservoir from which water passes directly to a waterwheel. 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.— Prie first working of a seam in distinction from pillar drawing. PorA:.— (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. PosszcA:i7ic/.— Overhauling old workings and refuse heaps for gold. Fossil . — Organic remains or impressions of them found in mineral matter. Fother (North of England).— i chaldron. Frame.— A table composed of boards, slightly inclined, over which water runs to wash off waste from sluice tin. Frame 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. (tOB 589 Free Jlfiw€r.— Licensed miner. Fresno (Mexican) .—An ash tree. Fronton (Mexican).— Any working face. FueUe (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. FxLse.—iX) A hollow tube filled 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. Galeme (Mexican).— A reverberatory furnace. See Cendradilla. Galera (Mexican).— A shed; any long or large room; a storehouse. G'aKagre.— Royalty. Gallery . — A horizontal passage. Gallos (Mexican).— Rich specimens of silver or gold ore, particularly those that show native silver or gold. Gallows Frame .— 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.” 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. Oas.— See Firedamp. Any firedamp mixture in a mine is called gas. Gas Coa?.— 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.— {1) 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 y or Pair of Gears.— {1) 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.— LaTgQ nodules of stone with a hollow in the center. Geordie.—A safety lamp invented by George Stephenson. Ge^/ser.— Natural fountain of hot water and steam. Gib.—{V) 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.—^QQ Billies. 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.—{l) 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. €hb Spontaneous combustion underground of fine coal and slack in the gob. 590 Gob GLOSSARY. Gut Gobbing C^.— 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 less parallel to the end or dip joints. Granza (Mexican). — Metallic minerals from the size of rice to that of hens’ eggs. Grasa (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. Graved.— Water- worn stones about the size of marbles. Gray Metal.— ^hsTe 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 Washing alluvial, loosened by pick and shovel, intrenches cut out of the bed rock, using bars of rock as natural riifles. 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 ) . — W orked-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. Gurt (Cornish).- Water runnel from dressing floor. Gutter.— {\) 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.— {!) At an angle of 45° from general or previous course. (2) Half on the level and half on the dip. Half Set.—OnQ leg piece and a cap. Halvans.—GangMQ containing a little ore. Hammer-and-Plate . — A signaling apparatus. Hand Barrow.— K 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.— y^oodenpmnp 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.— Residne from tin refining; contains much iron and arsenic. Ha?TOic.— 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 hy himself on his own account. Haulage Levers, jaws, wedges, etc. by which 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.— {1) 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.— (1) 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.— {!) 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.— Flacers 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.—{l) 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.— {1) 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.—^ee 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 . — Coal 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 lb. 1 ft. high per minute. Horse, or Horsebacks.— {1) Natural channels cut or washed away by water in a coal seam, and filled 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). - 7 -See Demasia. Hulk (Cornish).— To pick out the soft portions of a lode. Hundido ( Mexican) . — See Derrumbe. Hungry. —S^orthless looking. Hurdy Gurdy.—A waterwheel that receives motion from the force of traveling water. .HwsMngf.— 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. Hydraulicking . — Working auriferous gravel beds by hydraulic power. //ydrocarbcns.— 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.— haoTt 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 eifected. 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.— K 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. / 7 i-/orfc.— 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. Instroke.— Yhe. 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. Jaboncilio (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. — (1) A kind of coupling hook for connecting cars on an incline. (2) An allowance of liquor sometimes issued to workmen (almost obsolete). {^) See Jig. Jigging.— Sepamtmg 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.— {!) 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 “ dramng a jud.” Judge (Derbyshire and North of England). — A measuring staff. Jugglers, or J^itZars.— 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.-YooTQst lead ore. Keeker.— An official that superintends the screening and cleaning of the coal. Ked Wedge.— A long iron wedge for driving over the top of a pick hilt. Keeps, or Aeps.— 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.—{\) An iron bar of suitable size and taper for filling the keywaysof shaft and pulley so as to keep both together. (2) A kind of spanner used in deep boring by hand. Kibble.— 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.— {1) 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. Ltd 595 Lamas (Spanish).— (1) Slimes. (2) Argentiferous mud treated by amalga- mation. Lamero (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 ifew.— 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.— {1) A level stage for loading or unloading a cage or skip. (2) The top or bottom of a slope, shaft, or inclined plane. Land 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. Xap.— 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.— {V) 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 .— 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.— Yrom the side. Lath.— A. plank laid over a framed center or used in poling. Launder.— Water trough. Laundry Xox.— The box at the surface receiving the w^ater 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 (Statfordshire). — 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. Leader.— 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 Lip GLOSSAHr. Lum 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.—FevLcing placed around the mouth of a shaft, which is lifted out of the way by the ascending cage. Lignite— K 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 Coa^.— 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.— 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.— name given to a special sort of hydraulic nozzle used for sluicing purposes. Live Quartz.— K 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 TracA:.— Track used for loaded cars. Loader.— OiiQ 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 alwaj’^s 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.—{l) 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-Pillar 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 lb. Longwall.—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. Loot) (Cornish).— Sludge from tin dressing. Loose End.—{1) 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.