Cornell University Library The original of this book is in the Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031240769 arVl8674 Com9 " Unlvw » l «» Lto^T ^.rM,.,?LMearaph construction: olin.anx 3 1924 031 240 769 A MANUAL TELEGEAPH CONSTRUCTION. SCIENTIFIC WORKS W. J. MACQUORN RANKINE, C.E., LL.D., F.R.SS., Late Regius Professor of Civil Engineering in the University of Glasgow. I. A MANUAL OF APPLIED MECHANICS. Numerous Illustra- tions. Crown 8vo, cloth, price 12s. Sd. Ninth Edition. " Cannot fail to be adopted as a Text-Book. . . . The whole of the information is so admirably arranged, that there is every facility for reference."— Mining Journal. XL A MANUAL OF CIVIL ENGINEERING. With numerous Tables and Illustrations. Crown 8vo, cloth, price 16*. Twelfth Edition. HL A MANUAL OF MACHINERY AND MILLWORK. With nearly 300 Woodcuts. Crown 8vo, cloth, price 12s. 6d. Third Edition. "Professor Eankioe's 'Manual of Machinery and Millwork' fully maintains the high reputation which he enjoys as a scientific author; higher praise it is difficult to award to any book, It cannot fail to be a lantern to the feet of every Engineer." — The Engineer. TV. A MANUAL OF THE STEAM ENGINE AND OTHER PEIMB MOVERS. With Diagram, Tables, and Illustrations. Crown 8vo, cloth, price 12». id. Eighth Edition. V. USEFUL RULES AND TABLES for Architects, Builders, Engineers, Surveyors, &c. Crown 8vo, cloth, price 9s. Fifth Edition. " Undoubtedly the most useful collection of engineering data hitherto produced." Mining Journal. " A necessity of the Engineer. . Will be useful to any teacher of Mathe- matics." — A thenseum. VI. A MECHANICAL TEXT-BOOK; or, Introduction to the Study of Mechanics. By Professor Bankihe and E. F. Bakbee, C.E. Crown 8w, cloth, price 9s. Second Edition. " Likely to prove invaluable for famishing a reliable outline of the subjects treated of."— Mining Journal. V Th» Mechanical TexivBook forms an East Introduction to Pbofessor Kanklne's Series of Manuals. A MANUAL OF TELEGRAPH CONSTRUCTION: THtf MECHANICAL ELEMENTS OP ELECTRIC TELEGRAPH ENGINEERING. BY JOHN CHRISTIE DOUGLAS, MEM. SOC. TELEGBAPH EKUINEER3, EAST INDIA OOVI. TELEOEAPH DEPARTMENT. Sctonb Coition, faith ^npcnbicrs. PUBLISHED WITH THE APPROVAL OF THE DIRECTOR-GENERAL OF TELEGRAPHS IN INDIA. LONDON: CHARLES GRIFFIN AND COMPANY, 10 STATIONERS' HALL COCJRT. 1877. [Might of Translation Reserved.] (g) //cor NELL UNIVEP QiTv; % LIBRARY PREFACE TO THE FIRST EDITION, A telegraph structure must fulfil two distinct sets of condi- tions, the Mechanical and the Electrical. On the subject of the latter there are many special Treatises, on the former this book is the first of its kind. The special Treatises on Telegraphy, ■with the exception of that of M. Blavier, do not treat of Meehanical principles, these being very justly regarded as dis- tinct from the Electrical conditions, and their full exposition as out of place in a Treatise on the application of Electricity. Although the Mechanical principles and practice are common to other structures than Telegraphs, the particular case of a Telegraph structure requires separate treatment ; for some of the materials employed and the functions of the structure are peculiar to Telegraph structures. In no branch are the requirements of the Telegraph Engineer co-extensive with those of the Civil Engineer. Telegraph Engineering has several branches, as mast building, cable laying, &c, not pertaining to Civil Engineering, and Civil Engineering, again, includes many branches, as tunnelling, roads, railways, drainage, water supply, bridge building, &c, of no concern to the Telegraph Engineer. As examples may be instanced carpentry, brickwork, masonry, and earthwork : — the Telegraph Engineer has to join timbers in different ways, to make simple trusses, to build masts, &c. ; but he is not concerned with very complex frames, roofs, &c, and is not called upon to execute extensive works in brick or out stone. On the other hand, it is necessary that he should know the principles on which such PREFACE. are built, to enable him to construct plinths of stone and of brick with stone copes, and to fasten posts, cantilevers, &c, on and in work built by others. The ordinary mode of embanking employed by the Engineer is inadmissible in Telegraph Engineer- ing, for in the latter case the bank is always small in content, and is required to be of the best possible quality ; the deepest excavation the Telegraph Engineer has to make seldom exceeds 12 feet, but it has frequently to be made in bad soil, on the edge of a river, and with very indifferent appliances. In general, when the Telegraph Engineer has difficult work to perform, the cost of the work and the distance over which it is distributed are such that the appliances commonly used by the Civil Engineer are not available; hence the great importance of a knowledge of principles in order to admit of the means at command being duly utilised, and the work carried out with safety, economy, and rapidity. I have dealt particularly with principles, because, these being known, the manner of their application must depend in a great measure on local circum- stances. I hope the general adherence to this plan may render the work useful to the several Administrations, however widely their praotice may differ, and the Paragraphs, being numbered, may be readily referred to in official instructions. While thus assigning a prominent place to General Principles, I trust it will be found that the practical part of the subject has not been neglected, since I have endeavoured to supplement my own experience gained in India by a minute examination of the Telegraph systems of France and England, and of the principal processes of manufacture. I am indebted to the Director- General of Telegraphs in India for permission to use the official orders, &c, of his Department, to the Secretary to the Postal Department in England, and to the Director-in-Chief of the French Administration. My thanks are due to the Engi- neers of the English and French Administrations for their assistance, and also to several Engineering firms for infor- niation and facilities for observing processes and operations as actually carried on at present, in particular to Messrs. Siemens, Brothers, Messrs. Hooper & Co., Mr. Henly, and Messrs. Laird, Brothers. In writing the articles on Statics, Dynamics, Force, and Equilibrium and Stability, I have used the works of Baker, Blavier, Gregory Goodwin, Moseley, Poncelet, Poisson, Poinsot, Bankine, Stoney, Sheilds, Todhunter, Thomson and Tait, Weis- bach, "Whewell, Warr, ftnd T. Young. In the section on Friction I have referred to the works of Morin and Jellett in addition. In the chapter on the Strength of Materials I have used principally the labours, literary and experimental, of Ander- son, Barlow, Clay, Fairbairn, Hodgkinson, Tredgold, Kirkaldy, Morin, Navier, Gauthey, Poncelet, Prud'homme, Bankine, Bondelet, Vicat, and Pasley. For the chapter on Wood I have referred principally to the works of Tredgold, Tarbuck, Nicholson, and Newland. I am indebted to Mr. Kipping's work for much information on "Wooden Masts, and to the works of Grantham and Beed for some hints on Mast Building in Iron. On Iron Construction I have referred to the works of Fairbairn, E. Clark, Campin, Kirkaldy, Tredgold, Hodgkinson, Clay, Morin, Bankine, Sheilds, Unwim, Truran, W. Vos Picket, and others. For the chapter on Insulators I have used the articles in the Chemical Dictionaries of Watts and Wurtz, the volume by M. P. Desmoreux in the Ency. Eoret, the Dictionaries of Ure and Tomlinson, the Becords of the Patents Office, the Beport of the Committee on Cables, &c. For references on Botany I have used Professor Balfour's works. The section on Estimat- ing is in general terms that employed in India. It was devised by accountants and executive officials on consultation, and appears ad- mirably suited to the purposes for which such a system is required. For the section on the lifting of Heavy Bodies I have referred to Mr. Glyn's book on Cranes, and for the section on Mechanical Manipulation to Mr. Holtzapffel's work on the subject. I have VI PREFACE. preferred ordinary language to Mathematical Formulae whenever applicable. I have referred to many general works on Engineer- ing, as D. Stevenson on Engineering in N. America, the works of Mr. 'W. Humber, the Dictionaries and Cyclopaedias of Spon. Appleton, Nicholson, and Cresy; the Encyclopaedias Britannica and Metropolitana, Nichol's Cyclopaedia, and the English Cyclo- paedia. I have used several Engineers' Handbooks, the " Engin- eering " Journal, and am much indebted to the Journal of the Society of Telegraph Engineers, in particular to a resume 1 on Cables by Professor Fleeming-Jenkin. I have referred to several official pamphlets by Captain Mallock, and -to Mr. Cappet's report on the Prussian Telegraphs. J. CHRISTIE DOUGLAS. London, November, 1874. NOTE TO THE SECOND EDITION. In the present Edition the author has endeavoured to furnish such additional information as the progress of Science has rendered necessary since the first publication of the work; and has added a copious Index, which he trusts will be found useful. The new matter in the Appendices is based on data gathered from many different sources, official and private. The particulars of the Underground Line between Berlin and Halle were oblig- ingly supplied by the Direction of the Imperial Telegraph Depart- ment, and many details of the Indian Biver Crossings by Major J. Eckford, Officiating Director of Construction, to whom, as well as to all who have kindly assisted him in rendering his work more complete, the author's best thanks are due. Calcutta, August, 1877. CONTENTS. PART I. GENERAL PRINCIPLES OF STRENGTH AND STABILITY. Chapter I. — Forces, Couples, and Work. Section I. — Units of Force— Forces and Couples considered Statically. , 1. Force, its Definition, Equilibrium of, its Relations to Bodies; Statics and Dynamics defined, ..... 1 2. Units of Farce, ....... 2 3. Relation between Absolute and Gravity Units, ... 2 4. Representation of Forces, Graphically and Algebraically, . 3 5. Resultant, Component, Balanced Forces described, . . 3 6. Parallelogram of Forces, Three Forces in Equilibrio, . . 3 7. Triangle of Forces, ...... 4 8. Polygon of Forces, ....... 5 9. Parallelopiped of Forces, ...... 5 10. Resolution of Forces, Two Components, .... 6 11. Resultant. of any . number of Inclined Forces in the same Plane, acting on a Point, ...... 6 12. Resolution into Three Components, .... 6 13. Rectangular Components, ..... 7 14. Resultant of any number of Inclined Forces not in the same Plane 8 15. Forces acting on a Rigid Body, ..... 8 16. Moment of Force described and defined, .... 8 17. Couple — Description, Definitions, Moment of, Representation of, 10 18. Couples — Properties of, Parallelogram of, ... 10 19. Parallel Forces; Principle of the Lever, . . • . . 11 20. Resultant of a Couple and Single Force in the same Plane, or Parallel Planes, ....... 12 CONTENTS. PARA- GRAPH 21. Equilibrium of Parallel Forces, 22. Resultant of Parallel Forces, 23. Resultant of any number of Single Forces and Couples, 24. Distributed Forces described; their Intensity; Examples. 25. Gravity; its Resultant, Centre of Gravity, 26. Position of Centre of Gravity, 27. Extension of meaning of the term "Centre of Gravity" in Com- mon Language, ....... 16 28. Heaviness and Specific Gravity, ..... 17 29. Distributed Forces other than Gravity occurring in Practice; their Intensity and Resultant; Examples, . . .17 Section II. — Force considered Dynamically — Inertia — Work. 30. Dynamics, its Subject, ...... 18 31. Inertia; Velocity and Mass defined, . . . .19 32. Centre and Moment of Inertia, ..... 19 33. Velocity, Uniform and Variable, Composition, Resolution, and Momenta of Velocities, . . . . . .20 34. Momentum ; Moment of, as Measure of Force ; of a System or Group of Points, ....... 20 35. Work described and illustrated, . . . . .21 36. Kinetic Energy of a Body in Motion, . . . .22 37. Units of Work, ....... 23 38. Work done in turning a Body about an Axis, . . .24 Section III. — Friction. 39. Friction described; Laws of; Co-efficient of, . . . 24 40. Friction between Fibrous Substances, Hard and Soft Materials; its Limit, ....... 24 41. Use of Unguents, Laws of their Action, . . . .24 42. Friction between Axles and Bearings; between similar and dissimilar Materials; Effect of Smoothness or Roughness of Surface, ..... 25 43. Angle of Repose, Relation between it and Co-efficient of Friction, ..... 44. Stability of Earthwork and Blockwork due to Friction (Stability of Friction); Effect of Moisture on Angle of Repose of Earth, . 26 45. Angle of Traction; Angles of Repose for Vehicles on Roads of different Kinds, . . „„ . ^ • ■ • • 26 46. Friction between a Rope and Cylinder; the Principle of Knots, 26 47. Action of Driving Bands, .... 27 25 CONTENTS. 48. Brakes, Appold's Brake as applied in Cable-laying Machinery, 49. Co-efficients of Friction, Table of,. Chapter II. — General Principles op Strength op Materials. Section L— Definitions— General Notice of Strength, Elasticity, &c. 50. Load, Strain, Stress, Stiffness, .... 51. Elasticity: Moduli of, .... 52. Set 53. Proof Load, Ultimate Load, Factor of Safety, 54. Dead and Live Loads and their relative Factors of Safety, 55. Time during which Load applied, 56. Effects of Vibration and Shocks, .... 57. Eesilience or Spring, ..... 58. Conditions imposed on the Uses of Materials by their Natures and the Modes of Working them, 59. Eelative Strengths of Small and Large Masses of Material, 60. Elevation of Temperature and Strength, . 61. External and Gross Loads, Limiting Dimensions, 62. Allowance for Weight of Material in Designing, . 63. Appearances presented by Fractured Surfaces, . 64. Moduli of Strength, ..... 65. Different Forms of Strength, Elasticity, &c, 66. Applications of Materials according to their Qualities, . 67. Precautions necessary in applying Numerical Co-efficients and Moduli in Practice, ...... Section II. — Resistance to Pressure. 68. Resistance to Crushing compared with Pliability and Kesist- ance to Stretching, ...... 69. Phenomena of Fracture as dependent on Length as compared with Diameter, ....... 70. Laws of Resistance in Short Pieces for Pressures uniformly or otherwise distributed, ...... 71,. Influence of Form of Section on Strength of Built Pillars, 72. Phenomena of Crushing, how influenced by Nature of Material, 73. Moduli given in Tables ; Effect of Lateral Support, 74. " Strut " defined ; Elements determining the Strength of Struts, 75. Laws of Strength in Long Struts, .... 76. Formulae for Strength of Cast-iron Pillars, 77. Formulas for Strut of any Material, .... 78. Forms of Section of Struts, and Application of Formulas, PACK 27 28 29 29 31 31 32 32 33 33 34 34 35 35 35 33 36 36 37 37 38 38 38 38 39 39 40 40 40 41 41 CONTENTS. GKAPH 79. Formulas for Oak and Red Pine, . 80. Short Columns, ..... 81. Strength of Wrought-iron Cells, . 82. Failure of Long Timber Columns, 83. Pressure required to indent Wood transversely, . 84. Relative Strength of Pillars of different Materials 85. Telegraph Posts considered as Struts, PAOB 42 42 42 43 44 44 44 Section III.— Resistance to Tension. 86. Phenomena of Fracture of Tough Materials, . . .45 87. Phenomena of Fracture of Brittle Materials, . . .45 88. Successive Fractures of the same Bar, . . . .45 89. Strength of Fibrous Substances, Effect of Polling. Wire-drawing, and Ligatures on Wires, . . . . .46 90. Laws of Resistance as to Section and Direction of Strain ; Area on which Stress is calculated, . . . . .46 91. Influence of Lateral Dimensions and Shape, . . .47 92. Tie defined, . . . ■ . . . .47 93. Moduli of Tenacity; Ultimate and Working Moduli, . . 47 94. Effect of Temperature on Tensile Strength, . . .48 95. Effect of Shocks and Vibration ; Effect of Annealing, . . 48 98. Tenacity of Ropes and Chains ; Fox's Rule, . . .49 97. Mallet's or Poncelet's Co-efficient, . . . .50 Section IV.— Resistance to Shearing. 98. Phenomenon of Shearing described, 99. Resistance as Area, .... 100. Shearing Stress not uniformly distributed, 101. Common Instances of Shearing Stress, 102. Punching, ...... 50 50 50 51 51 Section V. — Resistance to Torsion. 103. Description and Examples of Torsion, 104. Moment of Load, ...... 105. Torsive Strength, how affected by Area and Shape of Section ; how expressed in Tables, .... 106. Laws of Torsional Stiffness, .... 107. Comparative and Absolute Torsive 1 Strength of different Mate- rials, • -..... 108. Shoulders on Shafting, .... 109. Twisting Fibres and Wires to form Ropes, Covering Cables, &c. 51 52 52 53 53 53 54 CONTENTS. Section VI. — Resistance to Transverse Load. PARA- GRAPH 110. Transverse Strength described; Beam defined and described, 111. Condition of Strained Bar ; Mode of Failure, 112. Distribution of Stress over Cross Section, . . , 1 13. Action of Loads below and exceeding Proof Load, compared, 114. Transverse Strength cannot be calculated from Resistance to Tension and Pressure, ..... 115. Efficiency of Matter increases as its Distance from Neutral Plane ; Flanged I^gams, ..... 116. Relations between Strength, and Depth, and Width of Beam 117. Functions of Web in Flanged Beams, 118. Bending Moment, how resisted, .... 119. Strength as affected by Length of Span, . 120. Amount and Distribution of Shearing Stress and Bending Moment over Length of Cantilever, 121. Amount and Distribution of Shearing Stress and Bending Moment in Beam supported at both Ends, 122. Distribution of Shearing Stress over Cross Section ; Proportions of Web in Flanged Beam, .... 123. Action of Distributed and Concentrated Loads compared, 124. Relative Strengths of Beams according to Mode of Support, 125. Relative Strengths of Fixed and merely Supported Beams, 126. Telegraph Poles considered as Beams, 127. Relative Strengths of Beams of Different Shaped Sections, Hoi low and Solid, ...... 128. Box, Tubular, and Lattice Girders; Telegraph Poles on these Principles, ...... 129. Strength of Beams and Telegraph Poles of Complex Form of Section ; how ascertained, .... 130. Allowances for Bolt Holes, &c, in Beams, 131. Built Beams ; Coupled Poles, .... 132. Forms of Beams in which Strength is proportioned to Bending Moment at each Section ; Cantilever, . 133. Forms of Beam supported at both Ends, . 134. The Principles applied to Telegraph Posts, 135. Allowance for Weight of Beam, .... 136. Beam Inclined to Load, ..... 137. Transverse Strength of Materials ; how represented in Tables, 138. Deflection of similar Beams as affected by Dimensions of Beam under Load less than Proof Load, 139. Deflection of similar Beams as affected by Dimensions of Beam for Proof Load, ...... CONTENTS. 140. Deflection as affected by Mode of Support, 141. Deflection as affected by Mode of Distribution of Load, . 142. Relations between Span and Deflection permitted in Practice, 143. Constants of Deflection, ..... 144. Formulas for Strength and Deflection, PAGE 72 72 72 72 73 Chapter III. — General Principles oe Equilibrium and Stability op Structures. Section I. — Frames. 145. Definitions, ...... 146. Conditions of Efficiency of Structures, 147. Frames defined— their Eigidity not due to Stiffness of Joints, 148. Nature of Stresses, and Mode of considering them, 149. Case of Single Bar, .... 150. Frames of Two Bars: Two Ties, . 151. Frames of Two Struts, .... 152. Frames of Strut and Tie, .... 153. Frames of Three or more Bars forming Closed Figures, 154. Frames of Three or more Bars forming Open Figures, 155. Braced Frames ; Trusses, .... 156. Funicular Polygon, .... 157. Telegraph Poles on Curves, 158. Examples illustrating Application gf the above Principles Telegraph Poles Strutted and Tied, 159. Examples illustrating Application of the above Principles Telegraph Poles Stayed, Coupled, and Trussed, to to 74 74 75 75 76 77 78 78 80 82 83 84 86 86 Section II.— Stability of Earth. 160. Frictional Stability, 161. Stability due to Adhesion, &c. , 162. Illustrative Examples, 91 91 91 Section III.— Stability of Blockwork. 163. Stability of a Single Block, . . ' . , .92 164. Moment of Stability, ..... 93 165. Application of Principles to a Structure composed of Several Blocks or Layers, •••... 94 166. General Application, and Influence of Height of Centre of G ravity on StabiUty, ....... 95 CONTENTS. Section IV. — The Catenary. PARA- GRAPH 167. Description of Curve— its Equations, 168. Description of Curve— Its Mechanical Properties, 169. Calculation of any Ordinate, and the Dip, 170. Maximum Span practicable with a given Material, 171. Length of Wire (Arc), ..... 172. Effect of Elasticity of Wire on Dip and Tension, 173. Effects of Change of Temperature on Dip and Tension, . 174. Points of Suspension differing in Height, to find Position of Vertex, ....... 175. Use of Curves Cut to Scale, . . . . 176. Minimum Horizontal Distance admissible with Points of Sus pension differing greatly in Height, 177. Application of the Formulae pertaining to the Parabola, Section VI. — Theory of Submersion, Recovery, die, of Cables. 184. Cable in Water compared with Wire in Air, 185. Modulus of Cable, ..... 186. Phenomenon of Sinking of Free Piece of Cable, . 187. Summary of Conditions of Submersion, . 188. Motion at Right Angles to Length ; Angle of Submersion, 189. Longitudinal Motion, ..... 190. Friction between Cable and Water, 191. Total Tension during Submersion, 192. Tension when Paying out is Stopped, 193. Calculation of Tension, or Dip of Land Line from Inclination at Insulator, ...... 194. Tension on Grapnel-rope and Cable hanging Stationary, . 195. Tension during Picking up, .... 95 96 97 98 99 100 100 101 102 102 102 Section V. — Stability, Motion, and Friction in Fluids. 178. Principle of Hydrostatics, ..... 103 179. Intensity of Pressure of Columns of Water and Air — Numerical Data, ........ 104 180. Maximum Intensity of Wind Pressure, .... 105 181. Motion of ImmerBed Body under Action of Gravity, . . 105 182. Friction between Liquid and Immersed Solid, . . . 106 183. Motion of Water in Open Channel ; Stability of River Channels, 106 107 108 108 109 110 111 112 113 114 115 115 115 CONTENTS. PART II, PROPERTIES AND APPLICATION'S OF MATERIALS; OPERATIONS AND MANIPULATION. Chapter I. — Non-metallic Materials not Insulators Proper. Section I. — Wood and its Application. Division I. — Properties, Preservation, and Carpentry. PARA- GRAPH 196. Organised Structure and Chemical Composition, 197. Theory of Seasoning and Drying, 198. Influence of Organised Structure on Mechanical Properti 199. Endogenous and Exogenous Woods, '. 200. Structure and Growth of Exogenous Trees, 201. Heart-wood and Sap-wood, 202. Best Seasons for felling Timber, 203. Selection of Timber, 204. Technical Terms, . 205. Classification of Timber, . 206. Felling and Natural Seasoning, 207. Artificial Seasoning, 208. Durability and Preservation, 209. Durability of different kinds of Timber actually employed, 210. Strength of Timber generally, Elasticity, 211. Factors of Safety, Resilience, 212. Fastenings, 213. Rules for Joining ; Joints Classified, 214. Lengthening Ties and Struts, 215. Beam, and Post and Beam, Joints, 216. Strut meeting Post, Beam or Tie, 217. Application of preceding Principles to Telegraph Construction, PAGB 117 117 118 118 118 120 120 121 122 123 123 125 126 129 129 131 131 133 133 135 136 137 Division II.— Masts. 218. Masts Classified, . 219. Selection of Wood, 220. Simple Masts, Shaping, . 221. Simple Masts, Proportions, 138 138 138 139 CONTENTS. 222. Simple Masts, Fixing Stay Hoops, 223. Simple Masts, Building in Lengths, 224. Simple Masts, Building in Thickness, 225. Compound Masts, the Standing Mast, 226. Compound Masts, the Running Mast, 227. Compound Masts, Heights in Practice, 228. Compound Masts, Staying, 229. Compound Masts, Ladders for, . 230. Compound Masts, Fitting Parts together, 231. Compound Masts for Ships and Telegraphs, Functions compared 232. Compound Masts, Rake, 233. Compound Masts and Simple Masts compared, . 234. Compound Masts, Faults to be avoided in Constructing Section II. — Earthwork. 235. Description and Classification, 236. Adhesion of Earth) . 237. Frictional Stability, Drainage, 238. Tools, 239. Excavating, . 240. Boring, 241. Filling and Embanking, 242. Sinking of made Earth, 243. Use of Puddle, 244. Measurement, 245. Labour of Earthwork, 246. Labour of Jumping in Rock, 247. References, Remarks on Adhesion, Section III. — Foundations. 248. Definitions and Description, .... 249. Objects to be attained by Preparation of Foundation, 250. Stability at Foundation Joint, .... 251. Foundations on Rock, ..... 252. Foundations in Earth having Frictional Stability, Firm Earth, 253. Foundations in Soft Earth, .... 254. Foundations in very Soft Earth, .... 255. Foundations in Mixed Strata, .... 256. Foundations under Water, .... CONTENTS. Section IV. — Cementing Materials. PARA- GRAPH 257. Calcareous Cements described generally, 258. Rich Lime, 259. Common Mortar, . 260. Hydraulic Lime and Mortar, 261. Pozzolanas, 232. Calcareous Cements Proper ; Adhesion of Mortar, 263. Application of Calcareous Cements, 264 Plaster, . 265. Insulator Cements, 266. Resin and Ashes, . 267. Sulphur Cements, . 268. Marine Glue, 269. Common and Mixed Glue, 270. Electrical, Flexible, and other Cements, Section V. — Concrete, BUon and Asphalt 271. Concrete, ...... 272. Beton . 273. Concrete and Beton compared with Masonry, 274. Concrete and Beton, and their Application, 275. Asphalt, ...... 276. Asphaltic Mastics, True and Factitious, and Concrete, 277. Applications of Asphalt, .... 278. Preparations for covering Cables, &c, Section VI. — Masonry and Brickwork. 279. Technical Terms, . 280. General Rules for Construction, 281. Shaping and Dressing Stones, 2S2. Different Qualities of Masonry, 283. Bond, 284. Volume of Mortar, 285. Miscellaneous Observations, 286. Brickwork ; General Rules, 287. Brickwork - r Construction, Bond, &c, 288. Brickwork and Masonry Combined, 289. Measurement and Labour of Masonry and Brickwork 290. Strength of Masonry and Brickwork ; Factors of Safety, CONTENTS. 291. Pointing 292. Inserting Cantilevers and Poles in Brickwork, PAGB 187 187 V Chapter II. — Metals and Alloys. Section I.— Iron. Division I. — Cast Ikon. 293. Cast Iron, Steel, and Wrought Iron, 294. Sources of Supply; Smelting, 295. Effects of Accidental Constituents, 296. Qualities of Cast Iron, .... 297. Casting, ...... 298. Effects of Heat, ..... 299. Strength and Elasticity; Density; Factors of Safety, 300. Cast Iron for Engineering Purposes, 301. Corrosion, ...... 302. Testing Quality, ..... Division II Malleable os Wrought Iron. 303. Properties Considered Generally, 304. Processes of Production, .... 305. Effects of Working on Strength, . 306. Manufacture of Bars and Plates, . 307. Bule for Calculating Weights of Bars, Plates, and Wire, 308. Welded Joints, ..... 309. Effects of Extremes of Temperature, 310. Co-efficient of Expansion by Heat, 311. Alloys; Tinning; Galvanising, . 312. Corrosion, ..... 313. Relative Strains and Sets of Wrought Iron and Cast Iron ; their Employment together, .... 314. Eed and Cold Shortness, .... 315. Relative Strengths of Cast Iron and Wrought Iron 316. Strength of Wrought Iron Considered Generally, 317. Effects of Repeated Shocks and Vibrations, 318. Tenacity of Bars and Plates, 319. Tenacity of Wire, 320. Ultimate Extension, 321. Resistance to Crushing, . b CONTENTS. PARA- GRAPH 322. Kesistance to Transverse Load, Shearing, and Torsion. 323. Tenacity of Riveted Joints, 324. Resistance to Bursting and Collapse, 325. Resistance of Plane and Buckled Plates, 326. Proof Load ; Factors of Safety, . 327. Stiffness of Beams and Telegraph Poles, , 328. Moduli of Elasticity and Resilience, 329. Fastenings, 330. Joints, 331. Struts, Ties, and Beams, 332. Iron Posts and Masts, 333. Wire Specifications, 334. Other Applications of Iron in Telegraph Construction, 335. Preservation of Ironwork, 336. Comparison between Iron and Wood as Materials of Construe tion, PAGE 213 213 213 214 214 215 218 219 221 223 227 230 236 238 ^238 Division III.— Steei and Steely Iron. 337. Processes of Production, . . . . . . 240 338. Properties, ....... 241 339. Comparison between Wrought Iron and Steel, Working Load, . 246 340. Application of Steel to Cutting Instruments and Tools, . . 246 341. Other Applications of Steel, . . . . 247 342. Application of Steel and Homogeneous Metal as Materials of Construction, . . . -. . . . 248 Section II. — Copper, Zinc, Lead, Tin, and 'Alloys. 343. Copper, 344. Zinc, 345. Lead, 346. Tin, 347. Alloys, •248 251 251 251 251 Chapter III.-=-Insui,ating Materials Proper. Section I.— Gutta-percha. 348. Sources of Supply, 349. Manufacture, 350. Chemical Composition and Properties, 351. Effects of Heat, .... 252 253 253 255 CONTENTS. TARA- OKAPH 352. Density and Heaviness, . 353. Tenacity, . 354. Applications (Joining Core, &c), 255 255 256 Section II.— India-rubber: 355. Sources of Supply— Crude- Caoutchouc, .' 356. Manufacture— Purified Caoutchouc, 357. Density and Heaviness, 358. Chemical Characteristics and Composition, 359. Solvents, . 360. Action of Heat, .... 3.61. Vulcanised Caoutchouc, . 362. "Vulcanite and Ebonite, 3433. Application of Caoutchouc as an Insulator, 201 262 263 263 264 265 266 268 2C9 Section III.— Porcelain, > -V * 12 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. must be fulfilled— i.e., the middle force must equal the sum of the extreme forces, as the moments of the couples must be equal the lengths of the arms must be inversely as the forces respectively, and it is evident the forces may be inclined without disturbing equilibrium if they maintain their parallelism to each other. This principle is that of the lever ; the three forces represented in the figure may represent the pressures of power, fulcrum, and weight, and the lever will be of the first, second, or third kind, according to the order in which these are arranged. As in the case of inclined forces, if three parallel forces are in equilibrio each must be equal and opposite to the resultant of the other two. 20. The resultant of a couple and a single force acting on a body in the same or a parallel plane is found as follows: — Set off from 0, fig. 8, the point of application of the given force F, a line - P equal and opposite to F ; through . draw the arm of a. couple and complete the couple by the force F, the moment of this couple being made equal to that of the given couple by increasing or decreasing the length of the arm in the inverse ratio of the force F to each of the forces of the given couple; it is evident the resultant of this system is the force FA ; for F and — F, being equal and opposite, neutralise each other, therefore the resultant is equal in magnitude to the given single force, its direction is parallel to that of the given force and in the same plane, but its point of application is shifted to the left or right accordingly as the given couple is right or left handed. Hence the resultant of any number of parallel forces must be either a single force or a single couple; for if it were a force and a couple, these could be combined into a single force. 21. The conditions of equilibrium of a system of parallel forces having their lines of action in one plane are as follows :• — lstly. The algebraical sum of the forces must be = 0; and, Ivdly, the algebraical sum of their moments relative to an axis at right angles to the common plane of their lines of action must be = 0. This is equivalent to stating that there must be neither motion of translation nor of rotation. If the given forces be not in one plane, then for them to be in equilibrio the second condition given above must be replaced by the following : — The sum of their moments relative to two axes at right angles to each other, and to the lines of action of the given force must be = 0. ' RESULTANT OF FORCES AND COUPLES. ' 13 22. 1. The resultant of any number of parallel forces whose lines of action are in one plane, equals the algebraical sum of the several forces; and the distance of the line of action of this resultant from an assumed axis, to which the forces are referred, is found by dividing the sum of the forces by the sum of theii moments relative to this axis. 2. The resultant of any system of parallel forces not in the same plane is found by taking two rectangular axes; the resultant in this case, as in the last, is the algebraical sum of the several component forces; the distance of the resultant relative to each axis is the quotient of the algebraical sum of the moments relative to that axis, by the magnitude of the resultant. If in the two cases given above the resultant be = 0, then the forces are either in equilibrio or their resultant is a couple. If the forces are not in equilibrio, then in 1, the moment of the resultant couple is the sum of the moments of the given forces relative to the axis chosen; in 2, two resultant couples are obtained, one about each of the chosen axes; the moments of these couples are the sums of the forces relative to each of the axes respectively, and their axes will be one on each of the chosen axes; if on each of these axes a line is set off in the positive direction represent- ing the couple (Paragraph 17), and the rectangle of which these lines are adjacent sides be completed, the diagonal will represent the resultant couple in moment and direction. The value of the moment of this ultimate resultant will be the square root of the sum of the squares of the two component couples; and generally the same formulae as were applied to single inclined forces may be applied to these couples, by using lines to represent couples in accordance with the rules already stated. Thus, the two component couples and their resultant couple are related to each other as the sides of a triangle, both in magnitude and direction; the cosine of the angle made by the resultant couple and either of the component couples is equal to the quotient of the component taken by the resultant; the value of either component is the product of the cosine of the angle between it and the resultant and the resultant. The resultant maybe found by taking the square root of the sum of the squares of the com- ponents, because, the axes being rectangular, the components and resultant are related as the sides of a right-angled triangle, in which the resultant is the hypothenuse; or the resultant may be found by taking the quotient of one of the components by the cosine of the angle between that component and the resultant. 23. The resultant ,of any number of forces and couples may be found by applying the methods already given for parallel and inclined forces and couples respectively; thus, the forces and 14 GENERAL PRINCIPLES OP STRENGTH AND STABILITY. couples being represented by lines in the conventional manner, if acting in one plane, two, and if acting in different planes, three rectangular axes are taken; to these axes co-ordinates are drawn, so that the single forces be resolved into resultants acting in the rectangular axes, and the couples are also resolved into couples acting round the same axes ; the several resultants thus obtained are compounded into a single force and a single couple respect- ively. If the moment of the couple and the resultant of the force each =f= 0,'the system is in equilibrio ; if the moment of the couple only = 0, the resultant force is the resultant of the system; when the resultant force only is = 0, then the resultant is a ■ couple. If the resultants of a system of couples and single forces be a couple and a single force, three cases are possible : lstily. Let the single force be at right angles to the axis of the couple; this case is one of parallel forces, for the couple may be turned until its forces are parallel to the single force, and a resultant of the couple and single force may be found (Paragraph 20), for it will be equal and parallel to the single force in a plane perpendicular to the axis of the couple, and at a distance from the point of intersection of the line of action of the single force and the axis of the couple equal to the quotient of the moment of the couple by the single force. 2ndly. If the single force act in a line parallel to the axis of the couple, then they cannot be compounded into either a single force or a couple ; the simplest equivalent of the system has been attained, drdly. If the axis of the couple and the line of action of the single force be oblique to each other, then the couple may be resolved into two component couples, one having its axis at right angles to the line of action of the single . force, and the other having its axis parallel to that line; the first of these couples may be compounded with the single force (Paragraph 20), but the single force so found cannot be compounded with the second couple : the two together form therefore the final resultant of the system of forces and couples. The moment of the couple is the product of the moment of the original resultant couple, and the cosine of the angle between it and the original resultant force. 24. Forces have been considered above as undistributed, but every force must be distributed over some surface or through some volume. The intensity of a force is the ratio between the force in units of weight and the area or volume over or through- out which it is distributed— e. g., a force of 10 lbs. distributed over 5 square feet of surface would have an intensity of 2 lbs. per square foot, a force of 9 lbs. distributed through a volume of 3 cubic feet would have an intensity of 3 lbs. per cubic foot. The only force distributed through volume which is considered in GRAVITY. 15 engineering is gravity; in this ease it is assumed that every particle of a body is equally attracted by the earth, the greater weight of one body compared with another being due, not to greater force acting on each particle, but to a greater number of particles acted upon. Instances of forces distributed over surface are furnished by every case in which a solid is subjected to force — e. g., in a wire subjected to tension the tensile force is distributed over the cross-sectional area of the wire, and is resisted by an equal and opposite force exerted by the wire, and also distributed over the sectional area at any conceivable cross section. For a distributed force may always be found either a resultant force, a resultant couple, or a combination of a single force and a couple, which is its equivalent in action on the equilibrium of the body. 25. Gravity is the force with which bodies tend to move towards the earth. It is exerted between each body and the earth, and between any given body and others surrounding it ; but the greater relative size of the earth renders it possible generally to neglect, without sensible error, the gravity between contiguous bodies, and regard that force only which is exerted between the chosen body and the earth. Each particle of matter is affected equally by gravity; the different weights of equal masses of different kinds of matter is assumed to be due to a variation in the number of particles in equal volumes. The relative greatness of the earth's radius renders it possible to assume that the lines of action of the force of gravity between the particles of the body and the centre of the earth are parallel. The force of gravity hence presents an example of parallel forces, the resultant of which must be equal to their sum, and act in their common direction. In the case presented by gravity the parallel forces are equal in magnitude, and all in the same direction ; hence, the resultant cannot be a couple, it must be a single force acting in the common direction. The position of the resultant relative to any axis being given by the quotient of the sum of the moments relative to that axis, by the sum of the forces; in this instance the forces being equal, this is simply the mean distance of the forces, or that line about which the particles of the body are most symmetrically arranged. Two rectangular axes being taken the line of action of the resultant is found ; if three axes be taken a point is found through which the resultant passes in every position of the body with respect to the earth, this point is the centre of gravity of the body; it is the central point around which the matter of the body is distributed most uniformly. For a body to be supported it is necessary evidently, that the gravitating forces acting on its particles be balanced by a force equal and opposite to their resultant; thus, if a body be 16 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. suspended or supported, the line of action of the resultant must pass through the point of suspension or support. The charac- teristics of the centre of gravity are as follows :--l. If the centre of gravity be supported, the resultant of all the forces of gravity acting on the particles will be opposed in every position of the body, and the system will be in equilibrio ; and every body supported by a single force must have its centre of gravity in the line of action of that force. 2. The algebraical sum of the products of each particle of the body into its distance from a given, plane, is equal to the product of the whole mass into the distance of its centre of gravity from the same plane. The centre of gravity may be defined as the centre of the parallel forces for the weight of the body. 26. Assuming a body to be equally heavy for the same bulk throughout its mass, then the centre of gravity of a geometrical figure is the position of the centre of gravity, assuming the figure to be filled with matter. If a body have a centre of figure, that point is also the centre of gravity; if it have an axis of symmetry, the centre of gravity is in that axis; and if it have a plane of symmetry, the centre of gravity is in that plane; as already stated, it is the centre of the body's mass. The common centre of gravity of a set or system of bodies is the centre of parallel forces for the resultants of their several weights. The centre of gravity of any triangle is in a line from the point of bisection of one side to the opposite angle, one-third of the length of this line from the side taken, or, it is the point of intersection of lines bisecting two sides at right angles. The centre of gravity of a cone or pyramid is on the axis at quarter the height of the figure from the base. In a conic frustrum the centre of gravity is given by the expression ■k • TT5 — ri o") in which L = lensth or axis, E. and r radii of greater and smaller end respectively. In a paraboloid it is two- thirds the axis from the vertex; in a frustrum of a paraboloid it 2R 2 + r 2 is J L . ^jsy- — from centre of the lesser end. In a hemisphere it is three-eighths of the radius from the centre. Irregular figures may be divided into triangles. 27. The centre of gravity has been called the centre of position, the centre of mean distance, that point which, being supported, the body is supported, &c. ; it is, as explained above, commonly defined as the point always traversed by the resultant of the system of parallel forces for the weight of the body or system of bodies. If the action of gravity be reducible to a single force in a line passing always through one point, fixed relatively to the CENTRE OP GRAVITY — SPECIFIC GRAVITY. 17 body, whatever be its position relatively to the earth, that point is the centre of gravity of the body; but it has been pointed out by Messrs. Thomson and Tait, that, except in a definite class of cases (the bodies being therefore termed centrobaric), there is no one fixed point which can be termed a centre of gravity; in common parlance the term " centre of gravity " has an extended signification, being used as equivalent to " centre of inertia " (Paragraph 32); and although the fundamental ideas involved in the two terms are essentially different, in ordinary cases a proxi- mate solution is available, according to which the extended meaning may be applied. 28. Gravity is, as already explained, the tendency to transmit into every particle of matter a certain velocity, absolutely inde- pendent of the number of particles; weight is the effort which must be exercised to prevent a given mass from obeying the law of gravity (Condorcet). The intensity of the weight of a body may be expressed in two ways, absolutely by the number of units of weight in a unit of volume, and relatively by the ratio it bears to the intensity of the weight of a standard substance. For the first the term heaviness has been suggested (Rankine) ; the second is termed the specific gravity of the given body. The heaviness of substances is stated by British engineers in pounds per cubic foot of volume ; and specific gravity is the ratio between the weights of equal volumes of the given body and pure water at a temperature of 62° F. and an atmospheric pressure of 14-7 lbs. per square inch. The weight of a cubic foot of pure water at the standard pressure and temperature is 62-355 lbs.; hence, the heaviness of any substance in pounds per cubic foot may be obtained by multiplying its specific gravity by 62-355. In France the unit of weight is the kilogramme, being the weight of a cubic decimetre of pure water at its maximum density (temp. 39°-l F.) ; as water at its maximum density is used as a standard instead of water at 62° F. as in England, the weight of any substance in kilogrammes is its specific gravity, and the heaviness and specific gravity are indicated by one number; but water at 39°-i F. weighs 62-425 lbs. per cubic foot, instead of 62-355 lbs., its weight at 62° F. ; thus numbers representing specific gravities on the French system, referring to a heavier standard, are for each substance slightly less than those referred to the British standard. The heaviness and the specific gravity of materials used in con- struction are important data, and are stated for each material in describing its properties. 29. The cases of distributed forces other than gravity most common in practice are those in which the force is either uni- formly distributed over the surface, and of one kind ; or uniformly 18 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. varying, and either of one kind, or of two kinds, the resultant of the two kinds forming a resultant couple. Instances of uniformly- distributed forces are furnished by the tension on a wire, and the pressure on a column, the force being equally distributed over the section of the wire or column. In this case the point of action of the resultant force, or the centre of force, is at the centre of gravity of the section ; it is equal to the whole force on the section, and its intensity is equal to the total force divided by the area of the section — e.g., 100 lbs. distributed over 10 square inches would be said to have an intensity of 10 lbs. per square inch. The resultant is evidently equal to the force per unit of area multiplied by the area of the section. When the force is not equally distributed over the section, it may generally be assumed to vary uniformly directly as the distance of the point chosen from a given line ; in this case the resultant will equal the mean intensity, multiplied by the area of the surface over which it is distributed : the point of application of the resultant will be the point where the force has its mean intensity. When the force distributed over a given area is of two kinds, as tension at one place and pressure at another, the resultant is found separately for each kind of force, and the two resultants thus found are compounded into one resultant force or a resultant couple. If the resultant forces are unequal, and of opposite signs, the resultant is their difference ; the point of action of the final resultant is found by joining the points of action of the provisional resultants, and taking the point in this line distant from each force respectively, inversely as the magnitude of the force (Paragraph 19) ; if the forces be equal and opposite, then they have not a single resultant, they form a couple which is the resultant couple of the system. An instance of this is described in another place as presented by a loaded beam. Section II. — Force considered Dynamically — Inertia — Work. 30. Except in defining the absolute unit of force, in the preceding section forces were considered statically; certain elementary ideas of the action of forces regarded dynamically and considered essential are the subject of this section. Dynamics applies to the conditions of solid bodies in motion; and as forces can only be known by their effects, the movements of solid bodies are regarded as the effects of forces, and from these effects are deduced the theoretical principles of the abstract mathematical science. Dynamics is distinguished from statics by the greater number of elements considered, the principal additional element being time; which, as already stated, is considered twice in the absolute unit of force (Paragraph 2). INERTIA — CENTRE OF INERTIA. 19 31. Matter at rest requires force to set it in motion; if motion were impressed upon it by any force, and the force ceased to act, the motion would continue for ever at the same rate, unless some other force acted to destroy or modify it. If a force continue to act on a body after impressing on it motion, then the motion will be increased, and will continue to increase so long as the force continue to act, provided no other force opposes this motion. The mass of a body is the product of its density by its volume — e. g., of two bodies of equal volume, if one had twice the density of the other, it would be said to have twice the mass. The velocity of a moving body is the distance it travels in a unit of time; the unit of distance commonly uSed is the foot or yard, the unit of time the second. The force necessary to impress a given velocity on a body is directly as the mass of that body — i. e., the greater the mass to be moved the greater will be the force required to im- press on it any given rate of motion. In other words, matter is itself assumed to be absolutely inert or passive, and all motion, cessation, and alteration of motion are ascribed to force; this, inertness of matter is termed inertia; and the fact that the force required to impress a given velocity on a body is proportional to the mass of matter, is expressed by the statement, that inertia is proportional to mass, or quantity of matter. 32. A point the distances of which from three planes at right angles to each other are respectively equal to the mean distances of a given group of material points from these planes, is termed the centre of inertia of the given groug. As a point so situated with respect to three planes at right angles to each other, must fulfil the condition for every other plane, the centre of inertia may be defined as that point the dis- tance of which from any plane whatever is equal to the average distance of the given points from the same plane, or whose distance from any plane whatever is equal to the sum of the products of each mass, into its distance from the same plane, divided by the sum of the masses. Applied to a material system, the points may be connected, as in a single body, or they may be detached ; they may be equal or unequal in mass, but in the latter case the greater must be conceived as divided; the point may fall within or without the mass or masses considered. The moment of inertia of any material point with reference to any axis, is the product of its mass and the square of its distance from the axis ; applied to a system of material points it indicates the exact energy of rotation in a rotating body. The term moment of inertia, conventionally used with reference to the section of a beam, &c, signifies the moment of inertia of the) system of points forming the surface of each section, about the 20 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. neutral axis of the section : the neutral axis passes through the centre of gravity of the section (defined in Paragraph 26). The moments of inertia for several common forms of section are as follows : — Rectangle. — I = ^ x 5 x d s ; Triangle.— I =^x5^x(lJ , + 1 0-) For hollow pillars the formula is almost the same ; it becomes — 1)3.6 _ ^3.6 .(2.) • — "a* p..j > The difference between the 3 - 6th powers of the internal and externa] diameters is tal&n, the constant c L is 13 tons for rounded, and 44-3 tons for flat-ended pillars. 77. The following approximate formulae are deduced from Mr. Hodgkinson's experiments by Mr. Lewis Gordon : — p = strength of pillar in pounds ; s = sectional area in square inches ; I = length, and d = least external diameter, both in the same unit of measure. For columns with both ends fixed and of any material — 1+a d* and with both ends rounded or jointed ; (3.) p =rf^ < 4) / represents the resistance of the material to crushing, and is — 1. For wrought iron, rectangular section, 36,000 lbs. ; 2. cast iron, hollow cylinder, 80,000 lbs. ; 3. timber, rectangular section, 7,200 lbs. ; and 4. for stone and brick, rectangular pillars, it is variable according to quality ; the crushing strength should be selected from the tables of resistances to crushing. In the four cases given, a is -g^, s^ts, istttj and shj respectively. The formulae given above apply to the forms very generally given to the different materials named. 