— 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. Lum GLOSSARY. Mer 597 Lump Coa?.— (1) 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.—A.n 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 AeedZe.- Needle used in surveying. Magnetic North .— direction indicated by the north end of the magnetic needle. Magnetic Meridian .— line or great circle in which the magnetic needle sets at any given place. Main i^oad.— The principal haulage road of a mine from which the several crossroads lead to the working face. Main Rod (English).— See Pump Rod. 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.— A.n 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. — (1) A refuge hole constructed in the side of a gangway, tunnel, or slope. (2) A hole in cylindrical boilers through which 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 henequen, 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.—Q\ay 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.^il) In coal mining, induratea 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 and electricity, and, as a rule, of a higher specific gravity than the non- metals. (3) (Mexican) All kinds of metalliferous minerals are called “metal” in Mexico. Metal de Ayuda— Fluxing ore of any kind. Metal de Cebo—Yeiy rich ore, usually treated in small reverberatory furnaces. Metal Ordinario.— Common ore. Melal Pepena.— The best class of selected ore. Metlapil (Mexican).— See Mano. MW.— Works for crushing and amalgamating gold and silver ores. Mill Cinder.— The slag from the puddling furnace of a rolling mill. Mill Hole.—A.n auxiliary shaft connecting a stope or other excavation with the level below. Mill 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 Oz7.— 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. Mp.— 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. Muckle . — 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.— YhQ upper grinding iron or rubbing shoe of amalgamating pans, etc. Mullock.— CoxmiTy rock and worthless minerals taken from a mine. Mundic.—lion pyrites. Naked Light.— A candle or any form cf lamp that is not a safety lamp. Narrow Work.—{l) 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.— NentilaXion 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 flow in one direction, or to ascend. Neck.— A cylindrical body of rock differing from the country around it. Needle.— {1) 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 roc.k to receive the end of a timber. Negrillo (Mexican).— Black sulphide of silver. Nick . — To cut or shear coal after holing. Nicking.— {!) 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.— Yho, 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 Owf.— The disappearance of a coal seam by the thickening of the adjoin- ing strata, which takes its place. Nitro . — A corrupted abbreviation for nitroglycerine or dynamite. Nittings.—RQfns,e of good ore. Nodular.— Blistered or kidney-shaped ore. iVbdwZes.— 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.— Smsdl lumps of coal that will pass through a screen or bars, the spaces between which vary in width from i to 2k 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 Sm,eUers.—M.en 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 Casf.— Workings having no roof. 600 Ope GLOSSARY, Pan Open Cutting.^{l) 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. Oroc/ie (Spanish).— (1) Retorted bullion. (2) (Mexican) Bullion containing gold and silver. Outburst. — A blower. A sudden emission of large quantities of occluded gas. Outbye. — In 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 Out. 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 producj: 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). — Ferruginous silver ores. Paddock.— {!) 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 Qold.—The very finest films of gold coating other minerals. Paleozoic.— The oldest series of rocks in which fossils of animals occur. Palero (Mexican).— A mine carpenter. Palm.— A 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.— {1) 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 OLOISSAR Y Pic 601 Panino f Mexican). —The peculiar appearance, form, or manner in which the metallife^us minerals present themselves m any given district PanMntoTPanning 0#.-Separating .gold or tin from its accompanying minerals by washing off the latter in a pan. ^S^?;ra.K?nS>o7to«rsVi“'?;^ a chattering noise nart of the ores in place of wages. Usually, the mine provides Sndles nowdir, and steel, and keeps the drills sharpened, and receives, in navnient of royalty and supplies, two-thirds or more of the ore taken ouU ^his contract is renewed weekly or monthly, etc., tion of ore retained by the miners is more or less, according to the richness of^the stones where they work. This is a cheap way of getting ore as far S^labor is concern^^^^^^^ But the miners must be constantly watched; Sherwie they will leave the mine in bad state. The proportion of pre assigned to the miners is generally bought from them by the mine owner himself, for various reasons. ^ i /o\ a Parting —{1) Any thin interstratified bed of earthy material. (2) A side track or turnout in a haulage road. down ore to a lower level (2) A pasLge left in old workings for men to travel in from one level to Pas^^v^.— A siding in which cars pass one another underground. A turnout. Pass-into.— When one mineral gradually passes into another without any coal mixed with 8 to 10 ^ of pitch or tar, and compressed 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. PaHiTSeidcanl^-Any paved enclosure more or less surrounded by build- hig“ In OTe-s^r?higyard. A floor or yard where argentiferous mud is treated by amalgamation. Paf Pir^.— That portion of an alluvial deposit that contains gold in payable quantities. Pay Out— To slacken or let out rope. Pay PocA:— Mineralized rock. Pay Mineralized part of rock. Peac/i /Stone (Cornish).— Chlorite schist. Pea Coal— A small size of anthracite coal (see page 434). Pm? — T^edecomposed^ partly carbonized organic matter Pebble Jack.— Zino blende in small crystals or attached to rock, but is found in clay openings in the rock. Pee (Derbyshire).— A fragment of lead ore. Pdla, or Plata Pella (Mexican).— Silver amalgam. PerdHous^—J^wooden covering for the protection of sinkers working in a Pc»(to-Af^ pieces of timber laid as a roof over men’s heads, to screen them when working in dangerous piaces, e. g., at the bottom of shafts. Pepenado (Spanish).— Dressed ore. pS^i^Tabk^-USn^oh^oW^^ table used in separating very fine ores from slimes. . . 14 ^ Petlanque (Mexican).— Ruby silver. ^et?rU^K"eu7trnfa»^^^^^^ or face of an excavation with a pick. 602 Pic GLOSSARY. Pla Picker.— {1) 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.— {1) 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.— K 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 Timhering.—^oWovf 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. 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.— {!) 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. Pillar -and-Stall.— See Breast-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. Pina (Mexican).— Same as Pella. Pinch.— A contraction in the vein. Pinch Owi.— 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. Undercutting and washing away gravel before the water nozzle. P^^.— (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.— Y\ie portion of a mine immediately around the bottom of a shaft or slope. See Shaft Bottom. Pitch.— {1) Rise of a seam. (2) Grade of an incline. (3) Inclination. (Cor- nish) A part of a lode let out to be worked on shares, or by the piece. Pit Coa?.