78. The strongest form for metal struts containing a given quantity of matter is the hollow cylinder ; or for long thin struts, a rod expanded at the centre into a parabolic spindle. Cast-iron columns are generally made in the hollow cylindrical form ; long 42 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. wrought-iron and steel poles for sheer legs and crane jibs are generally made spindle-shaped. The strength of cast-iron struts of the cross or hollow square form of section may be computed by means of comparison with the hollow cylinder; thus, the strength of a cross-shaped strut compared with a cylindrical one of the same diameter and sectional area, is obtained by multiplying a (formulae 3 and 4, Paragraph 77) in the formula for a hollow cylinder by 3 ; the strength of a hollow square diagonal equal to diameter of cylinder, and of equal sectional area, is obtained by multiplying a by f . The thickness of cast-iron hollow struts is not generally less than one-twelfth the diameter, and it is neces- sary, whatever the material employed, that the thickness bear a certain relation to the diameter of the tube to obtain the maximum strength with a given quantity of material. "Wrought iron is most economically employed in the tubular form, and may have any • form of section, as rectangular, triangular, circular, &c. ; the last named is the best when practicable. In calculating the strength of such forms by the formulae given, d is the least dimension of the rectangle circumscribed about the cross section. 79. Mr. Hodgkinson's formula for the ultimate strength of posts of oak and red pine is — P = A -to S ; or for square section, A y 2 , A being 3,000,000 lbs. per square inch, and d the least diameter. The resistance to direct crushing should also be calculated, and the smaller of the two quantities should be taken as the ultimate strength of the pillar. 80. In the case of short columns, the strength more nearly approximates to the resistance to crushing j for that portion of the strength which is used up in resisting flexure becomes less as the column is shorter, and a greater proportion of the resistance offered by the material to crushing is available to support the load. Mr. Hodgkinson's formula for long pillars of cast iron requires modification to render it applicable to short pillars : — Let 6 be the strength of the pillar calculated by formula 1 or 2, and c the resistance to direct crushing = 49 tons x area in square inches ; then the ultimate strength of the short pillar ® = IbT3c < 5 -> 81. The strength of square wrought-iron cells, tested as short columns, the thickness of plate being not less than one-thirtieth of the diameter, was found to be 27,000 lbs. per square inch sectional area of iron. When several such cells joined together STRENGTH OP STRUTS. 43 were tested the strength was increased to from 33,000 to 36,000 lbs. per square inch. These results apply to cells of circular transverse section, but not to those rectangular in section when the sides of the rectangle are very unequal. Small tubes are proportionately stronger than larger of the same thick- ness of material. 82. There exists difference of opinion as to the length as compared with diameter at which breaking by cross-bending commences ; on the authority of Rankine, 20 diameters has been stated (Paragraph 69), as this length for dry wood, Sganzin states it at 8 diameters, and Rondelet at 10. According to Rondelet the strength of -wooden pillars, in terms of the resistance to crushing offered by a cube of the material, is as follows : — Length in terms of least Strength as compared with that diameter. of a cube of the material. 12 -833 24 > -5C0 36 -333 48 -166 60 -083 72 -042 Such statements must be regarded as approximate only, differing probably with the kind of wood ; the resistance of a cube gives a high figure for the resistance to crushing. The following table is calculated from Mr. Hodgkinson's experiments on pillars of Dantzig oak and red deal of square section : — Material. Lcn D.O. D.O. E.D. R.D. D.O. D.O. D.O. In the above table it appears there is a want of agreement, and a difference between the oak and deal, which might have been anticipated. The column 17 diameters long did. not fail per- ceptibly by bending, but to all appearances was crushed : the relative length so far influenced the strength, that only about half the resistance to crushing was available to support the load ; a similar column 17 - 3 diameters long failed by both crushing and n diameters. 17 Strength, R. to crushing for equal cross sectional area being unity. ■553 27-4 •381 29 •478 29 •440 34-5 ■407 37 •453 46 •227 44 GENEEAL PRINCIPLES OF STRENGTH AND STABILITY. bending. The statements of Sganzin, Rondelet, and Rankine may- be probably reconciled as follows : — When the length is less than 8 or 10 diameters, the -whole resistance of the material to crushing is available to support the load ; but when this relative length is exceeded, the resistance is less than the resistance to crushing, although up to about 20 diameters there may be no bending perceptible. Rondelet's proportions furnish a useful rule for rough calculations. A long pillar may be regarded as a beam subjected to bending load : it bends and fails in the centre, unless the centre be made stronger than the ends. The form of a parabolic spindle given to shear poles is that form most economi- cal in a beam supported at both ends, and loaded in the centre. 83. The pressure per square inch required to indent wood one-twentieth of an inch transversely is given below from experi- ments made by Hatfield (quoted by Anderson) : — Lbs. White Pine, per Square Inch. 600 Sp. Gravity. ■388 Mahogany, Bay-wood, . „ St. Domingo, Oak, Ash, ..... 1,300 4,300 1,900 2,300 •439 •837 •612 •517 The above is important in considering the pressure on fastenings, clamps, saddles, &c. 84. The relative strength of pillars of different materials, deduced from experiments on long pillars with rounded ends (excepting in the case of red deal), is as follows : — Cast Steel, 2,518-0 „ Iron, . Wrought Iron, Oak (Dantzig), Deal, Red, 1,0000 1,745-0 108-8 78-5 85. Telegraph poles and masts fail almost invariably under excessive transverse strain; considered as pillars they have a strength greatly in excess of requirements, and there is no necessity therefore, excepting in very exceptional cases, to attend to the distribution of the vertical component of their load. The vertical load on a pole is only the weight of the wire between the lowest points of the spans on both sides of the post; or, in the case of a terminal post, between the post and the lowest point of the span ; it is the same for an angle post as for an intermediate post, and therefore but a small fraction of the ultimate load of the post considered as a strut. In the case of high masts, great care should be taken to fix the mast firmly and truly vertical (Paragraph 75). FRACTURE — BRITTLE SUBSTANCES. 45 Section III. — Resistance to Tension. 86. The phenomena of fracture by direct tension are simpler than those of fracture by crushing. A tough rod subjected to tension first stretches throughout its whole length ; when the proof load is exceeded, the elongation is much greater in pro- portion to the load than for loads below the proof load; the elongation of an iron bar may be doubled by the addition of one- eighth of the ultimate load, after the proof load has been exceeded. Short iron bars may stretch more proportionally than long ones : a bar 120 inches long stretched, with 32 tons per square inch, 26 inches ; a similar bar 10 inches long, with the same load, stretched 4-2 inches; the elongation per unit of length was thus in the two cases as 1 to 2. Mr. Kirkaldy found this was not the case with every description of iron ; in some kinds the elongation was the same for long and short specimens. When fracture is about to occur, the stretching is not uniform throughout the length of the bar ; the part where rupture is about to take place is drawn out and contracted transversely, and the bar fails at its weakest section. Sometimes the bar is drawn out suddenly at two places, and in exceptional cases even at three. 87. Brittle substances fail suddenly without presenting the phenomena of stretching exhibited by tough materials. The absence of indication when fracture is imminent is a source of insecurity when such substances are subjected to tension; this, together with the fact that brittle, as compared with tough sub- stances, are deficient in tenacity, causes the employment of the former to be avoided in favour of the latter, when tension has to be resisted. 88. The pieces of a metal bar broken by tension cannot be broken by a load less than that which broke the original bar. This has received two explanations : one is, the bar has been rendered stronger by being stretched, it being an ascertained fact that wire-drawing does increase the tenacity of the metal in the direction drawn; the other explanation is, the bar failed at its weakest section, and the unavoidable relative weakness of one part has saved the other parts from deterioration. Mr. Lloyd's experiments on four successive breakages of the same bar gave — 1st breakage, 23-94 tons 2nd , 25-86 „ 3rd „ 27-06 „ 4th , 2920 „ The iron was good ductile quality : it stretched one-sixth in length. 46 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. and was considerably reduced laterally. From the above it does not appear that the ultimate tenacity is reduced by the material being loa,ded with a load less than the ultimate load. Mr. Kirkaldy has observed that screw bolts are not necessarily injured although loaded nearly to breaking point. 89. The strength of fibrous substances is greater along the fibres than perpendicular or oblique to their direction; the numerical values given in tables are, unless otherwise stated, for tension along the fibres. This difference is very marked in the case of timber; but in metals in which the fibrous structure is due to rolling, the difference of strength is very small, excepting in thin masses as plates. Rolled metal gives earlier notice of impending fracture, and contracts more transversely under an ultimate load, in the direction in which rolled, than at right angles or oblique to that direction. In some cases there is a difference of strength in iron plates, according to the direction in which strained. M. Navier found a difference of about 10 per" cent.; the strength was 40'8 tons along the direction rolled, and only 364 tons across the fibre. Sir W. Fairbairn found the strength in the two directions almost the same, and he explains this by the different mode of piling the bars to make the plate. Mr, Kirkaldy found puddled steel and iron plates stronger, and the contraction at the point of fracture greater, when the plates were strained along, than when strained across, the fibres ; but the reverse was the case with plates of cast steel, thus confirm- ing Sir W. Fairbairn's observation. Wrought iron made by the Bessemer process, in the cast unhammered state had a mean strength of 18-412 tons; a flat ingot of the same iron rolled into boiler plate had a tensile strength of 30-50 tons, the strength was increased by rolling in the ratio of 1 8 to 32. The tenacity of metals is increased by wire-drawing; small-sized hard wires are there- fore proportionately stronger than large; hence a stranded wire is safer than a single wire of the same weight per unit of length and same degree of hardness, and strand wire is preferred for town lines and long spans for this reason. Stretching metal under a tensile strain, wire-drawing, and cold rolling diminish the specific gravity of the metal, increasing the tenacity, and rendering it more uniform. Binding a wire with a tight ligature determines its point of rupture; the wire invariably breaks at the ligature, and is weakened by the binding. 90. The ultimate resistance to breaking by direct and uniform tension offered by a bar or rod is (as in the case of resistance to pressure) directly as the area of its transverse section; but the tension must be applied accurately along the axis of the speci- men, or the ultimate load will be considerably reduced. Mr. DISTRIBUTION OF LOAD — TIE — MODULI. 47 Tredgold calculated if the line of tension were removed from the axis to half the radius of the section, only one quarter of the strength would be available ; but Mr. Hodgkinson's experiments on similar bars of the same quality iron gave 7 "5 tons along the axis, and 2-62 tons along the side, or rather more than one-third. The necessity for distributing the load so that its resultant may act along the axis of the bar is evident. When material is tested for its ultimate strength, the area of the fractured bar on which the intensity of the ultimate stress is calculated, is usually the original transverse area of the bar, sometimes this area reduced by the equal stretching throughout its entire length, and not the area of the section where the extreme and local contraction has occurred, which immediately precedes fracture ; but, in such sub- stances as iron, the local contraction is an element the considera- tion of which is essential to a just conclusion concerning the mechanical value of the material tested. The elongation, under imy load not exceeding the proof load, is evidently the intensity of the stress divided by the modulus of direct elasticity. 91. In experiments on iron rods, the square section proved proportionately stronger than the round by 14 per cent. Mr. Kirkaldy, in testing iron and steel, discovered that the lateral dimensions formed an important element in comparing either the rate of or the ultimate elongation ; and he found the ultimate strength materially affected by the shape of the specimen ; the strength was found much less when the diameter of the specimen was uniform for some inches, than when uniform for only a much shorter length. 92. Those bars or rods in a structure which suffer longitudinal tension are termed ties. The efficiency of a tie is not impaired by flexibility. 93. The modulus of tenacity is frequently expressed in length of the material, as in the case of resistance to pressure — e. g., if the ultimate tenacity of iron wire be 80,000 lbs. per square inch, and 12 cubic inches weigh 3-3 lbs., the length of the modulus of rupture is 24,000 feet or 4'5 miles — i. e., jn wire of this length, of any thickness, if hung perpendicularly, would be about to break at its point of suspension by reason of its own weight alone. The modulus of tenacity is calculated on the assumption that the wire or rod is suspended in vacuo; if it be suspended in any medium, the modulus in such medium will be greater than the modulus in vacuo, in a proportion dependent on the relation between the specific gravities of the material and the medium. If the specific gravity of the material be equal to or less than that of the medium, the modulus of the material in the medium will be infinite ; or more correctly, the material has no finite modulus in 48 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. such medium. If the specific gravity of the material be greater than that of the medium, then the material suspended in such medium has a finite modulus, and such modulus is to the modulus of the material in vacuo in the ratio of the weight of a given volume of the material weighed in vacuo, to the weight of the same volume weighed in the given medium. This will be evident when it is considered that the weight of the material forms the load — e. g., if iron weighed in vacuo have a specific gravity of 7-7, then in water it would lose -ff- of its weight, the modulus in water would be to that in vacuo as 7 -7 to 6-7; or it would be greater in water than in vacuo by ^ of its length in vacuo. Practically the density of the air is neglected, it being so much less than that of the materials, and almost invariably present; but when, as in the case of telegraph cables, the surrounding medium is water, it is necessary to consider the greater length of the modulus due to the superior density of the medium. In the case of a telegraph cable the term modulus is applied to the modulus of tenacity in water; as the cable is intended to be worked in water its modulus in air is not required. The terms practical and working modulus refer to the ultimate modulus divided by the proper factor of safety. The working modulus of a cable for use under water is the ultimate modulus in water, divided by a suitable factor of safety. The length of the modulus of tenacity expressed in the substance itself, is useful to the telegraph engineer in affording a mode of representing and expressing relations between strength and load in long spans and cables to be laid in deep water. 94. The effects of temperature on the tensile strength of iron are not completely ascertained; there is a general opinion that at low temperatures iron is more brittle or weaker than at higher tem- peratures, but this opinion is not founded on accurate investiga- tion. Mr. Kirkaldy found wrought iron of superior quality had its strength reduced 3 or 4 per cent, by the lowering of its temperature below 32° F., the load being applied suddenly; but when the load was applied gradually the difference disappeared. The tensile strength of plates has been found uniform between 0° and 400° F. The best bar iron has been found to increase in strength up to 320° F., after which it diminished; but no dimi- nution of practical importance occurs up to a much higher temperature. The tensile strength of materials is not affected to an extent of practical importance within the natural ex- tremes of temperature experienced in temperate and tropical climates. 95. Chains and other bodies of iron subjected to violent shocks and vibration become altered in structure ; they lose in time EFFECT OF ANNEALING— TENSION. 49 their fibrous structure and become crystalline, -weaker, and they ultimately fail. Sir W. Fairbairn thought the time requisite to produce fracture depends entirely on the intensity of the applied forces, the retardation or acceleration bearing some ratio to this intensity; the justice of this supposition is evident on considera- tion of the action of a load exceeding the proof load. The effect of annealing on iron the structure of which has been altered by shocks and vibration, is in a. great measure to restore the original properties; hence crane chains and similar bodies are periodically annealed to render them safe, while the screw shafts of steamers and similar bodies are often changed after having been in use a certain period, to avoid accident. The general effect of annealing is to reduce the ultimate tensile strength of iron, but to render it tougher, more ductile, and consequently safer under shocks. Brittle iron has a higher ultimate tenacity than softer metal, but the softer is obviously preferable for telegraph purposes, and for engineering purposes generally. 96. Materials are commonly subjected to tension under the form of ropes and chains; if a rope be doubled round a pulley the doubled rope has twice the strength of the same rope used singly ; but if the rope be passed over a rod or bar, as when a sling is passed over a crane hook, the strength of the doubled rope is less than twice that of the single rope. The same pheno- menon is observed in chains: a chain having the links studded to prevent their collapse under strain has only about two-thirds to seven-ninths the strength of an iron rod equal in section to both sides of the link taken together. The effect of the stud is to distribute the strain more uniformly over the section of the link (Paragraphs 70, 90, 100). In flat link chains Sir Charles Fox found that no additional strength was gained by increasing the size of the chain link at the eye without adding to the thickness of the eye ; and his experiments on links and bolts proved the following rule must be observed to attain the maximum strengthwith a given quantity of material: — The area of the semi-cylindrical bearing surface of the hole in the link, must be a little more than equal to the transverse sectional area of the smallest part of the bodv of the link; consequently, the bolts in such chains have to be made larger than the mere strength of the link would seem to indicate. The explanation of the phenomenon described is in the fact that a certain extent of bearing surface is necessary to pre- vent the stress being so intense as to injure one or both of the bodies in contact by pressure before the full tensile strength of the combination is reached. In the case of rope slings and ordinary chains this loss of tensile strength is unavoidable, and must be allowed for; but in chains with flat eyes and bolts, the 50 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. proper proportions may be attained, and unless they are there is waste. 97. The quantity of work required to break a bar 1 inch square in section, and 1 foot long by tensile strain, is termed Mallet's or Poncelet's co-efficient. It differs from the resilience of the bar, as already defined in considering the ultimate load instead of the proof load, and is equal to half the ultimate load multiplied by the ultimate elongation. It represents, as in the case of the resilience, the power of the material to bear shocks; but as in practice the proof load cannot be safely exceeded, the resilience appears more useful in practice. Section IV. — Resistance to Shearing. 98. Shearing and punching are not cutting, but detrusive action, one part of the body being pushed off the other part. Unlike cutting, the separation of the parts of a body sheared through takes place suddenly, as soon as the elasticity of the body sheared and that of the shearing body have been overcome. In cutting the separation is gradual, but in shearing the material gives way through its entire thickness at once, and the recovery from the strain takes place with a jerk. 99. The resistance to shearing is somewhat less than the tensile strength of a piece of material of equal sectional area. 100. In experiments on iron bars it was found — inclined shears required less force to drive than parallel shears; flat bars required the same force to shear them with parallel shears, whether they were sheared flat or on edge; but with inclined shears and bars on edge 8 per cent., and on flat 26 per cent, of the force necessary with parallel shears was saved. The maximum resistance to shearing is offered when the stress is uniformly distributed over the section, and it is only with this condition fulfilled that the strength is directly as the sectional area. In the case of riveting metal plates together, the rivets are made to fill the holes pre- pared for them by the hammering they are subjected to to form the head ; but when bolts or other fastenings are used to connect the links of chains, or under any circumstances which require the bolt to be loose, or which render it possible it may wear loose, the stress is no longer equally distributed over the whole trans- verse area of the bolt; the maximum stress exceeds the mean stress in a proportion dependent on the form of section. This proportion is, for a rectangle f , and for an ellipse and circle f. The sectional area should therefore be increased accordingly (Paragraph 96). SHEARING STRESS — TORSION. 51 101. As will be shewn hereafter, shearing stress occurs in beams, but it requires to be provided against more generally in fastenings, as rivets, bolts, pins, screws, joggles, &c, which, connect pieces subjected to tension, pressure, &c. "When the resistance to shearing offered by the material connected is low compared with that offered by the fastenings, there is a tendency rather to shear out a piece of the material than to shear through the fastenings; this case is presented when iron wedges, pins, &c, are used with wood, or hard wood joggles, wedges, &c, are used with soft wood. 102. Punching is the same action as shearing, but is applied in a different manner. The resistance to punching has been found by experiment on iron plates slightly higher than the resistance to shearing, but less than the tenacity of a bar of transverse sectional area equal to the detruded surface of the metal punched. The laws stated above for shearing apply to punching : an inclined punch requires less force to drive than a flat one ; small punches driven by hand are, however, made flat, but the operation is not in this case strictly punching throughout. In timber the resist- ance to shearing is greater across than with the fibres. Section V. — Resistance to Torsion. 103. Torsion or twisting is the strain to which shafts and the axles of wheels and pinions are subjected; it is of much more general occurrence in machinery and millwork than in structures within the province of the civil engineer. A knowledge of the principal laws regulating the resistance of materials to this kind of stress is however essential, as it is liable to be produced accidentally; in some cases it is unavoidably present, and it is sometimes produced intentionally. The following are instances of torsion : — The tension of a wire acting at the end of a long bracket tends to twist the supporting post, and if the insulator by which the wire is attached to the bracket stand above the bracket, there is a tendency to twist the bracket. A mast is twisted when a yard is close-hauled, particularly when this is done with a jerk; hemp, wire, &c, are twisted in the making of joints and ropes ; rope fastenings are tightened, sometimes improperly, by means of a lever inserted in a loop of the rope to twist the rope on itself. Although generally referred to shafting, the laws are of course equally applicable to any other case in which there is a twisting load acting under similar conditions. Torsion produces ultim ately fracture by a kind of shearing. 'OT 52 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. 104. The twisting moment of a load is the moment of the pair of equal and opposite couples, applied at different f points in the length of a bar, tending to twist the AiC^N portion of the bar lying between these points, fig. 12. / y^ B It is evident the arc of torsion is directly as the arm * I of the couples AB, the distance between them CD, and the load. With the ultimate load the rod is wrenched asunder. 105. If a bar be twisted, the material suffers more I strain the greater its distance from the axis of the Fig. 12. bar, and the strain is not therefore equally distri- buted over the section; but in whatever layer the mean strain may lie, the ratio of the distance of such layer 'from the axis to the diameter or radius of the section will be constant for the same form of section. In a cylindrical rod, the layer which suffers the mean strain and resists the load with the mean leverage being at a fixed proportionate distance from the axis, the diameter maybe substituted for such distance; and it may be concluded that the advantage or leverage with "which the matter of the shaft resists twisting is directly as the diameter of the shaft; the resistance is also directly as the quantity of matter strained, and hence as the area of the trans- verse section; therefore, by compounding, the area being as the square of the diameter, and the leverage as the diameter, in a solid cylindrical shaft the resistance is as the cube of its diameter; and in a hollow cylindrical shaft, as the difference. of the cubes of its internal and external diameters. The extra strength gained by arranging the matter in the hollow form is evidently due to the removal of the matter to a greater distance from the axis, by which its strength resists the load with greater leverage. A hollow rod is said to be three times as strong in resisting torsion as a solid cylinder containing the same quantity of matter, and of a diameter such as to just fit the tube. The square section is found to be one-fourth stronger than the con- tained circular section; but as the area of the square is 1-7 that of the contained circle, and the leverage is greater in the square, while the torsional strength of the square section is only 1-25 that of the circular, it follows the circular section is the stronger form. This has been attributed to the fact that the corners of the square form projections unsupported by intermediate matter. If any leverage be given to the load by causing it to act through a lever attached to the rod or shaft, or through a wheel, the moment of the load or its efficiency to strain the shaft will be its weight or pressure multiplied by the length of the leverage, or the radius of such wheel. Tables of torsive strength give the RESISTANCE TO TORSION. 53 load (proof or ultimate), in pounds, of a rod of material having 1 square inch sectional area, such load acting through a leverage of 1 foot. 106. The torsional stiffness of similar rods, whether circular, triangular, square, or very long rectangles, is as the square of the sectional area, or, in other words, as the fourth power of their lineal dimensions; in rectangular rods of uniform section it is inversely as the product of the cubes of the transverse dimensions divided by the sum of their squares. The stiffness of a shaft is inversely as its length; for, if a length of 1 yard be twisted through "25° with a givjgn force, 2 yards will be twisted through •25° + -25° = -5° with the same force, the total arc being the sum of the arcs through which each part of the rod is turned. In long shafts the angle of torsion is restricted below a definite limit of perhaps - 25° per yard run. Thin rods subjected to torsion, as in shafting when long, require to be made thicker than the condition of torsional strength alone would indicate, in order to give sufficient stiffness — e. g., wrought- iron shafts of less than 4 - 5 inches in diameter may require to be made heavier than requisite for strength to have sufficient stiffness, but above this size the stiffness does not demand special attention, as the shaft is stiff enough if strong enough. Additional strength is given to shafting to allow for sudden variations of load, caused by stoppage or starting of the machinery, £ g lg there is a waste of material if the beam be of uniform section from A to B, and the beam if uniform is really M k\ B 68 GENERAL PRINCIPLES OP STRENGTH AND STABILITY. weaker than the same beam made thinner towards B, because the weight of the material of the beam forms part of its load (Paragraph 61), and the removal of all such matter as does not increase strength leaves a larger margin of strength to bear an external load.. Part of the material of the cantilever may there- fore be so removed as to diminish the depth gradually towards B, the width remaining the same, fig. 16 ; in this case the square of the depth at any section must be proportionate to the distance of the section from A; the lower surface of the beam should be curved, and the matter below the dotted line in the figure removed. The curve is a parabola, and one-third of the material of the beam may be removed without impairing its strength. The upper instead of the lower surface of the beam may be curved in the same manner with the same result. Por a uniformly distributed load, the depth only being varied, the longitudinal section of the beam becomes a triangle with its apex at B. Instead of varying in depth, a canti- lever may vary in width, the width being ■j?i a if made proportionate to the bending moment at each section ; in this case, with the load at B, the plan of the beam is a triangle with its apex at B; with a uniform load the plan is two parabolas touching at B, fig. 17. 133. A beam supported at both ends may have its width or depth varied in a similar manner, according to the mode of application of the load; for a load concentrated at any section, the product of the width into the square of the depth at each section must be made proportionate to the distance of the section from the adjacent point of support. If the depth be constant, the width being varied, the plan of the beam becomes two tri- angles having their common base under the load, and their apices at the points of support; if the - depth only be varied, the longitu- dinal section presents two parabolas meeting under the load, and having their vertices at the points of support. "With a uniformly distributed load, the product of the width into the square of the depth at any section being made proportional to the product of the distances of the section from the points of support, the longitudinal section with constant width is an ellipse ; and the plan, the depth being constant, presents a pair of parabolas having their vertices in the middle of the length of the beam, and their common base in the middle of its width. From the above it appears a beam may be made sharp where' the bending moment vanishes, but this cannot be done, because the shearing force must be resisted; hence the bearing surface of the beam must be sufficient to resist the shearing force, irrespective of its LONG STRUTS — TAPERED POLES. 69 resistance being proportioned at each section to the bending moment. For this reason, in practice beams are made extended at the bearings to resist the shearing force and to prevent the beam turning. In practice the taper is not always confined to one dimension; in some cases both the width and depth are varied in order to proportion the strength of the beam at each section to the moment of flexure, the total variation being divided between the width and depth. Long crane jibs and shear-leg poles are bent like beams, and the best form for these is that of a parabolic spindle; this is the form a beam would assume if its cross section were circular, and its resistance at every section made proportional to the bending moment. Some- times a conical spindle is used, as approaching the parabolic form near enough in practice. In such a beam the ends should have two-thirds the area of the greatest section. The variations of width, depth being constant, are applicable to flanged girders of the T and double flanged sections. The tapering of beams is of great importance in metal beams, particularly when of great weight, as there is a proportionate saving in expense of manufacture and carriage, and additional available strength. Timber beams may be strengthened by adding smaller timbers, so as to increase the depth proportionately to the bending moment at each section, such practice being much more economical than adding to the thickness of the beam throughout its entire length. 134. Telegraph poles subjected to transverse strain should not be uniformly strong throughout their length: a pole fixed in the ground and unstayed should diminish in strength towards the top, and should have about two-thirds the strength at the point of application of the load it has at the base. The proportions of tied and strutted poles should also be regulated by the principles stated for beams. If an iinstayed pole be too much tapered it will break with its ultimate load above the ground line; the proportions should place the breaking point at the ground line ; therefore a timber post should not have a less cross sectional area at the point of application of the force than about two-thirds that at the ground line. A post if too weak should be strengthened in accordance with the above principles, by the addition of material, not necessarily through its whole length, but distributed prop6rtionately to the bending moment at each section. It should be remarked, in iron-plate posts of large size, if the plate be very thin compared with the diameter of the tube, the tube is stronger as its diameter diminishes; therefore, as the diameter of the tube decreases upwards, the gauge of the plate may be reduced where less strength is required. Thus, a mast in which the lowest segments are of 70 GENERAL PRINCIPLES OP STRENGTH AND STABILITY. ^-inch plate, may have upper segments of ^-inch plate with advantage, both on account of the smaller diameter of the upper segmental tubes, and by reason of the bending moment being less above than below. 135. The laws of strength in beams have been stated without reference to the weight of the beam; but the weight of the beam itself, when acting with the load, must be added to the external load to form the gross load, to bear which the strength of the beam must be proportioned. If the weight of the beam be small compared with the external load, as in short timber beams, the weight of the beam itself is neglected; but in heavy metal beams the weight of the beam cannot be neglected with safety — e.g., a cast-iron beam may use up one-fourth of its available strength in bearing its own weight. It is usual to design the beam pro- visionally to bear the external load only, then to calculate the weight of the beam, and increase the strength to bear the gross load, if the weight of the beam compared with the external load renders such increase necessary. In the case of a telegraph pole subjected to a transverse load, if the pole be vertical and the direction of the load horizontal, the weight of the post forms no part of the transverse load. 136. If a beam be inclined to the load, as in figs. 18 and 19, the lines A B perpendicular to the load represent the reduced Kg. 19. span on which the transverse strength of the beam should be cal- culated; in fig. 18 the inclined beam is stronger than a beam of the same length perpendicular to the load in the ratio AC : AB, the effect of inclining the beam being to reduce the span. For example, if GA, fig. 18, represent a post loaded at A, the resist- ance of the post would be that of a similar cantilever of length AB, placed in the line AB. If fig. 19 represent a beam sup- ported at each end, and loaded in the centre or elsewhere, its resistance is that of a beam of similar section perpendicular to the load and equal in span to AB. The case shewn in fig. 18 is presented by an angle post, the tie or strut of which has been accidentally removed; the post then gives to the load, until, by CONSTANTS OF STRENGTH — DEFLECTION. 71 reason of the decrease of leverage to AB, the compression of the earth, and the slacking of the line, equilibrium is established between the forces acting on the post. It is evident in the cases considered the load may be resolved into two components, one acting in the direction of the beam, and one at right angles to its direction ; the former component only producing bending stress, the latter producing pressure or tension in a cantilever, or pres- sure towards one support and tension from the other, in a beam supported at both ends. 137. The transverse strength of different materials is obtained by experiment ; the numbers given in tables of transverse strength signify the ultimate load in pounds acting in a direction at right angles to the beam's length, concentrated at the centre of a bar of each kind of material 1 inch wide, 1 inch deep, and supported on supports 1 foot apart. "With the data supplied by such a table it is evident the strength of any beam of simple form of section, given dimensions, arrangement of supports, dis- tribution of load, and nature of material, may be readily calcu- lated approximately from the principles enumerated above — the constants being used with caution, and experiment and observa- tion being preferred when attainable. 138. The deflection with a given load of any point in a beam is the displacement of that point from its position when the beam is unloaded ; the deflection of the beam is that of the point in it which suffers greatest displacement. When the load is less than the proof load, the deflection of a given beam is nearly proportional to the load ; but when the proof load is exceeded, the deflection increases irregularly, and in a greater ratio than the load is increased. For loads not exceeding the proof load : The deflection of solid rectangular beams of the same material, and under equal loads, similarly distributed, varies directly as the cube of the length, and inversely as the width and cube of the depth. The deflection of solid cylindrical beams is directly as the cube of the length, and inversely as the fourth power of the diameter. The deflection in flanged girders is directly as the sum of the areas of the cross sections of the flanges, as the cube of the length, and inversely as the product of the areas of the cross sections of the flanges and the square of the depth of the web. Stated generally, the deflections of similar beams of the same material, under equal loads, similarly distributed, are directly as the cubes of the lengths, and inversely as the breadths and cubes of the depths. 139. Under proof loads, the deflection of similar beams of the same material is as the squares of the lengths, . and inversely as the depths, the loads being similarly distributed. 72 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. 140. The deflection of a beam fixed at one end and loaded at the other is equal to that of a beam of the same material and section, supported at both ends, of twice the length, bear- ing double the load at its centre — i.e., a cantilever loaded at the end is deflected sixteen times as much as the same beam would be deflected, if supported at both ends and loaded in the centre with the same load. 141. If the load be uniformly distributed over a beam sup- ported at both ends, the deflection is only five-eighths that which the same load would cause if concentrated at the centre of the same beam. The deflection of a beam fixed at one end, and uniformly loaded, is three-eighths that the same load would produce if concentrated at the end of the same beam. 142. If a beam be bent beyond a certain point, its elasticity is injured, a sensible permanent set is produced, and the beam is weakened ; if the application of the excessive load be repeated, the beam will sooner or later fail. It is necessary, therefore, that the deflection of a beam never be allowed to exceed a certain proportion of the span ; this proportion is, for timber about -j-Itj-j ca st iron y^, wrought iron and steel yj^ ; if these proportionate deflections be exceeded, a permanent set. is pro- duced. In practice the deflection varies for the proof load between ^J^ and -g^, and for the working load between ^J^ and 1 g 1 00 of the span. The necessity for limiting the deflection, and the fact that rigidity decreases in a greater ratio than mere strength, renders it advisable in designing beams to decide upon the depth necessary to give the required stiffness, and then pro- portion the width so as to give the necessary strength ; this is the order generally followed. 143. The deflection in any particular case may be calculated be constants given in the i ollow ing t ible : — Constant Elm, ::> Larch, . 2,437 Pitch Pine, . 2,837 Eiga Fir, . 3,079 Beech, . 3,133 Oak (English), . 3,359 Mahogany (Honduras), . 3,571 Ash, . 3,807 Deal (Christiana), . . 4,176 Red Pine, . 4,259 Deal (Memel), . 4,500 Iron, Cast, . 41,740 „ Wrought (Swedish) . 64,221 Steel, Hammered, . . 78,822 FORMULAE — STRENGTH AND DEFLECTION. 73 The constants for wood are given on the authority of Messrs. Barlow and Tredgold respectively, that for cast iron on the authority of Mr. Bants, and the last two on that of Mr. Kirkaldy. In practice the amount of deflection should be obtained, if possible, by experiment or observation of similar girders of the same material. Constants should be applied with great caution (Paragraphs 67 and 299). 144. By means of the following formulae may be calculated the strengths and deflections of beams of simple forms. Let I, b, and d represent the length, breadth, and depth of a beam respectively, w its ultimate load, e the constant of transverse strength for the particular material — this constant being the ultimate load of a bar one inch square in section, supported at points one foot apart, and loaded in the centre ; m, a factor dependent on the arrangement of supports ; m^ a factor dependent on mode of dis- tribution of load ; then (Pxixcxmxm, » = j m = 1 for a beam supported at both ends, and £ for a beam fixed at one end; m 1 = 1 for a load in centre of beam supported at both ends, or at end of cantilever ; and 2 for a load equally distributed ; w, divided by a suitable factor of safety, is the working strength. If the ends of the beam be fixed, instead of supported, a factor m 2 should be introduced into the second member of the equation, the maximum value m 2 can have is 2. Let x be the constant of deflection ; this constant is the quotient of the ultimate load in pounds by the ultimate deflection in inches, the bar being one inch square in section, supported on supports one foot apart, and loaded in the centre — a, table of these constants is given above, Paragraph 143; Cj the deflection in inches, and w x the load ; w, a factor dependent on the arrangement of the supports, and «!> a factor dependent on the mode of distribution of the load ; then, under a load not exceeding the proof load — I s x w 1 x n x % Cl = ~/bxd 3 x.x ' With both ends supported w=l; with one end fixed w=16; with the load in the centre of a beam, supported at both ends or at the end of a cantilever, n^ = 1 ; when the load is evenly dis- tributed % = ! for a beam supported at both ends, and § for a 74 GENERAL PRINCIPLES OP STRENGTH AND STABILITY. cantilever. If a beam be firmly fixed at both ends the deflection is reduced to one-fifth of that of a merely supported beam. The above formulae apply to rectangular and cylindrical beams; the constants apply to beams of square section, and must be multi- plied by y£ to render them applicable to beams of circular section. The formulae are applicable to beams of any section, but not the constants ; hence similar beams of any given form of section may be compared by means of the formulas ; and their strength and deflection may be ascertained, if the constants be previously ascertained by experiment for the particular form of section. The following is a more general rule for finding the deflection of a beam : — w, x Z 3 Cl = 48xexl' e = modulus of elasticity of the material ; I = moment of inertia, of the section of rupture, or of the section of the beam if of uniform section (Paragraph 32). CHAPTER III. GENERAL PRINCIPLES OP EQUILIBRIUM AND STABILITY. Section I. — Frames. 145. A structure is composed of solid materials, which may be either stiff, as stone, wood, &c, or loose, as earth, sand, &c, the pieces of material being put together so as to preserve the form of the structure and arrangement of its component pieces, under the conditions to which the structure must be sub- jected while fulfilling its purpose. The several solid bodies com- posing a structure are termed its pieces ; the surfaces at which the pieces touch each other and are connected together are termed joints. If the structure be fixed relatively to the earth, the portion of the solid matter of the earth which immediately supports it is termed its foundation. 146. In order that it may fulfil its purpose permanently and efficiently, a structure must possess due stability, strength, and rigidity. Stability consists in the forces acting on the structure STABILITY, STRENGTH, AND RIGIDITY OF FRAMES. 75 as a whole, and likewise those acting on each component piece of the structure, being balanced. These forces are, in the former case, the weight of the structure, the external forces, and the upward pressure of the earth ; in the latter case, the weight of the piece, the external forces acting on it, and the forces acting between it and the adjacent pieces in contact with it. Strength consists in the forces acting between the parts of each piece of a structure into which the piece may be conceived to be divided, balancing each other. Rigidity or stiffness is intimately con- nected with strength, and both qualities are necessarily con- sidered together ; as defined in Paragraph 50, it is that quality of bodies or structures by which they resist change of figure. In forming a structure the material and dimensions of each piece, and the manner of combining the pieces into a structure, must be such that the alteration of figure of each piece and of the whole structure may be confined within certain limits, under every possible set of conditions to which the structure may bo subjected. In the term force, it should be remarked, the upward pressure of the earth supporting the structure, and the power by which bodies resist forces tending to fracture them (stress), are included. 147. A structure composed of bars or rods, or these combined with cords or chains jointed together, is termed a frame. In small works, as in joinery, the strength of the work is often dependent on the resistance offered by the joint to change in the relative positions, at the joint, of the pieces connected ; but in frame- work, both of wood and metal, of considerable size, constructed to withstand great loads, in general the rigidity of the joints does not contribute sensibly to the strength of the structure, and the bars, &c, may be regarded as movable about the joints, as if hinged there. Very little consideration will render evident the fact, that in the majority of frames constructed to bear considerable loads, the length of the bars affords so great a leverage to forces tending to disturb their relative positions, that it would be impracticable to make the joints strong enough to offer appre- ciable , resistance to destruction or distortion of the frame by movement of the bars about the fastenings ; the rigidity of such frames is necessarily dependent on the arrangement of the com- ponent bars and cords. 148. The stress in the component bars of a frame is a distributed stress distributed through their mass ; its intensity is measured as explained in Paragraphs 24 and 50. Forces acting on the component bars of a frame tend to displace the bars relative to each other at the joints where they meet ; this tendency to dis- placement is resisted by the stress at the joint. The point in the 76 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. joint through which, the resultant of the resistance passes is termed the centre of resistance of the joint. It is evident the maximum strength of the material cannot be available if the position of the centre of resistance of the joint deviate much from the centre of figure of the joint. If the centres of resistance of the joints be con- ceived to be connected by lines, the system of lines is termed the line of resistance of the frame. The loads on the joints and the component bars of a frame, and on the points of support when the frame is supported, are computed by considering the distributed forces acting on each bar or joint as concentrated in the line of their resultant or resultants acting through the centres of resist- ance ; and by compounding and resolving these resultants at the centres of resistance by the parallelogram of forces or theory of couples ; the total loads and stresses being found, the intensity of the distributed force is found by dividing the resultant by the surface or mass over which it is distributed. 149. The component bars subjected to transverse strain are termed beams, those suffering tensile strain ties, and those suffering compression struts — terms already defined in Chapter II. The action of a load on a tie, strut, and beam, and the mode of failure of each under an ultimate load, are fully considered in Chapter II. It is evident if a strut be movable, that its longitudinal equi- librium is unstable ; for, if its axis deviate from the line of direction of the pressures it resists, these pressures form a couple acting to increase the deviation from the line of pressures, fig. 20. If a tie be movable, its equilibrium is stable. This case is represented by fig. 20 with the directions of the forces B and C reversed, A representing the tie. If A, the tie or strut, lie in the line of action of the forces B, C, then the whole of these forces are resisted by the longi- tudinal stress on the rod A — i.e., the sum of the forces is employed in longitudinal tension or pressure of the rod A. If A be at right angles to B, C, then there is no longitudinal tension or pressure on A. At intermediate positions, as in fig. 20, the forces B, C may each be resolved into two rectangular components, one acting in the direction of A (2, 3), producing tension or compression of A, the other (3, 4) acting at right angles to A, forming one arm of a couple tending to rotate it on its centre. It is evident the arm of the couple referred to above is as the sine, and the efficiency of the tie or strut as the cosine of the angle 1, 3, 2 between the common direction of the forces and the line of resistance of the tie or strut. A strut requires therefore that care be taken to place STAYING— TWO BAR FRAMES. 