— 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 Poom.— 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 Mmnp.— 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. Trabajar de Plan.— To work to gain depth. Plancha (Mexican).— A pig of lead, etc. A plate, thick sheet, or mass of any metal. Pla OLOSSARY. Pop 603 Planchera (Mexican).— A mold of sand, earth, or iron, . to form pigs of lead. Plane— K main road, either level or inclined, along which coal is conveyed by engine power or gravity. Plane Table— K 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 Pam.— 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.— ThQ 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).— lodyrite. 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. PZa^e (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 Oeuvre (French).— Dressed galena. Plomillos (Mexican).— Shots of lead found in slags. Plomo (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. Plumb.— V ertical . Plummet. — (1) A heavy weig;ht 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.— Th.e solid ram of a force pump working in the plunger case. Plunger Case.— The pump cylinder or barrel in which the plunger works. Plush Popper.- Chalcotrichite. Plwm (Welsh).— Lead. Poblar (Mexican). — To set men at work in a mine. Pocket.— il) 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 TooZs.— Drilling tools used in drilling in the old fashiop with rods, now superseded by the rope-drilling method. Polroz (Cornish). — Waterwheel pit. Poling.— Behning metal, when in a molten condition, by stirring it up with a green pole of wood. Poll Pick.— A pick having the longer end pointed and the shorter em. uam- 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).— {1) 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.—{l) 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.— StTatSi 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 removiug the top of the lamp. Prill.— {!) 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.— timbering of a mine. Prospect— 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. — (1) 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.—{l) A bore hole driven for prospecting purposes. (2) A small heading driven in to find a bed or vein lost by a dislocation ol the strata, or to prove the quality of the mineral in advance of the other workings. Pudding Machine.— A circular machine for washing pa^y dirt. Pudding i^ocfc.— Conglomerate. Puddle. — (1) Earth well rammed into a trench, etc., to prevent leaking. (2) A process for converting cast iron into wrought iron. (Mexican). — The actual wmking 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. PuUey.—{\) 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. Overwinding or drawing up a cage into the pulley frame. Pi^Zp.— Crushed ore, wet or dry. Pump. — Any mechanism for raising water. Pump Po?).— See Boh. Pump Ring.— A flat iron ring that, when lapped with tarred baize or engine shag, secures the joints of water columns. Pump Pods.— 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.— pieces of decomposed rock found in placer deposits. Pyran (Cornish).— See Prian. Pi/n^es.— Sulphide of iron. Pyrometer.— An instrument for measuring high degrees of heat. Quajado (Spanish).— Dull lead ore. 0uarry.—{l) An open surface excavation for working valuable rocks or minerals. (2) An underground excavation for obtaining stone for stowage or pack walls. Quartz Bucket— K bucket for hoisting quartz. Quaternary.— Post-tQrtmry 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. Qtteme (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 huddle. Raff.—TYie coarse ore after crushing by Cornish rolls. Raffain (Cornish).— Poor ore. Raff Wheel.— A revolving wheel with side buckets for elevating the raff. Rdjter Timbenng.— That in which the timbers appear like roof rafters. Rag Burning (Cornish).— The first roasting of tin-witts. Ragging (Cornish). Rough cobbing. Rag BTied.— 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. Pam.— (1) The plunger of a pump. (2) A device for raising water. Ramal (Mexican).— A branch vein. Ramalear (Mexican) .— To branch off into various divisions. PambZe.— 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. Peamtng.— Enlarging the diameter of a bore hole. Receiving Pit.— A shallow pit for containing material run into it. Red-Ash Coal.— Coal that produces a reddish ash, when burnt. Red Rab (Cornish).— Red slaty rock. Reduced.—S^hen 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. Pee/.— (1) A vein of quartz. (2) Bed rock of alluvial claims. JieeJ Drive.— In alluvial mines, drives made in the country rock or reef. 606 Ref GLOSSARY, Riv Refining. —Yhe freeing of metals from impurities. i 2 e/racibry.— Rebellious ore, not easily treated by ordinary processes. Refuge Hole— A place formed in the side of an underground plane in which a man 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. Rendif (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.— MmevaX 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. Respaldo AHo.-TIoq hanging wall. Respaldo Bajo.— The foot-wall. Rests, Keeps, M'w.— Supports on which a cage rests when the loaded car is being taken off and the empty one put on. Resue —See Stripping. Retort— {!) 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. RfcA:.— 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.— iX) 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 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. J^zppm.gr.— Removing stone from its natural position above the seam. Riscos (Mexican).— Sharp and precipitous rocks; amorphous quartz found in veins or outcrops. 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. Sap 607 Road.—{l) Any underground passageway or gallery. (2) The iron rails, etc. of underground roads. Roasting.— Ueating 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.— ^ee Drawing an Entry. Eock.—A mixture of different minerals in varying proportions. Rock Breaker.— K machine for reducing ore in size by crunching it between powerful jaws. Rock Chute. — See Slate Chute. Rock Drill.— K 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 An inequality in the roof or floor of a mine. Roller.— A small steel, iron, or wooden wheel or cylinder upon which the hauling rope is carried just above the floor. Rolleyway.—A main haulage road. Rolling Ground.— ^hen the surface is much varied by many small hills and valleys. 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. — Coal 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. jRwbbZe.— 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 Coa?.- 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 Lift.— A sinking .^et 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 de buena 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.— Applmnces 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 ' Saf 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 he 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.— {!) 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 TFbrArs.— 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.— IncTustations 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. Scarifier. —A small dish used in assaying. Scovan (Cornish).— A tin lode showing no gossan at surface. Score (Cornish).— Purest tin ore. Scramming.— Cleaning up small bodies or patches of ore left in the ordinary process of mining. Scraper.— {1) 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.— il) 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. Fracturing the slate aloflg 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. SeaZmgr.— 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.— Blocks 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.— Detaehed 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.— AnXomatio, 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 flx 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.— {!) 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 w.Mghts. Shears, or Sheers (English). — Two tall poles, with their leet 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 Sludgen 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. — (1) 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. Sheading ( Cornish) .—Prospecting. Shoe.—{l) 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—{1) 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~Yo 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.—{l) A charge or blast. (2) The firing of a blast. (3) Injured by a blast. Shot-Firer.— See Shot Lighter. Shot Hole.—Tloe 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 Granular pieces like shot. Show.—S^hen 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.— {1) 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. Inclination. Side.—{1) 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 head wise direction. Sight.— {\) A bearing or angle taken with a compass or transit when making a survey. (2) Any established point of a survey. Sights— '^oh^ 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. SiU.—{\) Q'he fioor 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.— Cool 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.— In 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.— TY iq 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 mrm 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.-YYiQ 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 between 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 manway 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 Ricker.— (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 Tab'e (Cornish). — A buddle. Sleeve.— A ho How cylinder fitting over two pieces, to hold them together. 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. — (1) The pulp or fine mud from a mill or from a drill hole. (2) Silt containing a very fine ore, which passes oflF in the water from the jigs. Slings.— Rieees 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.— {!) 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. 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. -Leadi-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 d hilo de veta. — A drift tunnel. Socavon crucero.—A crosscut tunnel or adit. Socket. — (1) 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 at Soplete.—A blowpipe assay. Sorting. — Separating valuable from worthless material. Sounding.— {!) Knocking on a roof to see whether it is sound or safe to wwk 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.—{l) 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.— Five 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 picke,d piece of mineral. Speiss. — A basic arsenide or antimonide 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.—MaingSLnifeTous white cast iron. Sjpiking 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. Short 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 Brum.— 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.— Y]ie 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, Spad.—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. 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, Stamps. — 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 GLOSSARY. Sto Sta 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.— {i) Fine shale or dirt put into a shot hole after the powder, and rammed hard. (2) Tami)ing 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.— WsiteT-tight stone walling of a shaft cemented at the back. Stook.—A f)illar 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.—{l) To excavate mineral in a series of steps. (2) A place in a mine that is worked by sloping. (Stopingf.- Working out ore between two levels or on the surface, by slopes or steps. Stoping Overhand . — Mining a slope upwards, the flight of steps being inverted. Stoping Vnder hand. —Mining a slope 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 21" to 2" mesh and over a 1^" to li" mesh; small stove, known as No. 4, passes through a Ij" to 1|" mesh and over a Ij" to 1" 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.—{l) Windlass. (2) Landmarks. Stowing.— The debris 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.— X 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.—X system of getting coal by headings or narrow work. Strake.—A slightly inclined table for separating heavier minerals from lighter ones. Stratification.— ATT&ngement 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 Bor d-and- Pillar. 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.— ZoiniB or cleavages that are parallel to the strike of the seam. Striking i)eaZ.— 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. 5fr2p.— (1) 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. Stull. — 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 /Spra^/f.- The horizontal member of a square set of timber running longitudinally with the deposit. 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. — (1) 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.— Tho^e 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. Swally, 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.— Yxee from deleterious gases. Sweet Roast.— To roast dead or completely. The arc or curve described by the point of an instrument, such as a pick or hammer, when being used. Swinging P^a^e.— Amalgamated copper plates hung in sluices, to catch float gold. Switch.— {1) 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 GLOSSARY, Tep Synclinal The line or course of a syncline. Syncline.— 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. Taladfar.— To bore or drill. Tally'.— {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 GLOSSARY. Tra 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. TMW.- See Floor. Thimble.— {1) 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.— {1) A fault of dislocation. (2) The vertical distance between the two ends of a faulted bed of coal. Thrown.— Fanlted; broken by a fault. Thrust.— Cree^ 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. Therms (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. Calcite or carbonate of lime. Timber.— (1) Props, bars, collars, legs, laggings, etc. (2) To set or place timber in a mine or shaft. Timberer, 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 an 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.— T]ie 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.— {!) 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.—{\) 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. Torf a (Mexican).— A pie or cake; the heaps of argentiferous mud that are treated in the patio process of amalgamation. Tossingt.- Shaking powdered ore in water, to effect separation of heavy and light particles. Tovera (Mexican).— The tuyere of a smelting furnace. Tmcfc. — 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. C18 Tra GLOSSARY. Tum Train, or Tnp.— The cars taken at one time by mules, or by any motor, ox run at one time on a slope, plane, or sprag road, always together. Tram.— A mine car, or the track on which it runs. Trammer.— One who pushes cars along the track. Tramroad.