77 it exactly in the line of the pressures to be resisted ; and -when so placed, that means be taken to prevent deviation from this line. A tie may be employed without such special care or precaution, its equilibrium being stable; hence, in constructing land lines the tie is preferred, where admissible, to the strut. Struts are frequently stayed to prevent them deviating from the position of greatest efficiency. A stay is a rod or cord applied to the end of a strut or tie to keep this end in position, and prevent deviation of the strut or tie from the line of action of the load, the stay merely keeping the strut or tie in position tinder the action of the load, and not itself bearing any portion of the load. An instance of staying is presented by a high telegraph mast supporting a direct wire, furnished with stays stretched from near its summit to the ground ; but in an angle post the tie generally employed to act with the post in resisting the horizontal strain of the lines is not properly a stay but a tie ; for it bears in general its share of the load, and forms part of the frame composed of the tie and strut attached to the earth. In Chapter II., section 6, the case of a beam having the load and supporting pressures parallel is treated, and also the case of a beam placed obliquely to the load and sup- porting pressures ; in the latter case, the load being resolved into two rectangular components, one acting in the direction of the beam's length, the other acting perpendicular to its length, the magnitudes of these components represent the longitudinal and transverse stresses respectively. If the load be inclined to two parallel supporting pressures some fourth force must balance the longitudinal load, and in respect to such load the bar is a tie or strut, or tie on one side of the point of application of the load and strut on the other side. When the support- ing forces and the load are inclined to each other, the conditions of equi- librium are those of three inclined forces (Paragraph 6). If AC, fig. 21, represent a bar acted upon by three ' forces (A, B, C) in equilibrio, the relations of the forces are those of the sides of the triangle 12 3, drawn proportionate to the balanced forces in magnitude, and parallel to them respectively in direction ; and the magnitude of each force is as the sine of the angle between the other two. 150. A frame of two bars may be composed of two struts, two ties, or a tie and a strut, and must abut against, or be connected Fig. 21. GENEEAL PRINCIPLES OF STRENGTH AND STABILITY. with, two fixed points. \ Fig. 22. If fig. 22 represent a frame of two ties attached at A and B, and loaded at C, the load on each bar and on the supports is found by resolving the load into two components, Cd, Ce, acting in the directions of the bars, and representing the load on each bar and on the supports, both in direction and magnitude. The equi- librium is evidently stable, both in the plane of the frame and at right angles to that plane, as deviation in either direction must raise the load ; but the system may oscillate about A and B, and may need staying to prevent this. 151. If the diagram be inverted and the arrows reversed, the case represented is that of a frame of two struts, and the load on each bar and the supports is found as before, pressure being sub- stituted for tension. In this case the position of the bars is fixed in the plane of the frame; but in the plane at right angles to this the equilibrium is unstable, unless lateral stays be em- ployed to render it stable. An upright pair of shear legs fur- nishes an instance of a stayed frame of two struts; an angle pole strutted to the top is an instance of an unstayed frame of this kind. An angle pole with a short strut applied below the load may be considered as a bar acted upon by three inclined forces — viz., the external load, the pressure of the earth, and the pressure of the strut (fig. 21, Paragraph 149). Kg. 24 152. Frames formed of a strut and a tie are of very common occurrence in telegraph practice; an angle pole and tie' (some- times called a stay) furnishes an instance of this kind of frame. TIED AND STRUTTED POLES. 79 In this frame, as in other two bar frames, three inclined forces are balanced, and their relations must fulfil the conditions of the triangle of forces (Paragraph 7). The load being determined, it is resolved into two components acting in the directions of the two bars respectively; these components represent the load on each bar, and. the pressure and tension on the supports. The conditions are those of three forces in equilibrio, the load being balanced by the stresses on the bars. Figs. 23, 24, and 25 repre- sent three cases ; the stress on each bar is directly as the sine of the angle between the direction of the load and that of the other bar; thus, in the figures, the load 2 3, divided by the sine of the angle between the bars, equals the stress on either of the bars divided by the sine of the angle between the direction of the load and that of the other bar. Symbolically — Load : sin 1 ( component 1 2 : sine 3 < or ( „ 13: sine 2; the load on each bar may be readily found from the proportion, the load on the frame and the angles being given. Pig. 23 repre- sents the case of an angle pole placed perpendicularly and tied; sine 90° = 1, therefore the component load borne by the tie is the quotient obtained by dividing the load by the sine of the angle between the strut and tie. The efficacy of the tie is therefore as the sine of the angle it makes with the strut; thus, with the angle a = 30° the component load (1 3) on the tie is double the load 2 3; with the angle a = 90° this load is only equal to the load 2 3; while with angle a= 14°, the tie suffers a tension four times the horizontal load 2 3. The component load borne by the strut is also greater as the angle a is diminished; thus, for « = 14° this load is 4 times 2 3; for a = 30° it is 17 times 2 3; and for a = 90° it is 0, the whole load being borne by the tie. The necessity for anchoring the tie a proper distance from the foot of the mast or post to be tied is evident. Tt is evident the supporting forces at 4 and 5 are equal and opposite to the loads on the bars respectively, found as above. A frame composed of a tie and strut is stable in the plane of its lines of resistance, but it is only stable laterally when the direction of the load inclines from the line 4 5, joining the points of support; thus, fig. 24 is unstable, and fig. 25 stable, laterally. The frame, fig. 25, is rendered stable laterally by being stayed on each side. The 80 GENERAL PRINCIPLES OP STRENGTH AND STABILITY. mode employed above of finding the pressure and tension on each bar is equally applicable whether the frame of two bars form an independent frame, or two bars in a more complex frame. 153. In a frame of three or more bars the same laws apply as in less complex frames; but if the bars form a closed figure, the forces supporting the frame as a whole have to be computed in a somewhat different manner to that given above. In general the supporting forces may be found by considering the frame as a whole, and finding the resultants acting, through the points of support, as in the case of a simple beam; if a centre of resistance be also a point of support, the component load at such centre acting through the point of support must be neglected until the components at the other points have been found, and then the resultants of all these acting through the points of support are equal and opposite to the supporting forces. If a load be applied at a centre of resistance which is also a point of support, then the component of such load acting directly through the point of sup- port must be added to the pressure of the frame on that point of support, and an equal and opposite force must be combined with the supporting force at that centre to complete the solution. The conditions of equi- librium in a frame of three or more bars are obtained graphically by two simple operations, by which are found- Firstly, the system of forces which would balance each other if applied at the centres of resistance; and, secondly, the system of stresses on the several bars of the frame. The forces applied at the centres of resist- ance being balanced must obey the laws stated in Chapter I., section 1, and, if represented by lines, the lines will form a closed figure (triangle or polygon of forces) ; if in a projected frame the lines representing these forces . ., ,, .. ,. do not form a closed figure, then the line or lines necessary to complete the figure Fig. 26. LOAD AND STRESS IN FRAMES. 81 represent the force required to produce equilibrium. If the system of forces he given, a diagram of stresses can be made to resist the forces; if the diagram of stresses be given, the system of forces is also given. Let fig. 26 represent a frame of four bars acted upon by a system of inclined, forces applied at the centres of resistance; the forces being balanced, if they be represented by lines parallel to their directions, such lines -will form a closed figure (Paragraph 8, &c.) Let 1 2 3 4 be such a closed figure, from 1, 2, 3 and 4 draw lines parallel to each bar of the frame respectively; these will meet in 5, and represent the stresses on the ba*rs to which they are respectively parallel, due to the system of forces represented by 1 2 3 4. It is evident that, given a system of forces 1 2 3 4, a system of stresses can be designed to resist it; and given a system of stresses, the forces such will resist are obtained by joining the extremities 1 2 3 4, of the lines 5 1, 5 2, ) 2 ; or the square root of the sum of the squares, of the weight of a piece of the wire equal in length to the parameter, and of a piece BG equal in length to the arc between the vertex and the point taken. 169. The above formulae may be applied to the case of a tele- graph wire or cable to calculate such particulars of form, dis- tribution of load, T substituting for m its value — , and performing the multipli- cation — a; =^+2T + TOTB +&c ( 5 -> By means of this formula the height of any ordinate may be calculated — i.e., the height of the wire at any point G. The dip being the difference of height, rf = GH, may be found for any T abscissa FK, by subtracting from a; the modulus =— ; hence the dip of the vertex below any point in the span is — d =fi+2OT- +&c < 6 -> 98 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. If the supports be on the same level, and it be required to find the clip, in this case y= „ ; substituting this value in (6) — d =wi + im' +&c < 7 -) By means of the above formulas the dip may be calculated with any requisite degree of accuracy, the points of suspension being in the same horizontal line, or differing in height; and the depression of the wire at any horizontal distance from either point of support may also be ascertained. The tension at any point may be calculated from the difference of level between the point taken and the vertex ; the difference between the tension at the vertex and at any higher point is T 1 - T = u-c£. ..(8). In applying (7) to spans not exceeding 200 yards under the ordinary conditions of working load = one-fourth ultimate load, the first term only is generally sufiicient for practical purposes ; from which it would appear that the dip varies approximately directly as the square of the span and the weight of the wire per unit of length, and inversely as the tension. 170. The tension at either point of suspension is T 2 = T + srd ; as T 2 is increased, d decreases, and T increases and vice versd — i.e., as d is decreased, the horizontal component of the tension is increased, and its vertical component decreased. Thus there is a value of d for which the tension at each point, including the points of suspension, is a minimum. This will be apparent if it be considered as the dip is increased, although the tension at the lowest point of the span is diminished, that at the points of suspension Tnay be increased by reason of the greater weight due to the greater length of wire. If the points of suspension be in the same horizontal line, this minimum tension is attained when .t); (13.) By substituting 2v 2 for 2u 1; in (12), the effect of the lengthening on the tension T may be ascertained for a wire suspended between two points on the same level. If the points of suspension be not on the same level, then (11) must be applied, and the calculation performed for each side of the curve. It should be remarked that the first two terms are, as a rule, sufficient in practice; as the tension at the ends differs from that at the vertex, the tension t is the mean tension, and the maximum tension must be less than the proof load. 173. The effect of change of temperature on the wire is to alter its length, and alter consequently the tension and dip; if 6 be the co-efficient of expansion for each degree of elevation of tem- perature, for a difference of ± K degrees, the length of the arc will change from v to v(\±6~K), the upper or lower sign being used accordingly as the temperature is raised or lowered; but as the change of temperature causes a change of tension under which the length v is altered by reason of the elasticity of the" material, the ultimate effect of a change of temperature on the length of the arc is the difference between the expansion or con- traction due to change of temperature, and the consequent ELASTICITY AND TEMPERATURE — POSITION OF VERTEX. 101 contraction or expansion due to change of tension from T to T x ; hence, the alteration of length due to a difference of temperature = ± K, is from v to v(l ± 6K) { + x (T 1 - T)}. If the points of sus- pension be on the same level, v x being the length of the arc on each side of the vertex, then, previous to the change of temperature — 2v i = a + J^> ( A -) after the change of temperature — 2» 1 (l±*K){l+x(Ti-T)}=« + -gf ! (B.) If A be subtracted from B, 2« x be assumed = a, the term contain- ing a. and 8 as factors be neglected, and every term be divided by a, then — ±rK + KT 1 -T)=^- 2 (l-i f ) (H.) 2 2 By putting for T x its values (7) 5.-7 and ^-y— , the variation in the dip is obtained. The above equation should be applied by trying the value of T x or d respectively, which will satisfy it. 174. If the points of suspension are not on the same level, but one be at G- and the other at A, then the portion of the curve below the horizontal line NG- drawn through the lower point of suspension is symmetrical about the line BF, and the vertex B is not in the centre of the span, but nearer to the lower point of suspension. To find the horizontal distance of the lowest point or vertex from each point of suspension respectively, the differ- ence of level d 2 being given, the dip below the lowest point of suspension is (6) — d = ^, (C.) below the highest point — <*i=4t' (°-> the difference of level between the points of suspension d 2 = d j — d =§^{y\ ~y 2 )'> Pitting g+a; for y v and --a; for y, d 2 = ^x, or d T x = — - ...[15); the distance from the lower point of suspension ia. 102 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. " - S— , and from the higher point - + -?— . As only the first 2 on- Z a™ term of the series (6) is taken, this formula is only applicable to spans up to about 200 yards under ordinary conditions as to tension. If more terms of (6) be used, the formula is applicable to longer spans, and under other conditions as to. tension. Thus, if two terms of the series (6) be taken then— d * - vt + w&r + vimr ' and by substituting numerical trial values, the value of x may be obtained with sufficient accuracy for all practical purposes. 175. A ready mode of noting differences of level of the wire is to have the curve drawn to scale, and apply it to a drawing of the profile of the ground and the objects the wire is to pass over; the curves may be calculated by means of the series for the ordinate with sufficient accuracy for any purpose occurring in practice. The curves might be cut in sheet brass, and the values of the scales marked on the brass. A drawing of the catenary is given in M. Blavier's " Telegraphie Electrique " for use as described above, but the scales given with the curve do not agree. Many of the above formulae are contained in M. Blavier's work ; they are not all deduced in so simple a manner as above, and the series representing the length of the arc, and the formulae for the influence of temperature on the tension, &c, given by M. Blavier, are inaccurate. 176. When the difference of level between the points of sus- pension is very great, the curve formed by the wire may be only naif the curve ABC, fig. 36 ; in this case one point of suspension is at the vertex, and the dip is equal to the difference in level ; in this case (6) d = -^, or the distance of the supports is \ / = a . This is to be avoided in practice; and in doubtful cases either this formula should be applied to find the minimum distance admissible between posts greatly differing in height, or the distance should be found as follows : — It being decided to give the wire a certain dip d, below the lower point of suspension, then approximately (C)and (D) - y = A/ - — , and y x - \f — J— ; from which y and y having been found, the distance y + y\ is the distance the points of suspension must be placed apart to allow a dip = d below the lower point. 177. If a chain be loaded uniformly along a horizontal line — i. e., the load on any length, as BG, is proportionate to the hori- PARABOLA AND CATENARY — HYDROSTATICS. 103 zontal line FK, then the chain hangs in a curve, termed a parabola. In the calculations for finding particulars of form, = angle of immersion. The resistance of the water to the motion of the cable perpen- dicular to its length is given in formula (2). The velocity v is RATE GF SINKING TRANSVEKSELY AND LONGITUDINALLY. Ill less than /-, because the cable is not suspended horizontally; for as only one component of the weight is considered, and the components are taken at right angles to each other, the rate of motion cannot exceed / =v; cos w being the value of the component of the weight of the cable in the direction perpendicular to its length. Thus the Atlantic cable, weighing •2575 lb. per foot in water, could not sink faster than — V cos & -2575 _: _ qj •154 when oblique to the horizon. The weight of the cable overcomes the resistance of the water with a velocity which increases with this weight in water, directly as the cosine of the angle of immer- sion, and inversely as the co-efficient of the resistance the water offers to the motion of the cable. The introduction of the cosine is in accordance with the parallelogram of forces; it is evident, in considering the component of the weight perpendicular to the cable, that this has a less value the greater the angle of immer- sion, and when the cable is immersed at right angles to the surface of the sea, or vertically, this component vanishes. The velocity of sinking at right angles to its length, and the angle of immersion, are not affected by the length of cable in motion, as the resistance of the water acts equally on each portion of that length. 189. Considering now the component of the weight taken in the direction of the cable's length, this component is equal in magnitude to the weight of the cable in water, multiplied by the sine of the angle of immersion — it is opposed to the friction of the water and the tension at the ship. As the cable lies in the water as if it were on an inclined plane moving in the direction of the vessel, the tension at the ship is less than if the length of cable hanging in the water were suspended vertically, and is equal to the weight of a piece of cable as long as the depth of the sea. Therefore the tension on the cable is not increased by diminishing the angle of immersion ; so long as the depth remains constant, it is independent of the length of cable actually suspended in the water at any moment, the friction between the cable and water being neglected. Thus, if the vessel be urged at an increased speed, the angle of immersion will be reduced, a greater length of cable will be on its way to the bottom at each moment, but (friction being neglected) the tension on the cable at the ship 112 GENERAL PRINCIPLES OF STRENGTH AND STABILITY. will remain the same. If, in fig. 38, AC be the cable from the ship at A to the bottom at 0, if a pulley be conceived at A, and a length of cable AB continuous with CA, and equal to the depth of the sea, be sus- pended over the pulley A; then the weight of AB will balance that of AC lying on the inclined plane of water, friction being neglected. For by the parallelogram of forces the weight 2 3 of CA, being resolved into two com- ponents—viz., 1 2 and 2 4, 24 = 23x cos ACB, and 1 2 = 2 3 x sin ACB, the triangles are similar, and AB = AC x sin ACB, . ■. the weight of AB will balance the com- ponent of the weight of AC in the direction AC whatever the angle ACB, or the length AC, the cable being assumed free to move on the inclined plane AC without friction. Hence the tension at the ship, when the cable is laid in a straight line on a hori- zontal bottom, without slack, is — T = wh-/...(4:); in which w is the weight in water of a unit of length of the cable, h is the depth, andyis the resistance offered by the water to the cable's motion longitudinally. 190. The quantity f sensibly affects the result, and its value remains to be examined. The value of this quantity is assumed to vary directly as the square of the velocity with which the cable moves longitudinally; it varies directly as the amount of friction on each unit of the cable's length, and directly as the number of units of length in motion. In fig. 37, if DC represent the cable, and DCithe level bottom of the sea; in moving from the position DC to CjEB the element C will not move in the line CE at right angles to the cable ; instead of arriving at E the element C will arrive at G u for DC X = DC. The cable being laid without slack, in moving from the first to the second position it will have slipped through the distance EC 1; equal to the versed sine of CDC 1; the longitudinal velocity of the cable therefore is — v n = v x ver sin

le in the ground ; its ultimate durability is not settled ; it has lasted more .han sixteen years in Switzerland, and is estimated to last twenty years with- >ut renewal. In Italy it has not been in use so long, but will prove equally iurable ; it is used on coast lines exposed to storms, and with a minimum Bpacing of 90 metres, Jhe pine wood having failed. It is felled between November and March, oarked and seasoned before use. Slight curves are admitted in the poles, and only sound wood is used. The durability of pine wood poles-is variously estimated as follows : — England, average for unpre- pared round poles seven years. Boucherising is generally considered uncertain, creosoting is considered the best, but it may fail from want of care, &c. ; Norway, in five to seven years unprepared poles are mostly replaced ; Bouch- erised require slight renewals after ten years ; Switzerland, seasoned larch has been found good after eight or ten years ; Bavaria, injected timber lasts on an average only seven years; injected wood is very commonly employed ; Boucherised and creosoted most generally, and with satisfactory results. The following partial and supplementary measures are taken to in- crease the durability of poles :— The Italian chestnut poles are charred for 1'50 metre (4 '9 feet) to 4 centimetre (2 inch) deep. In Norway the Boucherised poles are tarred 2 feet above and below the ground line to prevent the salt being washed out by rain and humidity ; this is applied at once to seasoned wood, but one or two years later to unseasoned wood. Tar and iron pole roofs are commonly employed, but the end is attained cheaper in many cases by other means — e. g., in Austria the pole is cut wedge-shaped at top, and the upper surfaces are well painted with linseed oil. In France the tops are cut to a cone and painted. In Italy the tops are rounded. In Norway, when barking the poles care is taken not to injure the layer under the outer bark, as the preservation of this adds to the durability of the poles. There is considerable variation in the depth to which poles are inserted in the ground. The following are some additional examples :— Austria, 25 feet pole inserted 4'5 feet, the bottom of the hole being filled with stones. Bavaria 25 feet pole 5 feet, 31 feet pole 6 feet. Belgium, poles 21'3 feet to 29 '5 feet are inserted 4 '92 feet; poles up to 46 feet in length are inserted 6'76 feet, and poles 67 '6 feet long are inserted 9'84 feet. England, poles are inserted to one-fifth of their length, but not less than 4 feet, nor in good earth more than 6 feet ; in made earth they are inserted a foot deeper. Italy, poles 19 '68 feet to 26 '24 feet, inserted 120 metre (3 '94 feet), this is increased in soft earth and decreased in rock. Denmark, poles 26 '7 feet inserted 1'75 metre to 3 metres (5 74 feet to 6'56 feet). Norway, poles 23 feet to 26 "25 feet, inserted about 2 metres (6 '56 feet), more or less, according to nature of ground. In some places the ground becomes frozen several feet deep, and the thawing in spring would loosen the poles. Sometimes small stones are used round the poles, so that the latter are kept from contact with the surrounding earth ; the object is to strengthen the line against violent storms. Holland, poles are inserted 1 '50 metre to 2 metres (49 to 6'56 feet), according to size of pole and nature of soil. 436 APPENDIX. Switzerland, poles 2624 and 29-5 feet inserted 3-93 feet ; 32-8 feet poles inserted 4 9 feet, stones are used to fill in round the poles. In England poles are inserted a foot less in rock than in ordinary earth, or 3 to 5 feet ; in Australia they are inserted 4 feet in rock. ; in Bel- gium only 1 "97 foot ; in Norway very shallow holes are made in the rock, and a truncated square pyramid of stone is built round the pole, lime mortar being used. The dimensions of this structure are 2 - l metres (6 "79 feet) square at base, 1'5 metre (49 feet) at summit, and 1"5 metre (4 - 9 feet) high. In Italy poles are mounted with rammed earth, or earth and. stones; the mound is conical and 0'5 metre high ; in rock the holes are shallow, and rough masonry with lime mortar is used. The lines in the north of Germany, Denmark, and Norway, have to be built stronger than other European lines; the Norwegian lines are the strongest, the poles are closer, and inserted deeper than on other lines. In the north of Germany the wires may become encrusted with icicles to a thickness of 15 centimetres (6 inches) ; the weight of ice on one wire 60 metres (197 feet) span may exceed 3000 lbs. ; although this limit is rarely reached, less extreme cases are frequent and sufficiently severe to try the supports. Holes are commonly bored and dug, but in £he case of large poles the diffi- culty of lifting the poles into bored holes without the use of shears is con-( sidered a great disadvantage ; but it is contended, on the other hand, that by using a curved shovel to protect the sides of the hole while inserting the pole, shears may be dispensed with. In England the dug holes are stepped and made about 2 feet wide across, and 4 feet long in the alignment. In Austria and Belgium similar stepped holes are used. In Italy the holes are made only just wide enough at one end to admit the pole. In Denmark the holes are bored with an augur, this having proved cheaper, quicker, and stronger ; the lines are found to bear storms well. Boring tools are used in England, and give satisfaction. In Australia, whenever practicable, the holes are bored with earth augurs, boring holes not less than 12 inches in diameter and 5 feet deep ; when absolutely necessary the bar and shovel are used, but the excavation is not suffered to exceed 16 inches in dia- meter. Thirty miles of line constructed by the author in India was not damaged by a cyclone which took place just as the line was finished ; the holes were 3 feet square, a large quantity of broken brick was placed in each hole, the poles had cross feet, and some of them were on made earth. The continuation of this line was damaged, the poles having been set with earth only. Poles set in large holes may be made to resist storms by the use of stones or bricks for filling the holes ; but the expense must be greater, generally, than when small holes are bored or jumped. The use of boring tools is spreading, and of their general economy and utility there can be no room for doubt. Provision for a large number of wires is generally made in England by using higher poles, until the uumber of wires is so great as to render this difficult, when coupled and A poles are used necessarily. It is generally speaking preferable to provide for a large number of wires by using poles of the ordinary size, and using two separate sets of poles when the wires are too numerous, or the stress too great for one set. In Prance and Switzerland coupled poles are used on curves, as stated above ; a large number of wires is provided for by using two poles coupled by iron rods, the poles being almost or quite parallel to each other. In Austria A poles are preferred, they are manifestly stronger. In Italy when the wires are too numerous for one set of poles, a second set is erected, the two sets being kept quite distinct, with a view to rendering total interruption less frequent. The use of exceptionally large poles is avoided as far as possible at crossings. The wires are sometimes divided into two sets, thus ordinary sized poles are poles. 437 employed even with a very large number of wires. The wisdom of avoiding the use of very large poles is obvious ; these poles are proportionately dearer both to purchase and transport, they are less generally useful, and from the greater liability to faults proportionately weaker. Bolt holes made for coupling poles should be carefully stopped with white lead or other suitable stopping to keep out water. When poles are planted on curves without ties, or with ties having no straining screws, it is a common practice to plant the poles a little out of the perpendicular, in the latter case they are drawn up when the wire is strained, but sometimes, e.g. in Belgium, the poles on curves are allowed to remain slightly so inclined even when tied. In France coupled poles are used to separate very unequal spans. Poles overloaded with wires so that they would be thrown down by high winds, are cross stayed— i.e., two stays are erected to each pole extending at right angles to the alignment ; this is applied in England to poles planted in made earth. In Belgium every pole on»a railway line is stayed by a stay on the opposite Bide to the track, to ensure the pole falling clear of the rails in case of accident: Iron Poles. — Several patterns of iron poles have been used in France experimentally. One pattern resembles the Morton pole ; it is of galvanised iron, and has two longitudinal fins formed of the edges of the plates, through which the rivets pass the section ; inside the fins is almost circular. When necessary, as at angles, the pole is strengthened by a triangular plate riveted into the longitudinal joint and projecting. The insulator brackets are bolted to the longitudinal fins, and a set of iron projections may also be fixed to these fins to form a ladder for climbing the pole. These poles are said to be cheap. A very simple iron pole is in use in Switzerland. This pole is simply a tube in one piece. The metal is - 197 inch thick, the lengths are from 2'55 metres (8'37 feet) to 7'50 metres (246 feet); the extremes are exceptional, and the limits are practically 3 "45 metres and 570 metres. The poles are surmounted by points, the diameter below the point is 41 millimetres (1 6 inches) ; they are conical, so that a pole 570 metres (187 feet) long has a diameter at base of 75 millimetres (3 - 95 feet). These poles are fixed in pyramidal stone socles. When painted at intervals they are very durable, but they have proved inconvenient, because they could not be altered to carry additional wires. The mode of attaching the insulators to these poles is exceedingly simple ; the insulator stalk is bent at a right angle, and the horizontal portion is put in a hole quite through the pole and fixed by a wedge. Several engineers have designed poles of rolled iron bar of the forms of section most commonly employed in iron structures ; of such poles a French pattern of T iron and a Bavarian pattern of I section are good examples. The French pole is simply a piece of T iron set in a moulded block of beton. The beton block is pyramidal or rather J. shaped, its greatest horizonal dimension is placed across the alignment. It is strengthened by an iron band round its top, and has fifty to two hundred litres volume, i.e., 1 77 to 706 cubic feet. The iron passes almost through the beton block, and as a lightning conductor a wire soldered to the pole passes quite through. Beton blocks are cheaper, stronger, and as they can be made on the spot, and of any suitable shape, more convenient than stone blocks. The cross-arms are square bar iron, 1'24 metre (4 feet) long, and 25 millimetres (-98 inch) square. They are passed through holes in the web, and bolted to the flange ; each bar is fixed by two bolts, and carries four insulators. A T bar, weighing only about 5* lbs. per yard, and measuring only 138 inch in each direction, was found strong enough for a man to rest a ladder against, and to carry a No. 11 wire for a military line. When the earth is hard the 438 APPENDIX. blocks may be dispensed ■with, and for military purposes a triangular earth plate may be used. In Holland beton blocks have been used ; these blocks are T25 metre (49 inches) high, and 0'45 metre (17'7 inches) square, their upper surfaces are inclined, and are perforated by a square hole 19 '6 inches deep, slightly exceeding in tranverse dimensions the section of the pole. Cement is used to fix the pole. The Bavarian rolled iron poles are of 1^ section, and 5, 6, and 7 metres in length. This form was chosen for the same reasons as it is generally used — viz. , because the material is applied with the utmost mechanical advantage, and consequently at the minimum cost ; the utmost economy waB also desired in the fittings and fixture of the pole. The depth of the bar is 4 '87 inches, width of flanges 2 '94 inches, and thickness of web l - 3 inch. The cross-arms are of f iron bolted to the pole by bolts through the web ; the angle iron is -24 inch thick, and 1 '81 wide each way. The insulator stalks have flanges ; they are placed in holes in the cross-arms, and secured by nuts below. The poles are set in granite socles 4'27 feet high, and 1*39 foot square in section. The upper surface of the socle is inclined, and has a hole in it the shape of the section of the pole^ and 9 "85 inches deep. The pole is fixed by means of melted lead, calcareous cements having been found to crack in consequence of the vibration. Each pole is connected with the earth by a wire inserted in the lead used to fix the pole. A pole 16 4 feet long without cross-arms weighs 182 lbs. The flanged form is very economical, strictly it should taper upwards, but this is unattainable in rolled iron. The design of these poles and their fittings is an excellent one, but in most cases beton blocks or iron base plates would be more eco- nomical than stone socles. In applying the flanged form to telegraph poles, possible lateral loads must be considered and provided for, and in general greater lateral stiffness is necessary than in ordinary flanged beams. The necessary lateral stiffness is given by making the flanges relatively wide, but the flanged form. is in this respect obviously inferior to the box form. Several engineers have proposed to fix iron poles by driving or screwing them into the ground instead of placing them in holes previously bored or dug for their reception. Screw earth tubes were used in India for wooden poles and for some of the first iron poles, but their use has long been discontinued. Small military poles, invented by M. Lemasson, are tubes fitting together and fixed by screw clamps. The base is a steeled iron spike, it is driven into the ground by means of a large hammer, and the pole is then fitted to it. The Oppenheimer pole is the only pattern planted by driving which has been adopted for permanent lines. The base of this pole is 3 feet long, of a peculiar shape, somewhat like a triangular arrow or spear-head, with the corners rounded off; the material is cast iron, and the base is driven with its greatest width in the alignment. The upper part of the base has a socket to receive the end of the pole, this socket is filled temporarily by a suitably shaped piece of iron, the latter is covered by a rope pad, and the base is driven by a weight dropped on this rope pad. A light tripod, fitted with sheaves and a guide rod, is used to raise and drop the weight. After the base is driven the pole is fixed into it with cement, or preferably with iron wedges. These poles have a firm hold on the ground, the soil being compressed in erecting them. They are used on railways in Australia, and appear to have given satisfaction. The principle of driving the base is the only peculiarity in the design ; if this feature prove satisfactory it might be applied to poles of other patterns above the ground line. 439 APPENDIX V. EXAMPLES OP RIVER CROSSINGS. Spans. Span across the River Kistna at Bezwarrah, Madras Presidency, Eas„ Indies.— Distance between masts, 5070 feet. The sites on which the masts are erected are 405 feet and 406 feet respectively above flood level. The wire is of iron, and has seven strands, eaoh -145 inch diameter. The poles are 14 feet long, 10 inches square, and set 4 feet in rock. Insulation:— Each end of the span wire is passed round a groove in a marble ball, or rather pro- late spheroid, an iron Jtrap passed round the ball in a groove in a plane at right angles to that of the wire fastens the ball to the post. To improve the insulation each post is boxed in, the wire passing through slits in opposite sides of the box. This mode of insulating the bine has proved satisfactory. Teesta River Span, Assam, East Indies. — 2830 feet, masts 97 and 103 feet respectively. Wire, seven strand steel, each strand - 06 inch diameter; weight of rope 350 lbs. per mile, tenacity 26 cwts. Kotree Span across the River Indus, East Indies.— Span 1950 feet; six wires, each wire seven strands, tenacity 33 cwts. Masts 143 feet 9 inches and 150 feet high, clear, respectively. Lower masts tripods of cast-iron tubes braced together, and fixed on sockets set 10 feet in masonry. The tubes are cast in lengths of 6 feet 3 inches, have flanges, and are bolted together. These tripods are 93 feet 9 inches and 100 feet high respectively. The top masts are wrought-iron tubes, and stand 50 feet clear of the tripods. Span across the River Hooghly, near Barrackpore, Bengal. — Distance between masts 2135 feet. Masts 149 and 147 feet high respectively; differ- ence of level 14 feet 6 inches. Headway 70 feet clear. Wires, ten in number, placed 2 feet 6 inches apart, and of steel, weighing 350 lbs. per mile. The masts reaemble those of the Kotree span, described above. Span across the River Ganges at Benares. — Distance between masts about 2900 feet. The site of one mast is about 3 feet above flood level, that of the other at about flood level. The masts are simple, and built up of pieces about 30 feet long. One mast is of Saul wood, the other is almost entirely of saul, the remainder being of teak. They are built only in length ; the logs are joined by splices, each 6 feet long, and secured by three iron clamps 2 inches by 5 inches, tightened by bolts. The logs were not shaped, but used square, as purchased. Each splice is fitted with four stays anchored to the ground by large stones. The stays are of two strands of No. 1 B.W.G. wire, and those of alternate sets are in the same vertical planes, the anchors being placed at the angles of a. regular octagon. The top stays were originally placed at an angle of 45° with the mast, and all the lower stays were anchored at the same distance ; but the lower stays were afterwards altered and placed parallel with the upper ones. The masts are about 180 feet long, 16 inches diameter at base, and 5 inches at summit. It was originally intended they should be placed in pits 5 feet deep, a large slab of stone being placed in each pit for the mast to rest on, and the pit rilled up with charcoal or other suitable material ; but this was not carried out. Each mast stands on a stone slab in a pit, but the pit has not been filled in, nor is the foot of the mast otherwise fixed. Each mast was erected in two parts, the lower segment about 115 feet long, and the upper built of two pieces. The upper segments were used for rais- 440 APPENDIX. ing the lower ones. The scarf between the upper segments has its surfaces cut at right angles to each other (Kg. 40) for convenience of fitting, the other scarfs have oblique surfaces (Pig. 41). The diameter at the scarf between the segments is 9 inches. The wires are two in number, of steel, No. 10 B.W.G., calculated dip 100 feet; the wire between the masts and terminals is iron, No. 5J B.W.G. After the masts had been erected, and before the wires were up, a boat adrift fouled one of the stays, and broke off the top log at th» joint. It was then decided to remove this mast. The mast was successfully moved on end with stays fitted just as it stood, to a new site 80 yards further inland, and 150 yards along the river. The removal of the mast only cost about £16, 10s., and as compared with taking it down and re-erecting it, there was a great saving of time and money. This will no doubt form a precedent for moving masts in future. The removal in this manner was devised and carried out by Mr. H. A. Kirk, the assistant superintendent in charge of the work. The work was finished in January, 1874. The masts are still standing, and are likely to prove very durable. The only point in which they appear open to criticism is the oblique scarfs used for joining the pieces. There would have been less sacrifice of strength if the abutting surfaces of the pieces had been cut at right angles to the pressure, and long iron fish plates or splints and through-bolts used, instead of the hoops or clamps. Although placing stays of the several sets parallel to each other improves the appearance of the structure, it is a sacrifice of mechanical advantage. The placing of the foot of the mast below the surface of the surrounding ground is essential to prevent possibility of disturbance of the foundation, unless an artificial foundation be carried down several feet. If the mast be buried there is a gain in strength due to the end being fixed ; but if the earth is not filled in it is preferable to have an arti- ficial masonry foundation brought up to the level of the surrounding soil. Crossing of River Soane, Bengal. — This crossing consists of seven spans, six masts being erected in the river, and one on each bank. Of the masts erected in the river four are 70 feet and two 32 feet high, clear of the piers. The difference in height is to allow for the inequality of the spans ; the masts for the shorter spans being lower, the height of the wire above the water is the same at the centre of each span. The bank masts'are similar to those described in Article 332, page 230. They are made up of flanged tubes, trussed with iron rods and [_ i ron street braces, and stayed with rod stays. Their heights are 119 feet and 83 feet clear respectively. The masts erected in the river are not stayed. These are erected on small piers of ashlar masonry, each pier resting on a foundation of two wells 30 feet deep. The piers are similar in shape to river bridge piers ; they are erected at right angles to the current, and have a pointed cutwater at each end. Their dimensions are— length at bottom 12 feet 6 inches, greatest width 4 feet, height above wells 15 feet. The masts are in section of box form, the flanges or ribs being of plate iron, the double web of lattice work. The box form was preferred to the simple I, because stiffer laterally ; and the lattice web was preferred to plates, because it affords facilities for paint- ing and climbing. Cast-iron sole plates 5 feet x 3 feet are bolted on the top of the piers by bolts passing through the piers and secured to bars in the wells. The masts are secured to the sole plates by bolts, and this connec- tion is further stiffened by triangular fins standing 4 feet high. The plate flanges are placed parallel with the line wires and across the river. The masts are square in plan, 18 inches square at base, and 6 inches at top. The insulator fittings are bolted to the projecting edges of the flanges. The spans are 2.340, 1,500, 1,500, 2,000, 1,500, 1,500, and 2,340feet respectively ; the conductors are of seven strand steel wire, weighing 450 UNDERGROUND LINES. 441 lbs. per mile. The dip of the wire was cheeked by white lines painted on the masts ; that of the centre span was verified by actual measurement. The stream has a very strong current, and rises and falls very rapidly ; the spans ware necessarily made unequal, to get the best available foundations for the piers. American Spans of North- Western Telegraph Company. —The longest of these is upwards of 2,000 feet in length, and is across the Missouri. These spans are made of American compound wire. All factory joints are cut out, and the wire is joined by insoldered spring joints, described in the Appendix on wire. A solid joint in a long span of compound wire causes fracture. At each end of the span No. 9 iron wire is used, and this is continued for 20 or 30 feet over the stream to prevent the compound wire being used over the support where it would be damaged by chafage, &c. To allow of the wire being lowered during the cold weather when navigation has ceased, it is suspendedfrom a pulley. Drawbridges are crossed by erecting high frames on the fixed portion and spanning the draw. As this cannot be done with a large number of wires, in this case a light iron tower is erected on the draw span, from the top of this tower a three-inch iron rod extends upwards with a collar on it every 3 feet ; the cross-arms carrying the insulators are centred on this rod, rest on the collars, and are free on the vertical bar. The wires hold the cross-arms while the tower and rod turn with the bridge. On another American crossing, in the Pacific coast system, a four- wire con- ductor cable was used. The specification was not obtained. The span was 3,600 feet. Cables. Cables Connecting Vancouver's Island with Washington Ten-i'ory (America). —Three sections, 6, 4, and 2 miles in length respectively. Conductor seven strands, each a pure copper wire, two layers gutta percha, j-V thick, one layer machine banding, one layer tarred hemp guard, twelve No. 9 gal- vanised iron wires, laid spirally. Cable manufactured in San Francisco by the Construction and Maintenance Co. The bottom is bad and the tides very heavy; the average life of the cables has been about three years, excepting the crossing of 3,600 feet referred to above; rivers on the Pacific coast system are crossed by cables like that described above ; the crossings are short. The latest type of Indian river «iable is across the Pudda, in Bengal. Length 3,290 yards, conductor seven strands, each a eopper wire -036 diameter, three layers gutta percha ; total diameter -32 inch ; four layers tanned jute, and twelve galvanised iron wires, each -254 inch diameter, between 3 and 4 B.W.G.— total diameter 1-224 inch, tenacity 18J tons. APPENDIX VI. UNDERGROUND LINES. The systems of construction described (pp. 349, 382) are those in use in England and France principally. In most large Continental cities, the 442 APPENDIX. number of wires being few, readiness of access to them is of less import- ance; permanent cables are therefore preferred to tubes, the wires in which may be changed. These underground lines are laid in multiple con- ductor cables of the type used for subaqueous lines. Each cable contains from five to seven conductors, insulated with gutta percha, and protected by iron wires. These cables are jointed and tested with the care bestowed on subaqueous lines, and once laid they are exceedingly permanent. They may be laid deeper than tubes, and hence better protected against deterioration. In Belgium, two or more of these cables are laid in a brick trough, the trough filled up with sand, and the whole covered with earth. This system is quiet successful. In Switzerland, cables are laid on the ground for crossing the mountains, where an aerial line would be liable to interruption from snow and ice. The longest and one of the most recently constructed underground lines is that between Berlin and Halle. This cable contains seven insulated conductors, each composed of seven copper wires 6 millimetre ('0236 inch) diameter. Each conductor is covered with two layers of gutta percha and two layers of Chatter- ton's compound, — viz., one layer over and betweeu the copper wires, the second between the layers of gutta percha. The thickness of each in- sulated wire is 5 millimetres ('197 inch). Tarred hemp is spun on to 17 millimetres ('669 inch). The cable is protected by sixteen galvanised iron wires of 4 millimetres ('157 inch) diameter; these wires close up com- pletely against one another. This line is an experimental one ; the design, although empirically chosen, has evidently been selected after careful con- sideration of what has already been done, and from the results obtained. Mr. M. A. Holtzmann has been experimenting at Amsterdam on an original system. The insulating material is termed "brai" liquid, and is a residue from the distillation of coal tar. When cold, this material is a flexible solid, which has been found to be unchanged after having been buried ten years. Gutta percha soaked in a mixture of equal parts "brai" liquid and creosote was not apparently altered, but in case of doubt the gutta percha may be protected by tape saturated with *. protective. The mode of con- struction consists in laying troughs of creosoted wood in a trench, filling these with melted brai liquid, and, when the liquid is cool enough, the wires, thinly covered with gutta percha, are laid in the trough and covered with a lid. It is claimed that absence of brittleness in the compound, and its chemical permanence, fit it for the purpose if it is buried sufficiently deep to ensure protection against great variations of temperature, and the lines cost only about half the cost of cables. This system is experimental, and has been tried for upwards *>f two years on 5,000 metres of 12-wire line (Journal Telegraphique). In Holland, the underground wires are laid in tube3 of pasteboard and asphalt manufactured at Hamburg. The system was invented by M. Jaloureau. It was commenced experimentally, in 1865, by laying a line of 2,580 metres in Amsterdam, and the experiment has been followed by great extension of the system, and its adoption by the Nether- lands government. The tubes are in lengths of 7 feet, and are used of 2 and 3 inches diameter. They are joined by abutting their ends, covering the joint with a short segment of tube to fit, and cementing with bitumen applied hot. The material employed becomes very fluid when heated, and very strong when set. The ease with which the work can be carried out, the fact that the tubes are hermetically sealed, the cheapness of the materials, and facility of transport, are in favour of this system. The largest number of wires placed in a 3 -inch tube is 40. In the English system as many as 72 wires are placed in a 3-inch pipe, and 128 in a 4-inch. Portland cement is used in England to cement the pipes together, as well aa UNDERGROUND LINES. 