—A mine track or railroad. Tram Rope.— A hauling rope, to which the cars are attached by a clip or chain, either singly or in trips. Tramway.— A small, roughly constructed iron track for running wagons or trucks on. Transfer Carriage.— MoYsible platform or truck used to transfer mine cars from one track to another. Transome (English).— A heavy wooden bed or supporting piece. Trap.— (1) A steep heading along which men travel. (2) A fault of dislo- cation. (3) An eruptive rock. (4) A dangerous place. Trap Door.— A small door, kept locked, fixed in a stoping, for giving access to firemen and certain others to the return airways, dams, or other unused portions of the mine. Trap Dike.— A fault (not necessarily accompanied by displacement of strata) in which the spaces between the fractured edges of the beds are filled up by a thick wall of igneous rock. Trapiche (Spanish).— A primitive grinding mill. Trapper.— A boy employed underground to tend doors. Traveling Road.— An underground passage or way used expressly, though not always exclusively, for men to travel along to and from their work- ing places. Treenail.— A long wooden pin for securing planks or beams together. Treloobing (Cornish).— Stirring tin slimes in water. Trend.— The course of a vein, fault, or other feature. Tribute.— A method of working mines by contract, whereby the miners receive a certain share of the products won. Tributers.— Miners paid by results. Trig.— A sprag used to block or stop a wheel or any machinery. Trilla (Mexican). — The same as Torta. Trip . — The mine cars in one train or set. See Train. Triple-Entry System . — A system of opening a mine by driving three parallel entries for the main entries. Triturate. To grind or pulverize. Trolley.— {\) A small four-wheeled truck, used for carrying the ore bucket underground. (2) An electric motor. (3) The arm of a motor that con- ducts the electric current from the wire above the track to the machine. Trommel.— A drum, consisting of a cylinder- or cone-shaped sheet-iron mantle (generally punched with holes) that revolves; used for washing or sorting ores. Trompa (Mexican).— A funnel-shaped mouthpiece of cooled slag that forms within a smelting furnace over the tuyere opening. Trompe . — An apparatus for producing ventilation by the fall of water down a shaft. Trouble.— A dislocation or fault; any irregularity in the bed. Trough Fault— A wedge-shaped fault, or, more correctly, a mass of rock, coal, etc. let down in between two faults, which faults, however, are not necessarily of equal throw. Troughs, or Thirling.— A passage cut through a pillar to connect two rooms. Truck . — Used synonymously with Barney. Truck System . — Paying miners in food instead of money. Cylindrical projections or journals, attached to the sides of a vessel, so that it can rotate in a vertical plane. Trying the Lamp.— The examination of the flame of a safety lamp for the purpose of forming a judgment as to the quantity of firedamp mixed with the air. Tub.—{1) A mine car. (2) An iron or w^ooden barrel used in a shaft, for hoisting material. Tubbing.— Oast iron, and sometimes timber, lining or walling of a circular shaft. Tubbing TTed^rd’s.— Small wooden wedges hammered between the joints of tubbing plates. Tubing.— Iron pipes or tubes used for lining bore holes, to prevent caving. Tumbar (Mexican).— To knock down ore, etc. Tambe (Mexican).— The act of knocking down and taking out ore. Tun GLOSSARY. Ven 619 Tunnel.— K horizontal passage driven across the measures and open to day at both ends; applied also to such passages open to day at only one end, or not open to day at either end. Turbary.— A peat bog. Turbine.— A rapidly revolving waterwheel, impelled by the pressure of water upon blades. Turn.—{1) The hours during which coal, etc. is being raised from the mine. (2) See Shift. (3) To open rooms, headings, or chutes off from an entry or gangway. (4) The number of cars allowed each miner. Turnout.— A siding or passing on any tram or haulage road. Turn Pulley.— A sheave fixed at the inside end of an endless- or tail-rope hauling plane, around which the rope returns. See Tail-Sheave. Turntable.— A revolving platform on which cars or locomotives are turned around. Tut ITorA:.— Breaking ground at so much per foot or fathom. Tuyere.— TY iq tubes through which air is forced into a furnace. Two-Throw.— WYiQTi, in sinking, a depth of about 12 ft. has been reached, and the debris has to be raised to the surface by two lifts or throws with the shovel, one man working on staging above another. Tye.—An inclined table used for dressing ores. Unconformability.— When one layer of rock, resting on another layer, does not correspond in its angle of bedding. Tinder cast. —An air-course carried under another air-course or roadway. Underclay.— A bed of fireclay or other less clayey stratum, lying immediately beneath a seam of coal. Undercut.— To remove a small portion of the bottom of the bed or the under- clay, so that the mass of coal or mineral can be wedged or blasted down. Underhand Stoping . — See Stoping Underhand. Underhand Work . — Picking or drilling downwards. Underholing, Undermining.— To mine out a portion of the bottom of a seam or the underclay, by pick or powder, thus leaving the top unsupported and ready to be blown down by shots, broken down by wedges, or mined with a pick or bar. Underlie, or Underlay . — The inclination of a lode at right angles to its course, or strike; the true dip. Underviewer, or Underlooker.— An inside foreman. Unit.—{1) The unit of metals is 1^ of whatever ton is used. Generally, the 20-cwt. ton, equal to 2,240 lb., is employed, but, when dealing with copper ores, the 21-cwt. ton of 2,352 lb. is taken; therefore, the respective units are 22.4 lb. and 23.52 lb. (F. Danvers Powers). (2) Ores are quoted at a certain price per unit or per cent, of valuable material in the ore. If an iron ore contains 40^ of metallic iron that is worth 5 cents per unit, the value of the ore is ^2 per ton. Unwater.— To drain or pump the water from a mine, or shaft. Upcast . — The shaft through which the return air ascends. Upraise.— An auxiliary shaft, a mill hole, or heading carried from one level up toward another. Upthrow.^A fault in which the displacement has been upward. Vapor (Mexican).— Steam; heated and stinking gas sometimes found in mines, which causes candles to burn dimly and go out. Vaso (Mexican).— A reverberatory furnace used for smelting rich ore, or for cupeling silver. Fa^.— Large wooden tub used for leaching or precipitation. Vein.— See Lode. Often applied, incorrectly to a seam or bed of coal or other mineral. Veinstone.— The non-metallic portion of a vein associated with the ore. Vena (Mexican).— A thin vein, not over 3 in. thick— a knife-blade vein. Vend (North of England).— Total sales of coal from a mine. Vent, or Vent Hole.—{l) A small passage made with a needle through the tamping, which is used for admitting a squib, to enable the charge to be lighted. (2) Any opening made into a confined space. Ventilating Column . — See Motive Column. Ventilating Pressure.— The total pressure or force required to overcome the friction of the air in mines; the unit of ventilating pressure or pressure per sq. ft. of area multiplied by the area of the airway. Ventilation.— CiienldAion. The atmospheric air circulating in a mine. 620 Ven GLOSSARY, Wat Ventilator.^ Any means or apparatus for producing a current of air in mine or other airways. Vestry (North of England).— A refuse. Veta (Mexican).— A metalliferous vein of rock; a true fissure vein. Loosely, any mineral deposit. Veta Clavada.—A vertical vein. Veta Echada.