443 clay, lead, and yarn ; but in any case a stopping of yarn or tow is applied first, to prevent any of the cementing material falling into the pipe. In America, for -the Western Union Co., tubes are being used for the underground lines ; in New York city and Philadelphia the wires will soon be necessarily laid underground. Two new systems are being tried in America, the particulars of which have been supplied by Mr. C. H. Haskins. A New York manufacturer of glass-lined water pipes has invented one system, the other is the invention of Mr. David Brooks. In the first system a cluster of glass tubes, embedded in paraffin, is inserted in a wrought-iron pipe ; at the joints the ends of the tubes, ground flat, are placed together with coupling plates. There is a groove in the face of each coupling plate, and, after the plates have been bolted together, this groove is filled with a water-tight preparation. Naked wires are used, drawn through the glass tubes. All the wicket-gates of the Centennial Exhibition are connected with the*treasurer's office by this means, and communication has never been interrupted. In Mr. Brooks' system a tube is laid, in the usual manner, with small flush test-boxes at the street corners, &c. , a cable covered with hemp saturated with paraffin is drawn in, nearly filling the tube ; paraffin oil is then forced in, and leakage is compensated by pouring in oil at the test-boxes. The practice of making the insulated wires up into cables by binding them together with tape or yarn has been discontinued in England, because the tape rotted and obstructed the tubes ; but a tape covering saturated with Stockholm tar is used over each wire. If tape be used, cotton tape, being more durable than hemp, should be preferred. Hooper's Telegraph Works Co. manufacture a core covered with a braided covering of flax yarns, the whole being saturated at 280° to 300° Fahr. with a special compound. The yarns are spun on in the same manner as the catgut on a riding- whip ; the compound is a brown, waxy material. The preservative enters the felt cover- ing of the core, particularly in the thicker sizes, and, if itself chemically per- manent, the great utility of such an air-tight covering cannot be doubted. Core so protected is stated by the manufacturers to be reliable "when partially submerged and partially exposed to the air," and it appears likely to prove more durable for underground lines than the thinly covered gutta percha core commonly employed. This kind of core is being used in Eng- land as field telegraph wire, and some has been supplied to the English Postal Telegraph Department. The French government lines are of gutta percha covered wire protected by tape. The conductor has four strands ; xt is covered with only one layer of gutta percha to '2 inch diameter. The gutta percha is covered by two layers of cotton tape, previously treated with sulphate of copper solution as a preservative; the inner layer of tape is tarred with Stockholm tar. The covered wires are made up into cables containing from three to seven conductors. The lines are laid in cast-iron tubes, made in pieces 8 feet 2 inches long ; the joints are leaded, and every 50 metres a section of pipe ef a larger diameter is fitted so that by sliding this section along the main tube, access may be obtained to the cable. The joints at these places are also stopped with lead, so that the tube is sealed and the cable protected against the infiltration of water or gas. 444 APPENDIX VII. DEEP-SEA SOUNDING WITH PIANOFORTE WIRE. The following mode of sounding, devised by Sir W. Thomson, has been employed in several important cable-laying expeditions, adopted (somewhat modified) by the American navy, and is being generally adopted. The wire used is pianoforte wire of the best quality, about 22 B.W.G. , weighing 14£ lbs. per nautical mile, and bearing 230 to 240 lbs. tension without breaking. The wire cannot be joined by soldering, as it is then liable to break at the joint. It is spliced as follows : — The ends to be joined are slightly warmed and coated with marine glue for about 3 feet, to promote surface friction ; the ends so prepared are laid together, forming an overlap of 3 feet, and from the centre of the splice the end of each wire is wound round the other in a long spiral, having one turn per inch, the ends are then tightly served with twine. This joint does not weaken the wire as would a stiff-soldered joint, wire ligature, or short twisted splice, and it is easily made in a few minutes. The wire is made in lengths of about 200 yards. To the outer end of the wire is fastened a galvanised iron ring, weighing about half a pound ; to this ring is attached about 5 fathoms of hemp line, to the end of which is attached the sinker. The iron ring serves two purposes— viz. , that of a coupling between the hemp line and the wire, and of an auxiliary sinker to keep the wire tight when the sinker rests on the bottom. The hempen line is inserted that it may coil on the bottom; because if the wire were con- tinuous to the sinker, and permitted to coil on the bottom, it would become kinked. The sinker is of lead, and for depths not exceeding 3000 fathoms under ordinary conditions, weighs 30 to 35 lbs. For 4000 fathoms or more, the inventor thinks it would probably be found desirable to use a sinker weighing 100 lbs., with an appliance for detaching it on reaching the bottom. In the American navy the practice of detaching the sinker is adopted more generally, not only for great depths. The sounding machine may be divided into two parts — viz., that for letting the line out and controlling its motion while running, and that for hauling the wire in after the bottom has been reached. The sounding wheel is of thin galvanised sheet iron, made as light as admissible, in order that when the weight touches the bottom the inertia of the wheel may not cause an excess of wire to be run out coiled on the bottom, and consequently kinked. The circumference of the wheel is one fathom, with a correction for the increased diameter due to the wire wound on it. This wheel is fitted with a very simple brake, its framing is movable on a slide, elevated above the deck, and projecting over the taffrail, that the wheel may be readily run horizontally on board and out over the taffrail as required. The sounding line is preferably let out over the stern. The brake consists of a rope passed round the circumference of the sounding wheel. This rope is fixed at one end and weighted at the other, consequently it presses on the circumference of the wheel. The rate of change of pull of such a cord per radian {i.e., angle whose circular measure is unity) round the wheel is equal to the amount of the pull at any point multiplied by the co-efficient of friction ; the whole tangential resistance which the cord applies to the circumference of the wheel is equal to the excess of pull at one end above that at the other end of the cord. The apparatus for hauling in the sounding line consists of a castor pulley projecting over the taffrail and an auxiliary pulley. The castor pulley is the same in principle as the castors fitted to furniture, and DEEP-SEA SOUNDING WITH PIANOFORTE WIRE. 445 is so fitted that when the ship rolls the plane of the pulley remains vertical; this is also assisted by a counterpoise. The wire is passed over the castor pulley in hauling in. If the ship rolls, this pulley accommodates itself to the wire ; if the ship drifts laterally, so that the wire streams to one side, the pulley takes an oblique direction. Thus this appliance renders it prac- ticable to haul in the line when the ship is rolling heavily or drifting. The auxiliary pulley is used for hauling in the wire and taking the strain off the sounding wheel. If the wire were raised directly by the sounding wheel, the pressure on that wheel would be enormous; for if the tension on the wire be 50 lbs., each turn of wire would compress the wheel at the two ends of any diameter with a foroe of 100 lbs., and this being the effect of each turn it would be multiplied by the number of turns. The interposition of the auxiliary pulley prevents this pressure to any required extent. The auxiliary pulley overhangs its bearings, so that one or two loops of wire may be put round its edge. This pulley being turned in the proper direction by two handles worked Dy men, or by a band hauled on by men, or driven by an engine, hauls in the wire, which, as it leaves this pulley, passes on to the sounding wheel again. The assemblage of parts described above— viz., the sounding wheel with brake, wire, and sinker, the castor pulley, and the hauling in pulley— constitute, with suitable framing, a simple sounding machine. The castor and auxiliary pulleys are placed lower than the sound- ing drum, and when hauling in the sounding drum is drawn on board on its slides and placed over the auxiliary pulley. When a sounding has to be made, the sounding wheel is run out on its slides over the taffrail, the sinker and hemp line attached, and the weight dropped. By means of the brake a measured resistance, more than sufficient to balance the wire out at each moment is applied to the drum; as the wheel revolves the person in charge watches a counter which registers the number of fathoms or turns of the wheel, and he adds for every 250 fathoms such a weight to the brake cord as shall balance, by its resistance to the wheel's motion, the weight of the additional wire. Hence the resistance on the wheel is always more than the weight of the wire out. The force with which the weight reaches the bottom is less than that due to the full weight of the sinker in water; when the sinker reaches the bottom the wheel is pulled in one direc- tion by the weight of the wire only; but this being more than counter- balanced by the brake resistance, this resistance acts to stop the wheel when the bottom is reached, and to prevent the wheel flying round by its inertia. In fact, the effect of this arrangement is to feel the bottom, and the wheel stops almost immediately the bottom is reached, not running on more than one turn at most. To take an illustration :— For a depth exceeding 1000 fathoms, 3000 fathoms is considered a convenient leDgth to put on the wheel; this length weighs about 43 lbs. If the depth exceed this, then a second length on another wheel is spliced on to the first, this operation taking about two minutes. The lead weighs 34 lbs., and the resistance put on the drum by means of the brake is kept 10 lbs. in excess of the weight of wire out; thus only 24 lbs. of the weight of the sinker acts as moving force. As the wire runs out, for every 250 fathoms or turns of the wheel the brake resist- ance is increased by 3 lbs., the weight of 250 fathoms of the wire in water. When the sinker reaches the bottom its weight is taken off the line ; but as 10 lbs. of this was balanced by brake resistance, this resistance stops the wheel within one turn, and the bottom is felt in as great a depth as 4000 fathoms. The stoppage of the wheel is almost instantaneous under these conditions. After the bottom has been reached, which is known by the stoppage of the sounding wheel, the sounding line is held up by two men with thick leather gloves, or better, by a spun-yarn stopper. This relieves 446 APPENDIX. the wheel; a little more wire is unwound, and the wheel with its bearings is run on board on its slides; the wire is then passed round one quarter the eircumference of the castor pulley and three quarters of a turn, or one turn and three quarters round the hauling-in pulley, the latter is turned by two or four men, and the wire is wound on the sounding wheel simultaneously by one or two men working on handles fitted to its shaft. The auxiliary pulley takes from two-thirds to nine-tenths of the strain of the wire off the sounding wheel. On board the cable S.S. " Faraday " the hauling" in is effected by a steam winch. The bottom is reached at a depth of 2,000 to 3,000 fathoms in thirty to fifty minutes. With 3,000 fathoms of line out, probably 400 feet per minute is a safe speed for hauling in; the last 1,000 fathoms may be easily and safely got in in seven or eight minutes. To attain these speeds more men than the numbers stated above would have to be employed, and a mechanical appliance for increasing speed, or a donkey-engine, may be used. In a heavy sea the rate of hauling must be slower. An arrangement proposed by Professor Jenkin can be readily applied, by which the men or engine may haul in as fast as they please, and yet be unable to put more than a certain tension on the wire, the line coming in fast when the strain is easy, and not at all when the ship is rising and producing such a pull that, if hauled upon at all, the wire would break. With twelve or fourteen men hauling on a multiplying arrangement, the 34-lbs. sinker may be got in from a depth of 2 miles in fifteen minutes. With a heavy sinker (100 to 150 lbs.) and detaching apparatus, the sounding might be taken with only about twenty minutes' detention of the ship. A sounding in 1,000 to 1,500 fathoms, with recovery of sinker, may be taken with detention of the- ship for fifteen to twenty minutes, while the lead is going down, and then going full speed a-head. For flying soundings to 200 fathoms the speed of the ship is reduced to 4 or 5 knots for the sinker to reach the bottom, and then increased up to full speed. CJnder these conditions a boy can haul in the line with a 34-lbs. sinker from 150 fathoms, and it may be hauled on from 200 fathoms with ease by one man or by two men. With 3,000 fathoms of line out it will be generally found convenient to keep the ship hove-to while hauling in ; with 2, 500 fathoms, or less, the ship may be driven slowly a-head with increasing speed; with 1,500 fathoms out the ship may be safely driven a-head at 5 or 6 knots, and the last 500 fathoms may be taken in with ease and safety while the ship is going a-head at the rate of 10 to 12 knots. The wire, when not in use, is preserved by immersion in a solution of caustic soda. In the American modification of the apparatus soldered joints are used to join the wire, a stronger sounding wheel is used, the weight is detached at the bottom, and the hauling-in pulley is dispensed with. The preservative used is oil, as caustic soda would attack the solder. The advantages of sounding with wire over the ordinary method are — Very great saving of time, very great saving of labour, great facilities for taking flying soundings, it being unnecessary to detain the ship as by the old method— e.g., flying soundings may be taken in from 100 to 200 fathoms with the ship going 4 to 5 knots. The sinker is saved and specimen of bottom obtained when this would be impracticable by the old method. Many of the practical difficulties of deep-sea sounding are removed, and soundings may be taken under conditions which, under the old method, would have rendered sounding impracticable, or the results inaccurate- e.g., under the old method, when a long length of cord is out the lateral friction between the cord and water is so great that the pull of the lead is neutralised, and the ship must be kept over the line for hours to let it out and haul it in, not only is the detention considerable, but in a current it is very difficult to keep TEMPORARY LINES. 447 the ship over the line. The machine ia very simple, and therefore not Costly. It is used in the "Hooper " and the " Faraday," and its use on cable ships will be general, the facility with which flying soundings may be taken during the laying of a cable being of the greatest importance. In flying soundings the true depth is estimated. The following formulae are useful: — If 1= length of line out, a = horizontal distance travelled by the ship less horizontal distance travelled by sinker in reaching the bottom, the true depth, where the lead touches the botfcom.is greater than I - a and less than ^l»Z.' a i, For flying soundings within 200 fathoms, taken with the ship going 4 to 6 knots, the strict adjustment of the brake resistance described above is impracticable ; in this case the resistance is fixed at from 5 to 10 lbs. , a sudden decrease in the speed of rotation of the wheel indicates when the bottom is reached, and the wheel is then stopped by hand. - APPENDIX VIII. TEMPOBARY LINES. The following are the general results of the experience gained during the Abyssinian, Ashantee, and Looshai expeditions, the Franco-German war, the famine in Bengal, and the autumn manoeuvres in England. Ground Wire. — For short lengths required to be laid rapidly and to be used for a short time only, india-rubber covered wire is generally employed. This may be laid on the surface of the ground, buried in a shallow trench, or it may be laid on the ground where admissible, and raised on poles or buried at road crossings, and raised on poles at river crossings. The arrangements for paying out and picking up the wire at a trot by the use of horses and mechanical appliances are practically useless ; the wire has to be laid and taken up by hand. The india-rubber core is usually protected by hemp coverings, tarred or saturated with a special compound. A soft copper conductor, as used in submarine cables, has been found in practice too weak for ground wires for military temporary lines ; the addition of iron or hemp in the usual way to give great additional tenacity is obviously impracticable. To obtain additional tensile strength, Major Mallock proposed the use of a compound conductor consisting of one pure copper wire surrounded by six soft iron wires, in lieu of the pure copper conductor. It is stated that wire of this kind has been adopted in the Italian army. An experimental waggon load (3 miles) was ordered for the British army, and a length of one mile was favourably reported on by a committee appointed for the purpose. The following figures show the relations between the old pattern (copper con? ductor) and the new (compound conductor) :— Old Pattern. New Pattern. Copper Conductor. Compound Conductor. Tenacity, . i 125 lbs. 375 lbs. Weight, per mile, . • 282 „ 285 „ Conductivity (relative), . • 2„ 1 „ Diameter of new pattern slightly less than that of old. The committee found the new wire might be safely used for spans of 330 448 APPENDIX. yards, and might be drawn well up ; but the old pattern could not be raised off the ground over so long a span. The following is the specification : — Conductor, one tinned copper wire, diameter '0135 inch, conductivity 90 per cent, that of pure copper, surrounded by six wires of best soft iron, dia- meter of each '0135 inches. Insulator, one layer of vulcanised india-rubber to ■176 inch diameter. Protection, one spiral layer tape, and oue braided covering of best Italian hemp, drawn through compound. Diameter of com- plete cable, maximum '35 inch. Insulation 100 megohms per mile. Conduc- tivity, maximum resistance 40 B.A. units. Tenacity about 450 lbs. The somewhat lower conductivity is of little consequence, as the wire is used in short lengths. In dry weather local faults in the dielectric are of little con- sequence in a ground wire, bare places even cause no inconvenience. When the wire has to be buried, as in crossing a road, it has been suggested that it be inclosed in a piece of india-rubber tubing. This was tried by Captain Lambert, and with markedly beneficial results. For lines required to be more permanent and of greater length than those for which ground wire is suitable, light wire, supported on light poles or trees, is used, permanent lines, when preseut^bliug used as far as practica- ble. The wire generally used is of iron, and thinner than that used for per- manent lines. For the Looshai expedition the wire used was No. 9| B.W.G., weighing 300 lbs. per mile ; No. 16 copper wire was used for temporary connecting lines. In the Abyssinian and Franco-Prussian campaigns copper wire was used. In the first case the wire was exceedingly pure copper, No. 16 B. W.G. ; although spans of 200 to 300 yards were practicable, the wire stretched, particularly when the poles were shaken. During the Franco- Prussian campaign it was found necessary to use forty poles to the mile with copper wire. The temporary lines used during the Ashantee campaign were No. 11 iron wire, weighing 3 cwts. per mile, and this proved excellent for the purpose. A stranded wire of three No. 18 wires has been sug- gested as nearly as good as one No. 11, and a half hundredweight lighter per mile. A good homogeneous stranded wire would no doubt prove suitable. A homogeneous wire was tried in Abyssinia, but failed ; it was used for 20 miles, and the wire appears to have been bad in quality. Major Mallock proposed a compound stranded wire, the same as described' above, for ground cable, he having found that six iron wires round a central copper wire is almost as strong as if the centre wire were also of soft iron. This wire has the following advantages : — Conductivity, V s , and weight f#, that of iron of same size; hence for equal conductivity the weight of compound wire is only % that of iron wire. American compound wire has been proposed. As compared with No. 11 B.W.G. iron wire, the weight of American wire is only 0. A simple joint might be devised for temporary lines. The only objection to this wire is its stiffness, which would be incon- venient when rolling it up and running it out. The fact that compound wire is more readily corroded than simple wire, is of no importance in the case of a temporary line. Insulators. Insulators may frequently be dispensed with ; the necessity for their use depends on the nature of the supports, the climate, and the time the line has to stand. In the Abyssinian campaign no insulators were used ; old seasoned bamboos were used as supports, and Major St. John thought them as good as porcelain insulators, unless rain was running down them. In Bengal" the TEMPORARY LINES. 449 lines erected were 541 miles long, and a year's experience was gained. No insulators were used, and it was found that bamboos, in open ground ex- posed to the sun, remained sufficiently clean for one monsoon ; but when the poles were under trees and constantly in the shade, they became covered with a kind of spongy mildew, the presence of which was fatal to insulation. On the Abyssinian lines no difficulty was experienced in working over 100 miles without relays. When the wire has to be fixed to living trees, insula- tors are necessary. In the Loo3hai and Ashantee expeditions insulators were used; small porcelain insulators gave complete satisfaction. In the latter case some ebonite insulators were used; they were defective, split occa- sionally, and proved very unsatisfactory. The field insulator used in India is simply a smaller pattern of the porcelain line insulator; it can be spiked to a living tree, to rock, or bound to a small tree or bamboo by wire serving. Its breaking ^train is 3 cwts., its resistance 2,000 megohms, and it can be used with No. 9 wire. Spiking and binding are the usual means employed for fixing insulators, but in the Ashantee campaign they were fixed into the top of the bamboos as follows :— The bamboo was cut off level 6 inches above a ring, a serving of No. 11 wire was put round it to nreyent it spliting, and a plug of soft wood was driven into the bamboo to fill it, the insulator stalk was then inserted in an auger hole made in the wooden plug. In Abyssinia the wire was simply put into a slit about 6 inches deep, cut across the bamboo pole, and it was turned two or three times round the end of every second or third pole. The experience of the Bengal famine lines indicates that the best kind of insulator for use with double bamboo supports (shears) is a hanging insulator, suspended from where the bamboos cross. Supports. — When no timber is available near the spot, or the line has to he taken over hills up which poles would have to be carried, or, in fact, whenever poles must be carried long distances, light iron tubes packing into each other, or other form of iron pole, may prove economical and efficient ; but when bamboos or other suitable wood can be obtained readily it is generally preferable. The bamboos for the Abyssinian campaign were sent from Bombay, and no doubt proved cheaper and more useful than iron poles would have done, as with the latter insulators would have been essential. As far as possible, living trees should be used as supports when available on the route. This was done to a great extent in the Ashantee and Looshai expeditions. In the Abyssinian and Ashantee expeditions single bamboos were used as supports in the open. On the Bengal famine lines each of the supports was of two bamboos, tied together near the top with wire, and then opened at the bottom like shears ; the lower ends of the bamboos were placed 9 feet apart, and inserted 18 inches in the ground. On the Ashantee lines single bamboos were used, planted 60 to 90 yards apart, and inserted 2 feet in the ground ; stones were used to make the hold on the ground firmer. On the Bengal lines it was found better to use three bamboos in the form of o tripod at each angle. When single bamboos or other light poles are used the angles must be tied. The ties are usually of wire, and attached at the lower end either to pickets inserted in the ground or to buried stones. On the Ashantee lines wire ties and pickets were used. The light wire used for temporary lines is usually stretched by hand, tackle being superfluous. For working temporary Hues it is generally con- sidered better to use full sized instruments than small portable instruments; the instruments forming so small a proportion of the weight to be carried, the additional weight of the full sized instruments is inappreciable, whereas the small instruments are more troublesome to use. The lines not being constructed so strongly as permanent lines, having a higher resistance and 450 APPENDIX. frequently inferior, insulation, a reliable and sensitive instrument is a, necessity. The batteries used are required to be portable and readily pre- pared for use. On the Bengal lines, which differed in many respects from military lines, the ordinary Minotti battery was used ; this battery could not be used for military lines. The Ashantee lines were worked with the Leclanch6 battery ; the Marie Davy battery wa3 used in Abyssinia and during the Franco-Prussian war ; both these batteries proved satisfactory. The objection to the former is that it cannot be repaired excepting at the manufactory ; the other has not this defect, if a supply of spare porous cells be supplied, and it is therefore preferred. When stores and labour are available, temporary lines may be put up very quickly ; the difficulties which have been most felt are want of labour and transport. In Bengal 541 miles of line were erected, and thirteen offices opened in thirty-five days, including the purchase of bamboos. On one occasion an officer put up 3l| miles in two and a half days, he having to purchase the bamboos and super- vise the distribution and construction. APPENDIX IX. ADDITIONAL DATA. The following data were accidentally omitted from the body of the work. Such data are frequently stated as if they had a fixed value ; in these cases the values are merely averages. The values given below are merely approxi- mations sufficiently near for most practical purposes. When the quantities are very lar^e, or other circumstances rendera close approximation necessary, specimens of the materials to be used should be weighed and measured. Weight of 1 oubio foot in las Dry timber, Fir of different kinds, Elm, and Chestnut, . 30 to 44 Beech and Birch averages 43 to 44-4 Oak, 43 to 62 Indian Teak 41 to 55 Saul and African Teak average about 60 Brick, 125 to 135 Brickwork, dry, 112 Masonry, 116 to 144 Sand, dry, 88'6 „ damp, 118 Clay, 120 Mud, 102 Granite, 164 to 172 Limestone, 169 to 178 Quartz, 165 Sandstone, 130 to 157 The above are adopted from Professor Bankine, after com- parison with other authorities. Hemp as ordinarily applied in serving, Russian or Italian, about 39 Russian, Tarred gg WIND OR WATER PRESSURE. 451 Weight of 1 cubic foot in ibs. Manilla, 41 Hemp 77 „ tarred, Ill Hooper's Material, . 