—An inclined vein. Veta Serpenteada.—A vein with frequent changes of direction or course. Veta Soda. — A vein that joins another. Veta Ramal. — A branch vein. Veta Recostada.—An inclined vein. Viewer.— general manager or mining engineer of one or more collieries, who has control of the whole of the underground works, and also gen- erally of those on the surface. Vinney.— Copper ore with green efflorescence. Vuelta ( Mexican) . — In refining silver, the moment when all impurities have been removed from the silver under treatment. Vug, or Vugh (Cornish).— A cavity in the rock. )IVagon.— A mine car. Wagon Breast.— A breast in which the mine cars are taken up to the working face. Tra27m^/.— Picking stones and dirt from among coals. Wale (North of England).— Hand-dressing coal. Walking Beam.—^ee Working Beam. Wall.—{1) The face of a long wall working or breast. (2) A rib of solid coal between two breasts. Walling.— ^ee Steening. Walling Cribs.— OAk cribs or curbs upon which walling is built. Walling Stage.— A movable wooden scaffold suspended from a crab on the surface, upon which the workmen stand when walling or lining a shaft. Wall Plates.— T\ve two longest pieces of timber in a set used in a rectan- gular shaft. Warners. — Apparatus consisting of a variety of delicately constructed machines, actuated by chemical, physical, electrical, and mechanical properties, for indicating the presence of small quantities of firedamp in the mines. At present, most of these ingenious contrivances are more suited to the laboratory than for practical application underground. Warning Lamp.— A safety lamp fitted with certain delicate apparatus, for indicating very small proportions of firedamp in the atmosphere of a mine. As small a quantity as 3^ can be determined by this means. TFas/i.— Drift, clay, stones, etc. overlying the strata. Washer.— A jig. Wash Dirt.—ThaX portion of alluvial working in which most of the gold is found. Wash Fault.— A portion of a seam of coal replaced by shale or sandstone. Washing Apparatus, or Washery.—{1) Machinery and appliances erected on the surface at a colliery, generally in connection with coke ovens, for extracting, by washing with water, the impurities mixed with the coal dust or small slack. (2) Machinery for removing impurities from small sizes of anthracite coal. . Washout.— Ttie erosion of an appreciable extent of a coal seam by aqueous agency. Wash Place.— A place where the ores are washed and separated from the waste, usually applied to places where the hand jigs are used. Waste.— {1) See Goaf. (2) Very small coal or slack. (3) The portion of a mine occupied by the return airways. (4) Also used to denote the spaces between the pack walls in the gob of longwall working. (5) Refuse material. Waste Gate (English).— A door for regulating discharge of surplus water. Water Blast.— The sudden escape of air pent up in rise workings, under con- siderable pressure from a head of water that has accumulated in a connecting shaft. Water Cartridge. — A waterproof cartridge surrounded by an outer case. The space between being filled with water, which is employed to destroy the flame produced when the shot is fired, thereby lessens the chance of an explosion should gas be present in the place. Water Gauge.— An instrument for measuring the pressure per square foot producing ventilation in a mine. Water Hammer.— The hammering noise caused by the intermittent escape of gas through water in pipes. Wat GLOSSARY. Won 621 Water-Jacket— K jacket filled with water, to keep cool a cylinder or furnace. Water Level.— Kn underground passage or heading driven very nearly dead level or with suflacient grade only to drain off the water. Water Right — privilege of taking a certain quantity of water from a watercourse. Watershed .— elevated land or ridge that divides drainage areas. Waterwheel (English).— Overshot, undershot, breast wheels. A wheel pro- vided with buckets, which is set in motion by the weight or impact of a stream of water. Weather.— To crumble by exposure to the atmosphere. Weather Boor.— See Trap Door. Web.—Tlae face of a longwall stall in course of being holed and broken down for removal. The length of breast or face brought down by one mining. Wedging.— The material, moss or wood, used to render the shaft .lining tight. Wedging Crib.— A curb or crib of wood or cast iron wedged tightly in place and packed, in order to form a water-tight joint and upon which tubbing is built. Wedging Down.— Breaking down the coal at the face with hammers and wedges instead of by blasting. Weeldon.— Old ironstone workings. Weigh Bridge (English).— A platform large enough to carry a wagon, resting on a series of levers, by means of which heavy bodies are weighed. Weize.—A band or ring of spun yarn, rope, rubber, lead, etc. put in between the flanges of pipes before bolting them together, in order to make a water-tight joint. Welt—{1) The well of a furnace is the deepest lying portion or hollow in which the metal collects. (2) A sump, or a branch from the sump. Whim.— A winding drum worked by a horse. Whim Shaft— A shaft through which coal, ore, water, etc. are raised from a mine by means of a whim. Whin . — A hard, compact rock. Whin Dike.— A fault or Assure filled with whin and the debris of other rocks, sometimes accompanied by a dislocation of the strata. Whip.— A hoisting appliance consisting of a pulley supporting the hoisting rope to which the horse is directly attached. IE Medamp.— Carbonic oxide {CO). A gas found in coal mines, generally where ventilation is slack. A product of slow combustion in a limited supply of air. It burns and will support combustion. It is extremely poisonous. White Tin.— The commercial name for metallic tin. TEMs.— See Tin- Witts. Whole Working.— The first working of a seam, which divides it into pillars. Wild Zmd.— Zinc-blende. Wild Rock.— Any rock not fit for commercial slate. Win.— To sink a shaft or slope, or drive a drift to a workable seam of mineral in such a manner as to permit its being successfully worked. Winch, or Windlass.— A hoisting machine consisting of a horizonal drum operated by crank-arm and manual labor. Wind Bore (England).— The bottom or suction pipe of a lift of pumps, which has suitable brass holes or perforations for suction of water or air. Wind Gauge.- An anemometer, for testing the velocity of air in mines. Winding . — The operation of raising or hauling by means of a steam engine and ropes, the product of a mine. Winding Engines . — Hoisting or haulage engines. Wind Method.— A system of separating coal into various sizes, and extracting the dirt from it, which in principle depends on the specific gravity or size of the coal and the strength of the current of air. Wind Sait— The top part of canvas piping, which is used for conveying air down shallow shafts. Wing Bore.— A side or flank bore hole. TEin^'s.— See Rests and Keeps. Winning . — A sinking shaft, a new coal, ironstone, clay, shale, or other mine of stratified material. A working place in a mine. Winnowing Gold. — Air-blowing. Tossing up dry powdered auriferous mate- rial in the air, and catching the heavier particles not blown away. TEmse.— Interior shaft connecting levels, sometimes used as an ore chute. lEon.— Proved, sunk to, and tested. 622 WOR GLOSSARY. ZON Work.^{l) To mine. (2) Applied to mine working when affected by squeeze or creep. Workable.— Kny seam that can be profitably mined. Worked Owt.— When all available mineral has been extracted from a mine, it is worked out. Working. — Applied to mine workings when squeezing. Working Barrel.— water cylinder of a pump. Working Beam (English).— A beam having a vertical motion on a rock shaft at its center, one end being connected with the piston rod and the other with a crank or pump rod, etc. Working Cbsi.— The total cost of producing the mineral. Working Face. — See Face. Working Home.— Getting or working out a seam of coal, etc., from the boundary or far end of the mine toward the shaft bottom. Working on Air. — A pump works on air when air is sucked up with the water. Working Working outwards or in the direction of the boundaries ol the collieries. Working Place.— Yhe actual place in a mine at which the coal is being mined. Workings.— Y\ie openings of a colliery, including all roads, ways, levels, dips, airways, etc. Work Lead. — Base bullion, silver lead. Wrought Iron.— Iron in its minimum state of carburization. Wythern (Wales).— Lode. Xacal (Mexican).— A miner’s cabin; a storehouse for mining goods; a shaft house. Yardage, Yard Work .—Price paid per yard for cutting coal. Yard Pnce.— Various prices, per yard driven (in addition to the tonnage prices), paid for roads of certain widths, and driven in certain directions. Yellow Ore (Cornish).— Chalcopyrite. Yield.— The proportion of a seam sent to market. Zone.— In coal-mining phraseology, this word means a certain series of coal seams with their accompanying shales, etc., which contain, for example, much firedamp, called a fiery zone, or, if m«ch water, a watery zone. INDEX, Absolute Pressure, 195, 345. temperature and pressure, 344, 345. Abuse of instruments, 80. Abutments (dams), 154. Acceleration in jigging, 440. on inclined planes, 399. Acid waters. Pumps for, 165. Acres to square feet, 4. Adiabatic compression, 195, 198. Adjustable bars, 432. Adjustment of Burt’s solar attach- ment, 48. of compass, 38. of level, 53. of transit, 41. Afterdamp, 351. Agonic line chart, 40. Air and mercury columns, 347. brattice, 394. bridges, 393. columns in furnace ventilation, 384. Compressed, 194. compression. Theory of, 194. compression. Horsepower neces- sary for, 406. Air compressors, 194. Classification of, 194. Compound, 194. Construction of, 194. Cooling, 195. Dry, 196. Duplex, 194. Horizontal, cross-compound, 194. Rating of, 195. Simple, 194. Stage, 194. Straight-line, 194. Vertical, 194. Wet, 196. Air currents, Conducting, 393. currents. Splitting of, 373, 378. leaks, 186. lift pumps, 164. required for ventilation, 362. transmission, 196. Airways, Similar, 372. Alabama method of mining, 297. Alternating current, 217. current dynamos, 224. current motors, 226. Alternators, 225. Multiphase, 225, 226. Single-phase, 225. Three-phase, 226. Two-phase, 226. Altitude, Effect of, on air compres- sion, 195. Aluminum, Electric properties of, 209 . American coals, 168. gauge wire, 208. measures of area, 4. measures of length, 2. measures of volume, 5. Amount crushed by rolls, 424. of charge, blasting, 331. of gas liberated per ton of coal, 352. Analyses of American coals, 168. Analysis of coal, 173. Andre’s formula for shaft pillars, 285. Aneroid barometer, 339. Angle of inertia, 398. of rolling friction, 398. reading, 45. Annunciator system, 232. Anthracite coal, 169. Cubic feet in ton of, 449. Handling, 443. Sizes, of 434. Specific gravity of, 109. mining. Costs of, 323. mining methods, 305. Percentages of different sizes of, 323, 326. Preparation of, 442. screens. Duty of, 434. Tests of compressive strength of, 290. Apothecaries’ weight, 1. Appliances in mine ventilation, 381. Arc, Error in, 76. lamps, 214. Area, Measures of, 4. of circle, 31. of ellipse, 32. of largest square inscribed in a circle, 28. of parallelogram, 28. of polygons, 30. of tract of land. To find, 52. of trapezium, 30. of trapezoid, 30. of triangle, 28. Areas, Calculation of, 77. of circles, 1 to 1,000, Table of, 545, of circles, to 100, Table of, 561. Arithmetic, 15. Arithmetical progression, 20. Armature, 216. ‘Arrangement of drill holes, 244, 335. of mine plan, 381. of slope tracks, 413. Ascensional ventilation, 381. Ash (coal), 171. Ashworth - Hepplewhite - Gray lamp, 358. Asphyxiation, 451. Atmosphere, Composition of, 337. Weight of. 337. Atmospheric pressure, 339. 623 624 INDEX. Atom, 341. Atomic volume, 341. weight, 344. Austrian measures of length, 3. Avoirdupois weight, 2. Back of Ore, Caving a, 320. Balancing a conical drum, 396. Ball mills, 427. Barometer, 339. Barometric elevations, 340. variations, 339. Barrel!, J., 62. Barrier pillars, 287. Bar signals, 235. Base lines, 46. Batteries, Electric, 229. Battery cells. Composition of, 231. water, 430. working, 307. Beams, 102, 105. Bearing in, 283. value of masonry, 107. Bedded deposits, 279. materials. Prospecting for, 238. Bell wiring, 230. Belting and velocity of pulleys, 193. Bending rails, 412. Bends in pipes, 153. Bent plumb-line method of slope sur- veying, 73. Biram’s ventilator, 387. Bitumen, Prospecting for, 249. Bituminous coal, 169. Cubic feet in ton of,,449. Handling, 443. Blackdamp, 350. Blacksmith coal, 173. Blake crushers, 419. Blasting by electricity, 332. Bleeding from scalp wounds, 451. Blossburg method of mining, 298. Blower fans, 386. Board measure, 13. Boiler, 176. Care of, 185. capacity, 181. Choice of, 179, 180. cleaning, 186. coverings, 183. feed-pumps, 161. iron, thickness required, 187. scale, 181. tests, 188. Boltheads,Weight of, 116. Bolts per mile of track, 117. Bolts, Weight of, 116. Bonnett, 268. Bord-and-pillar, 280. Bore-hole records, 244, 250. holes, 242. Bottoms, Slope, 413. Boxes for electric fuses, 224. Box regulator, 375, 377. Boyle’s law, 195, 345. Brass, Weight of. 111, 112, 114, 115. Brattice, Air, 394. Breast boards, 270. wheels, 157. Bridges, Air, 393. Briqueting, 448. British imperial measure (liquid and dry), 5. measures of area, 4. measures of length, 2. measures of volume, 5. thermal unit, 168. Brown coal, 170. Brown’s method of mining anthra- cite, 306. Brown & Sharpe gauge, 208. Buckets, Conveying, 446. Buggy breasts, 291. Buildings, 283. Bulling, 330. Buntons, 270. Burt’s solar attachment, 47. Butt cleats, 284. Cables, Electric, 209. Cableways in mining, 278. Calculation of areas, 77. of mine resistance, 366. of wires for electric transmission, 210 . California method of mining, 300. stamps, 428. Calorie, 168. Calumet classifier, 435. Cams for stamps, 429. Cannel coal, 170. Capacity of boilers, 181. of electric cables, 209. of mining machines, 337. of pumps, 161. of shaking screens, 432. of standard steel buckets, 446. Capell ventilator, 389. Carat, 12. Carbonic-acid gas, 350. oxide gas, 349. Castings, Weight of iron, copper, lead, brass, or zinc. 111. Caving a back of ore, 320. methods, 320. waste only, 320. Cells, Various types of, 231. Centers, 59. Centigrade to Fahrenheit, 366. to Reaumur, 366. Centrifugal fans, 386. pumps, 164. roller mills, 426. Chain, Surveyor’s, 42. cutter machines, 337. pillars, 287. Chains, Iron, 129. Chamber-and-pillar method, 318. Chambering, 330. Channels, Flow in, 142. Character of fioor and roof on size of pillars, Infiuence of, 280. Charging a hole, 330. Charles’ law, 345. INDEX. 625 Chemical compounds, 341. equations, 341. symbols, 341. Chemistry of gases, 341. Chimneys, 189. Chinese measures of length, 4. Chock, 268. Choice of a boiler, 179, 180. Chokedamp, 350. Churn drills, 242. Chute breasts, 292. mining, 309. Circles 31 areas of, 1 to 1,000, Table of, 545. areas of, ^ to 100, Table of, 561. Circuit, Electric, 205. Circular mil, 207. Circulation of boilers, 181. Circumferences, 1 to 1,000, Table of, 545. if to 100, Table of, 561. Clanny lamp, 356. Classifiers, Hydraulic, 434. Classifying apparatus, 431. Cleaning safety lamps, 358. Clearfield method of mining, 295. Cleats, 284. Clinometer, 44. Closed work, 279. Close workings. Shots in, 861. Closing surveys, 68. Coal, 169. Analyses, 168. analysis, 173. Anthracite, 169. Bituminous, 169. Blacksmith, 173. Brown, 170. Calorific Power, 168. Cannel, 170. Coking, 170. Composition of, 170. dealers’ computing table, 452. Domestic, 173. dust. Effect of, 360. Free-burning, 170. Gas, 173. Hardness of, 171. Iron-making, 172. Lignite, 170. Preparation of, 418. Prices of, 326, 327. Production of U. S., 326. Prospecting for, 238. Running of, 312. Semianthracite, 169. Semibituminous, 169. Sizes of. 173, 434. Specific gravity of, 109, 171. Splint, 170. Steaming, 171. Storage of, 291. Strength of, 171. washers, 436. Weight of, 170. Coals, Cubic feet in ton of various, 109, 170. Cockermegs, 268. Coefficient of contraction (water), 135. of discharge (water), 135. of discharge with weirs, 140. of rolling friction, 398. of roughness for water channels, 144. of velocity (water), 135. Coefficients of friction for various materials, 95, 96. of friction of air in mines, 367. Cog, 268. Coins, 10. Coke, 172. ovens. Cost of, 328. Coking coals, 170. coal. Cost of, 328. Collar, 268. Collimation, Line of, 53. Colorado method of mining, 302. Color of coal ash, 171. Columns, Safe loads for, 106. Combustibles, 166. Combustion, Spontaneous, 291. Common fractions, 15. Commutator, 216. Comparison of aluminum and copper for electric use, 209. of hydraulic formulas, 149. of methods of shaft sinking, 262. of vacuum and plenum systems of ventilation, 386. Compass, 38. To adjust, 38. To use, 39. vernier, 39. field notes, 44. Complement of angle, 34. Composition of atmosphere, 337. of coals, 170. of forces, 95. of fuels, 169. Compound, Chemical, 341. lever, 92. wound dynamos, 219. Compressed air, 194. haulage, 403. haulage problems, 404. Compressibility of liquids, 133. Compressive strength of anthracite, 289. Condensers, 176. Conducting power of various sub- stances, 184. Conductors (guides), 398. (electrical), 207. for electric-haulage plants, 214. Cone, 33. Conical drums, 394. drum. To balance, 396. Connecting outside and inside sur- veys, 68. Connections for continuous-current motors, 223. Connellsville method of mining, 293. Constant-current circuit, 206. potential circuits, 206. power, 372. 626 INDEX, Constant pressure, 372. pressure circuits, 206. quantity, 372. velocity, 372. Constants for mine gases, 349. for wooden beams, 103. Construction of air compressors, 194. of dams, 133. of a mine furnace, 383. Contents of a coal seam. To find, 52. - of cylinders, 6. Continuous-current motors. Connec- tions for, 223. vernier, 45. Contraction, Coefficient of ( water) ,135. Control of roof pressure, 284. Conversion factors (hydraulic), 141. of thermometer readings, 366. tables, 7, 10. Conveyors, Horsepower of, 445. Coordinates, 51. Copper, Electric properties of, 209. Weight of. 111, 112, 114, 115. Wire, 208. Cornish pumps, 158. rolls, 423. underhand sloping, 316. Corps, Mine, 66. Corresponding mercury and air col- umns, I'able of, 347. Corrugated rolls, 422. Cosecant, 35, 454. Cosine. 35, 453. Cost of briqueting, 449. of coke ovens, 328. of coking coal, 328. of drilling, 244-247. of haulage, 409. of mining anthracite, 322. of sinking, 263. of stamping, 430. of unloading coal, 447. of well drilling, 242. Cotangent, 35, 453. Cotangents, Natural, Table of, 464. Coverings, Boiler and pipe, 183. Coversed sine, 35. Coyoting, 321. Cracking rolls, 421. Crib, 268. Cribbing, 270. Cross-section of electric wires, 207. Cross-sections, Construction of, 249. Crushing load of wood, 105. machinery, 418, 431. mills, 426. rolls, 423. rolls. Table of, 425, 426. Cube, 33. root, 19, 545. roots. Table of, 545. Cubes, Table of, 545. Cubic feet occupied by ton of various coals, 449. Culm, Flushing of, 314. 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. Declinatiom 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 pump), 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 (IT. 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. Electrical Expressions and Equiva- lents, 205. 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, 3'2. 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 wi^h solar attachment, 47. Estimates of current, 212. Evolution, 19, 545. Excitation of dynamos, 218. Exhaust fans, 386. Expansion oi gases, 344. Exploder, Electric, 332. Exploring workings, 361. Explosions, Exploring worki ngs 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. 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, 44. 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 Boiiers, 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. Hawksley’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 surveying, 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, 286. Hydraulic classifiers, 434. gradient, 147. placer mining, 278. Hydraulics, 135. Hydrocarbons, 349. Hydrogen disulphide 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, 3^2. Lead, Weight of. 111, 113, 114, 115. Leclanche 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 5. 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. INDEX. 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. Parallelopiped, 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. 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, 161. 632 INDEX, Pitch at which anthracite will run, Table of, 443. distance, 51. Pitching work surveys, 68. Pittsburg method of mining, 295. i’lacer 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-Sooysmith 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. 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, 104. 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. Raises, 316. Rapid firing of boilers, 187. method of splicing a wire rope, 127. Rate of diffusion, 346. INDEX. 633 Rating of compressors, 195. Ratio of steam and water cylinders in pump, 160. Reaumur to Fahrenheit, 366. Reciprocals, 545. Recoil of 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. RemcA^al 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. V 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'lron 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 dejpth of, 340. 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. Sheet-metal gauges, 122d. 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 INDEX. ' f, Sinking a sha^ft, 5^59. 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, 396. 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. Squibbing, 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. Sloping, 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. Turbines, 158. Turnouts, 413. Two-phase alternators, 226. 636 INDEX. Undercasts, 393." ll Undercutting, 283. j Underground prospecting, \\ 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. fiow 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. Weight of atmosphere, 337. boltheads, nuts, and washers, 116. bolts, 116. castings. 111. chains, 130. coal, 170. flat wrought iron, 115. ^ases, 344. iron pipe, 113. materials, 102. plates of steel, wrought iron, etc., 112 . standard steel buckets, 446. water, 107, 130. wire ropes, 119. wrought iK)n, 114. Weight on pillars at different depths. Table of, 287. Weights and measures, 7. Weir 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. y Undershot, 157. Whitedamp, 349. Whiting system of hoisting, 395. Williams’ method of mining, 312. Wing dams, 156. Winslow, Arthur, 81. Winzes, 316. Wire gauge 122d, 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. f Wrought iron, Flat, 115. Wyoming region. Costs of mining in 325. Zinc, Weight of, 111. .OHf J1L_ m 1 I '7^ I' > • j ‘ " 'O ! ii 7 ^ ' i ■] . .* ■ '■ ’ ! ['-V' ^:,t^ . ■ , ■ . ' - } V' 4 Hade in Italy www.coltbrisystem.com