73-50 The above are taken from Clark and Sabine's Electrical Tables. Paraffin, 54 25 to 54-38 India-rubber 57 "3 to 58 74 (Messrs. Clark and Sabine give 56 44.) Ebonite about 81 - 7 The heaviness of somejsinds of wood (dried) may vary upwards of 100 per cent., and any material naving an organised structure, like hemp and wood, must vary considerably in heaviness. Sand must vary in heaviness accord- ing to the size of the grains, and mud according to the quantity of water held in it. Average values are only averages of certain measurements made and recorded; their use is simply to make rough calculations where great accuracy is unnecessary or unattainable. These remarks may appear unne- cessary, but the frequency with which absolute values of this kind are given justify them. Not only are fixed values given, but these are given to two places of decimals— eg.. Teak, oak, and mahogany are stated to weigh 46-56, 60-62, and 53-25 lbs. per square inch. It is not apparent how the writer arrived at such figures ; and whether they are averages of Indian and African teak, every European variety of oak, and of Honduras and Spanish mahogany ; in any case they can be of but little practical utility, and may mislead. ADDENDUM TO ART. 180, PAGE 105. Wind ob Water Pressure. The intensity of wind pressure on a cylindrical surface has been stated as equal to about half that on a plane surface equal in area to the plane pro- jection of the cylindrical surface. This estimate, given by the best authori- ties, on consideration of the following will be seen to be incorrect :— Let the pressure of a current of wind or water on a plane surface of unit area, placed at right angles to the current, be = P. If the plane surface be inclined to the current, the pressure on it will be less than P. If it be inclined so that its edge be presented to the current, the pressure on it will = 0, hence the pressure on a plane surface varies between P and accord- ing to its inclination to the current. For simplicity, imagine the current horizontal, and the plane acted upon vertical. The current force acting on the inclined plane may be resolved into two components, one in the plane, the other at right angles to it; the former exerts no pressure on the plane, the latter is obtained by multiplying the current force by the cosine of the angle between the plane and a plane at right angles to the current. If the latter component, found as above, be now again multiplied by the cosine of the above angle, the product will be the pressure exerted by the current on the inclined plane in terms of P, the pressure it would exert on a plane ac 452 APPENDIX. right angles to its direction and equal in area to the projection of the inclined plane. Hence, the pressure on a surface inclined to the current is the product of P and the square of the cosine of the plane's inclination. Suppose a solid body exposed to the current, the section of the body being a triangle, and the apex of the triangle presented to the current, the limits of pressure are P and 0. If the third side of the triangle be at right angles to the current, the pressure on each of the other sides varies as the cos 2 between the side taken and the third side, and cos 2 P represents the pressure on a unit surface. Hence the sharper the edge presented to the current the less the resistance to the current. From the above may be calculated the pressure of a given current acting on a body whose horizontal section is a triangle; this pressure is manifestly equal to P. cos 2 x area exposed on each of the planes presented to the current. The above is true of a cylinder, each point of the cylindrical surface being assumed coincident with the tangent at that point; but in this case the angle varies constantly and is not fixed, as in the case of the triangular prism. On the cylindrical surface the pressure varies between P at the most prominent point and at the extremity of the diameter of the section drawn at right angles to the current direction. At any intermediate point the pressure is Pxcos 2 as before, and the sum of the pressures at all points is=-§P. In the above the effects of friction and adhesion between the particles of the fluid in motion have not been considered, hence it is manifest the above values are too small for practical application. The friction between water and an immersed body varies with the nature of the surface of the latter and the square of the velocity of the current. Hence if the triangular prism described above had its presented angle sharpened and its sides prolonged, a point would be reached at which the friction against the sides would counterbalance the diminution of resistance con- sequent on the greater sharpness of the presented angle. As a matter of fact the resistance of a cylindrical body to a current of water has been found in practice to be about £ P instead of $ P indicated by the above formula. The resistance to a current of air is between f P and £ P. INDEX. Abrading tools, 293, 294. Abscissa, catenary, 96. Absolute unit force, 2, 3, 23. Absolute and gravity units of work, 23. Abutment defined, 82. Accelerated velocity, 20. Adhesion of earth, 153, 161, 162. mortar and cement, 173, 187. Age of tree, how exhibited, 119. Ages of trees at maturity, 122. Alloys of iron, tinning, galvanising, 204, 205. soldering, 302, 303. American offices (Western Union), 405. Anchors, burying and fixing, 338, 339,376. for stays and ties, 332. Angle of immersion (cable laying), 109,110. ' ° Angle-pole and tie (a two-bar frame), 78, 79. Angle-poles, stresses on contiguous, 84-86. load on, in terms of wire tension (table), 86. Angle of repose (generally), 26. (earth), 91. Angle, right, to set out with chain, 313. Angles of repose (table of), 28. insulators at, 343. setting out, 366. wire guards at, 344. Angle of traction, 26. Angular measurements, surveying by, 315. Annealed wire, 210-212. Annealing cast-iron, 193. its effect on tenacity, 49, 210. Annealing malleable iron, 209. A poles, 66, 67, 329. Appold's brake, 27. Arc, catenary, 96, 100. Area, measures of (British and French), 307. Arm of couple, 10. Arrangement of wires on poles, 338, 339. Arris-wise defined, 123. Artificial cements (calcareous), 172. foundations, 165, 166. Asphalt, 177-179. covering for cables, 179, 387, 388. Asphaltic mastic for underground lines, 178, 179, 352. Atlantic cable, 1866, 392. French, 392. Atmospheric pressure, 105. Axis of couple, 10. Axis, neutral, in beams, 55, 56. Balanced forces, 1. Bamboo poles, 218, 326. Bands and drums, friction between, 27. Banks and beds of rivers, their stability, 107. Banks of earth, slopes of, 91, 153, 154. Base plates to poles, also Mallet's plates, 92, 214, 374. Battery room, 407. Baulk defined (carpentry), 122. Beam, bending moment, 59, 60. distribution of stress over section of, 56. defined and described, 55. with fixed ends, 62. length and strength, 60. load distributed, 61. moment of load on, 59. oblique or inclined, 55, 70, 77. and post joints, 135, 136. shearing stress in, 59, 60. shearing stress in flanged, 58, 59, 61. stress (longitudinal) in, 57. width and depth affecting strength of, 58. 454 INDEX. Beam, web in flanged, its functions, &c., 58-61. Beams, built, 66, 67. bolt and rivet holes in, 66. deflection of (any load), 71, 72. deflection of (proof load), 71, 72. deflection of, admitted in practice, 72. fittings and fastenings to, 66, 67. flanged, 57, 58, 225, 226. flanged, strength, of, 65, 66. forms of section of, 57, 58. formulas for strength and deflec- tion, 73, 74. iron, 225, 226. joints for lengthening, 135. joints between,, 135. load (gross) in,- 70. loaded above and below proof, compared, 56. neutral axis in, 56. neutral plane in, 55. rigidity in designing, 72. tubular strength of, 64, 65, 225, 226, 227. Bellhanger's joint, 346. Bench mark, 306. Bending load, fracture by, 56. moment (beam's), 59, 60. Berlin office, 406. Bessemer process (iron), 199. steel, 240. steel, tenacity of, 244. Bethell's process for preserving wood, 128 Beton, 176, 177. Binding line to insulators, 346. Birmingham wire gauge, 234. Blister steel, 240. Blocks connected by plane joints (stability), 92-94. tackle, 279. Blockwork, its resistance to pressure, 39. its stability (plane joint), 92-94. stability of friction, 92-94. stability of position, 92-94. Bolts (ironwork), 221. proportionate dimensions of, 132. their application, 132. Bond in masonry and brickwork, 182, 184, 185. Bone, 276, 277. Boring and digging compared, 158. pole holes, 157. tools, 292. Boring rock, labour of, 161. Boucherie's process for preserving wood, 127. Box girder poles, 65. Boxes, joint and draw, for under- ground lines, 351. Bracing and staying frames, 84. Brackets or cross arms, forms and arrangement, 336-8. Brackets, &c. , erection of, 376, 377. insertion in masonry, &c, 187, 188. Brake, Appold's, 27. cable laying, 27, 391. Brakes, 27. Brass, 252. Brazing, 305, 306. Breaking load defined, 31. Brick, tenacity of, 172. Brickwork, bond in, 184, 185. factor of safety, 187. insertion of cantilevers, &c, in, 187, 188. labour of, 186. and masonry, technical terms, 179, 180. and masonry, rules for construct- ing, 180, 181. and masonry combined, 185. rules for constructing, 184. strength of, 186, 187. Britannia joint, 346. British absolute Kinetic unit, 2. British and French standards (mo ; duli of elasticity), 30. specific gravity, 17. Brittle substances, elasticity of, 31. Bronze aluminium, 251. or gun metal, 251, 252. Built timber masts, 140-143. Buoyancy, centre of, 104. Cable, Atlantic, 1866, 392. French, 392. coiling, 402. conductor, 385, 386. conductor, joints in, 385, 386. conductor and insulator, relative sectional areas, 389. conductor, diameter and weight, 386. conductor, selection of copper for, 249, 250. conductor, laying strands of, 386. core, gutta percha, 256, 386. core, Hooper's india rubber, 270, 271. INDEX. 455 Cable, core, strength and elasticity of, 386. core, hemp covering of, 386, 387. described 1 , 385. deep sea, construction of, 388, 389. friction in water, 112, 113. huts, 237, 238, 325. intermediate, 388. iron covering or guards of, 387. laying, 394. laying short cable, 395. modulus of tenacity, 48, 108. picking up, 398, 399. pressure, tests of, 4Q2. protection of, in river, 402, 403. river, choice of site, 325, 371. ships "Faraday" and "Hooper," 395. . stowage in ship, 392. storing, 402. suspended or moving in water, 99, 107, 108. submersion (conditions of), 109, 110. sinking velocity, 106, 108, 109. sinking, transverse component, 110, 111. Binking, longitudinal component, Ill- Cables, Hooper's compound for. 278, 279. joints between thick and thin, 388. multiple conductor, 386, 387. splicing, 399: short, for rivers, &c, 353, 354. slack allowed in, 395. strength, factors of safety, 391. twisting wires in making, 54. Cable, tension at ship, 113. 114. tension, paying out stopped, 114, 115. tension on bight of, 115. tension on raising, 115, 116. Cairns for poles, 183, 374, 375. Calcareous cements, 168. Camp equipage, 418. Cantilever defined (see also Beam), 55. and girder compared, 61. insertion in brickwork and masonry, 187. deflection of, 72. strength proportioned to bending moment, 67, 68. shearingforce and bending moment, 60. Caps, mast, 145, 146. Caoutchouc (see India rubber), 261. Carpentry, technical terms, 122, 123. in telegraph construction. 137, 138. Carriage, hints on, 418, 419. Case hardening, 241. Cast iron, casting, 192, 193. castings, their structure, 191. castings, large and small, strength, 193. castings, strength of, 194. for engineering purposes, 195. co-efficient of expansion, 193. corrosion of, 196. density, heaviness, 194, elasticity and resilience, 195. factors of safety, 194. impurities, effects of, 190. and malleable iron compared, 195, 205, 206. and malleable iron combined, 206. and malleable iron, relative strengths, 207. malleable, 192, 196. pillars, strength of, 40-42. poles, 195. proof load, 194. properties of, 189. qualities and selection, 190, 191, 195, 196. repeated fusion, its effects, 191, 192. testing, 196. temperature affecting strength, 193. toughened, 192, 194, 243. Cast steel, 241. Catenary equations, 96. defined and described, 95. length of wire (arc), 100. mechanical properties, 96, 97. and parabola compared, 102, 103. in water, 99. Cement, diamond, 176. electrical, 176. India rubber, 176. marine glue, 175. Muirhead's insulator, 175. Portland, 173, 174. Roman, or Parker's, 173, 174. resin and ashes, 175. tar and clay, 179. Cementation (steel), 240. Cementing materials, 168. Cements, insulator, 174, 175. natural and artificial, 171-174. sulphur, 175. Centre of gravity, 15-17. of gravity and. stability, 95. of inertia. 17, 19. 456 INDEX. Centre of resistance of joint, 76. of resistance or pressure, plane joint, 92. Centres of buoyancy and pressure, 104. Chain, 279. flat-linked, 49. Chain surveying, 309, 313. ties, 224, 225. Chains, tenacity of rods and, 49. testing, 215. Chatterton's compound, 256. Chilling (casting), 191. Clark's compound, or asphalt, 179. Claws, wire, or devil's, 297. Clay puddle, 160. Climbing masts, appliances, 149, 150. appliances, 298, 299. Cold shortness (iron), 190, 206. Commutators and connection boards, 405. Compass, its use in surveying, 308. Component force defined, 3. Compression of earth by ramming, 160. Concrete, 176, 177. Connection boards and commutators, 405. Constants and co-efficients, their use, 37. of deflection (table), 72. of transverse strength (timber), 131. Construction, general remarks, 384. Control, or testing poles, brackets, &c, 342. Copper, 249. soldering bits, 250. wire formulse for cable core, 249, 250. wire for cable core, 249, 250. wire joining, 250. Corrosion, cast iron, 196. malleable iron, 205, 238. steel, 246. wire in railway tunnels, 345. Couple, defined and described, 10. Coupled or A poles, 66. Couple equivalent, defined, 10. and force, resultant of, 12. moment of, 12. Couples, resolution and composition of, 11. Cross arms or brackets, forms of, 336. arrangement on poles, 338, 339. Cross stays, 330. Crosstrees, masts, 144. Crushing, resistance to, 38. Crystal varnish for paper, 300. Currents in rivers, &c, 106. Curvature correction, surveying, 316. Curves on lines (load on poles), 86. Curves set (catenary), their use, 102. Datum points (levelling), 306. Dead load defined, 32. factors of safety for, 32. Deep-sea cables, 389. Deflection of beams any load, 71, 72. proof load, 71, 72. in practice, 72. and poles (iron), 215, 216. girder and cantilever compared, 72, constants of (table), 72. formula? for, 73, 74. Derrick, 285. Designing beams, 72. (dimensions), 321. lines, 323. Devil's claws, 297. Diameter, given (of masts), 143. Diamond cement, 176. Digging pole holes, 156, 157. and boring compared, 157. Dimension, limiting, 35. Dip of wire, 97, 98, 100-102. points of suspension, different levels, 102. or tension from inclination at in- sulator, 115. Distributed forces, 14, 18. Distribution (estimating for), 361. (in construction), 372. Dowels in masonry, 183, Drainage of earthwork, 154. Draw boxes, 351, 382. Drawing instruments, 316. paper, 317. Drawings, 317. of lines and offices, 321, 322. Driving bands, friction of, 27. Drying timber, 123, 124. oils, 278, 279. Dry rot in timber, 127. stone masonry, 183. Durability of gutta-percha, 254. india rubber, 269. timber, 126, 129. Dynamical measures of force, 2. Dynamics defined, 1, 18. Dynamometer, cable, 393. for line wires, 294, 295. INDEX. 457 Earth, adhesion of, 91, 153, 161. angle of repose of, 91. frictional stability of, 91, 154. plates, 327. ramming round poles, 92. slope of banks of, 91, 154. Earthwork (see above, also embank- ing and foundation), 152. labour of, 160, 161, tools for, 154, 294. Ebonite, 268. Economy in construction, 355. applying materials, 37. Elastic flexibility, 29* Elasticity, brittle substances, 31. co-efficients of, 29, 30. limit of, defined, 31. modulus, how expressed, 30. strength and resilience, moduli, 36. of timber, 129. and temperature, 35. of wire, affecting dip or sag, 100. Elastic or proof strength defined, 31. Electrical cement, 176. Embanking, filling holes, 159. Endogenous wood, 118. Energy, kinetic, 21, 22. potential, 22. of shock (proof strain), 34. English bond (brickwork), 184, 185. Equilibrium of forces, 1, 8, 11. couples, 11. Erection of (poles, &c), 375. masts, 284. wire, 377. wire on high masts, 382. Estimating, 356. Exaggeration (section scales), 318. Excavating, 154. Eyebolts for wire, 296. Eye on end of single wire or rope, 223. splice, wire rope, 223. Factor of safety defined, 31. telegraph cables, 391. Factors of safety, brickwork and masonry, 187. cast iron, 194. generally, 32. iron ties and stays, 215. malleable iron, 214. ropes, 282. timber, 131. Falling bodies, velocity of, 2. "Faraday" cable ship, 395. Fastenings for ironwork, 219-223. Fastenings for metal, in timber, 128. Felling trees, seasons for, 120. modes of, 123. Fid (masts), 146. Field book, 314. Files, floats, and rasps, 293. Fished joints, 134. Fitting (mast building), 150. Flanged beams, 57. functions of web, 61, 65. Flemish bond (brickwork), 184. Flexibility, elastic, defined, 29. Flexure, moment of, 59. Fluid, friction, 106. perfect, defined, 103. pressure, resultant, &c, 104. resistance, 105, 106. Flush or draw boxes, 382. Fluxes for soldering, 304. Flying levels, 316. Force defined, 1. measures of, 2. measured by momentum, 19, 20. moment of, 9. relation to body defined, 1. resultant defined, 3. several ways applied to materials, 36. unit, kinetic, 2. unit, gravity, 2. units compared, 2. units in practice, 2. Forces, component, defined, 3. composition and resolution of, 3-8. and couples, composition of, 12, 13. distributed, 14. equality of, 1. parallelogram of, 4. parallelopiped of, 5. parallel, 11. polygon of, 5. represented graphically and alge- braically, 3. triangle of, 4. Formulae for beams, 73. trigonometrical, 311. Foundation defined, 74. joint, stability at, 163. Foundations, artificial, 165. depth of, 163. mixed strata, 166. natural and artificial, defined, 162. on earth, 163. on soft earth, 164. on rock, 163. on sand, 166. 458 INDEX. Foundations, sinking of, 162. under water, 166. Fox's rule, flat-linked chains, 49. Fracture, brittle substances, 45. phenomena of, 35, 36. by bending load, 56. by pressure, 38. by tension, 45. steel, 243. Fractures, successive, by tension, 45. Frame defined, 75. Frames, rigidity, stress, strain, sta- bility, and strength of, 75-84. horizontal thrustor resistance of, 82. lines and centres of resistance in, 75. open, 82. staying and bracing, 83. trussed, 82. of three or more bars, 80. two-bar, 77. French Atlantic cable, 392. measures, area, 2, 307. measures, length, 2, 307. measures, mass, 2. measures, moduli of elasticity, 30. measures, specific gravity, 17. polish, 300. rule for load on ironwork, 215. Frictional stability of earth, 26, 91, 154. Friction, 24. of cable in water, 112, 113. co-efficient of, 24, 27. driving bands and drums, 27. fluid, 106. rope round cylinder, 26. stability of, 26, 92, 94. surfaces and materials varied, 24, 25. unguents, their effects, 24, 25. Funicular polygon, 84. Furniture and fittings for offices, 408. Fusion, effects of, repeated (cast iron), 191. Galvanising, 204. and varnishing wire, 349. Gauges, wire, &c, 234, 296. Gauss' absolute unit force, 2. Gin or gyn, 285. Girder (see Beam). and cantilever compared, 61. defined, 55. shearing force and bending moment, 60. Girder, strength proportioned to bend- ing moment, 68. Girders, box, lattice, and tubular, 65. Glue, common, 175. marine, 175. Goodyear's process (vulcanising), 267. Grapnel rope, tension on, 115. Gravity and absolute units com- pared, 2. centre of, 16. centre of, and stability, 95. specific, 17. unit force, 2. unit work, 23. variation of, 2. work done against, 21. Gros3 load, 35. load on beam, 70. Grouting, 173. Growth of trees, 118. Guards, iron, on cables, 387. Gutta-percha, 252. cable core, 386. core jointing, 257. lead-coated joints, 352. Gypsum, or plaster of Paris, 174. Hamilton's iron poles, 216. Hancock's process (vulcanising), 267. Handles to percussive tools, 294. Head, mast, 143. Heat, source of, for soldering, 303. Heel, mast, 143. Height of poles and wires, 326. Hempen core covering, 386. ropes, 279. Hill lines, setting out, 368. Hodgkinson's formulae for pillars, 41. Holes for poles, digging, 374.' for poles in rock, 326. Homogeneous metal, 241, 244. wire (tenacity), 244. "Hooper" cable ship, 395. Hooper's cable core, 270. compounds for cables, 278. Horn, 276. Hounds (masts), 144. Housing (masts), 143. Huts, cable, 325. Hydraulic cements, 171 . lime, 170. mortar, 171. Hydrostatic principles and deduc- tions, 103. Immersion, angle of, 109, 110. INDEX. 459 Impact and vibration, effects of, 33. India, office fittings in, 403. India rubber, 261. absorption of water by, 263. action of heat on, 265. cable core, 269. cable core, jointing, 271. cement, 176. chemical properties of, 265. indurated (ebonite), 268. manufacture of, 262. solvents of, 264. sources of supply, 261. specific gravity, 263. vulcanising, 266. _ Indian wire gauge, 235. Inertia, 19. centre of, 17, 19. moment of, 19. Inspection of lines, 411. Instruments, drawing, 316. levelling and surveying, 307. Insulating material, Hooper's patent, 278. material, Madsen's, 279. materials, 252. Insulator, asphalt as an, 178. cements, 174. Insulators (line), attachment and sup- port of, 336. attachment of wire to, 342, 347, 382. angle and double, 343. described, 339. hooded, 340. porcelain, 274. shackle, 344. fixing stalks in, 343. stretching or winding, 342. supporting and suspending com- pared, 340. swinging, 341. testing or control, 342. Iron, alloys of, tinning, galvanising, 204. properties, composition, &c, 188, 196, 203. refining, 189. smelting, 198. Iron, malleable, 196. beams, 225. beams, deflection, 72, 215. Bessemer, 199. cable huts, 237. and cast iron (stiffness), 205. and cast iron in combination, 206. Iron cells as struts, 42. corrosion and preservation. 225, 238. co-efficient of expansion, 204. effects of vibration, &c, on tex- ture, 207. effects of forging and rolling on strength, 200. effects of loads exceeding proof, 45. manufacture, 197. masts, 227. mechanical properties, 203, 205. modulus of elasticity, 219. proof strength, factors of safety, 214. red short and cold short, 190, 206. rolling bars and plates, 202. and steel welding, 247. strain, ultimate, 212. struts, 223. telegraph poles, 216, 226, 326. tenacity at different temperatures, 203. texture affecting strength, 46, 200. in telegraph construction, 236. ties, 224. weight formula for bars, plates, and wire, 202. Iron wire, tenacity of, 21 1. and wooden structures compared, 238. Ironwork, deflection, 215. fastenings for, 219. testing, 215. working load, 215. Isometrical projection, 319. Ivory, 276. Joggles and wedges (timber joints), 132. Joining gutta-percha core, 257. India-rubber core, 271. lead-coated gutta-percha core, 352. ropes, 283. timber, principles of, 133. timber, straps, 133. thick and thin cables together, 388. wire on ground, 378. Joint boxes, 351. Britannia, 346. levers, hooks, and holders, 296. plane, stability, 92. stability at foundation, 163. twisted, or bellhanger's, 346. Joints, allowance for, in deflection, 215. 460 INDEX. Joints in beams, 135. between beams, 135. in cable conductor, 386. in cables (splices), 399. classified, 131, 133. denned, 74. fished, 134. in ironwork, 222. in masts, 135, 152. mortice and tenon, 135. oblique, strut meeting beam, &c. (timber), 136. post and beam, 135. riveted, 213, 219, 221. scarfed, 134. shouldered tenon, 135; in struts, 135. in ties, 133. welded, strength of, 202. wire, 223, 346. Keys and wedges, 221. Killing wire, 233, 279. Kinetic energy, 21. Knots in ropes, 27, 283. in timber, to detect, 121. Knot in timber, 120. Labour of brickwork and masonry, 185. of boring rock, 161. of earthwork, 160. estimate for, 361. hints on, 419. organisation of, 378. Lashings to tighten, 54. Latticework poles, 65. Laying long and short cables, 395. strands, cable conductor, 386. Lead, 251. Lead -coated gutta-percha core (joints), 352. Length of wire (catenary), 99. measures of, British and French, 307. Level, mirror, 308. spirit, 295. telescopic, 309. water, 309. Levelling defined, and definitions, 306. operations of, 315. Levels, flying (verifying), 316. Lever, principle of, 11. Lightning and. contact wires, 347. dischargers for offices, 406. Lightning spikes, wires, and other pole fittings, 376. Lime, pure, rich, or fat, 168. hydraulic, 170. Limit of elasticity, 31. Limiting length of span wire, 97. Limit to size in construction, 35. Line of resistance (frames), 76. Line wires, straining up, 283. Lines, construction of, 365. designing, 323. drawings of, 321. estimates for, 356. local, and offices, 352. numbering, for distinction, 335. railway, distance from rails, 323. selection of routes for, 323. setting out, 365. setting out on hills and slopes, 368. setting out, angle poles and ties, 366. setting out, town overhead, 369. temporary, 218, 326, 382. underground, 349, 369. Live load defined, 32. Load applied with impact, 33. bending, fracture by, 56. dead, 32. defined, 29. distribution of, on beam, 61. exceeding proof load (iron), 46. gross defined, in designing, 35. live, 32. moment of, beams, 59. on angle poles, 86. proof, 31, 32. and stress in frames, 76. and strain, their relation, 31. transverse, 55. ultimate or breaking, defined, 31. working, defined, 31. working on iron structures, 215. working on timber, 131. brickwork and masonry, 186. Loads on beams, above and below proof, 56. factors of safety for dead and live, 32. Local lines and offices, 352. London, central office, 405, 407. Lubricants, unguents, 24. Machines for covering cables, 387. Madsen's insulator for cables, '279. Magnetic compass (surveying), 308. Malleable iron (see Iron). INDEX. 461 Malleable cast iron, 192, 196. Mallet's buckled platea, 214. or Poncelet's co-efficient, 50. Mallet, serving, 297. Manganese in steel, effects of, 243. Manilla ropes, 279. Marine glue, 175. Masonry and brickwork, 179. and brickwork combined, 185. bond in, 182. dry stone for facing banks, 183. dry stone cairns for poles, 183. factors of safety, 187. fixing ties and stays to, 332. labour of, 185. mixed kinds of, 183. obelisks for wire, 184. plinths for poles, 183, 374. pointing, 187. poles, cantilevers, &c, inserted in, 187. qualities of, 181. rubble, 183. rules for construction of, 180. shaping and dressing stones, 181. technical terms, 178. thickness and volume of mortar, 182. Mass denned, 19. units of, 2. Mastic, asphaltic, for underground lines, &c., 177, 352. Mast-building, 140. Mast, compound, details of, 143. defined, 123. depth inserted in ground, 139. head, 145. stays and their attachment, 139. top, 147. Masts classified, standing and com- pound defined, 138. climbing, 149. depth buried, 139. examples of ships, 147. examples of telegraph, 148. fitting caps, &c. , 150. iron, erection of, 227, 284. iron in navy, 227. iron, telegraph, 229. heights of telegraph, 148. joints in, 63, 152. protection of, 139. proportions of, simple, 139, 152. putting wire on high, 382. rake of, 151. selection of timber for, 138, 353. Masts, sites for, 324, 370. standing and compound compared, 151. staying, 149. telegraph and ships, compared, 151. telegraph, considered as fixed beams, 62. telegraph, faults in construction of, 152. topgallant and royal, 147. trimming and shaping, 139. Materials, conditions imposed by nature of, 34. economical application of, 37. estimates for, 359. Measures of length and area, British and French, 307. Measuring on ground, 309. Mechanical drawing, 319. Messages, conveyance over office building, 407. Mirror level, 308. Models, relative strength of, 35. Modulus of catenary, 95. resistance to crushing, 40. tenacity (working or practical), 47. tenacity of cable, 108. Moduli of strength, elasticity, and resilience for same material, 36. numerical, precautions in applying, 37. practical and working (cables), 48. Moment, bending, or moment of flex- ure, 58. bending, in cantilever, 60. bending, in girder, 60. of couple, 10. of force, Ac, 9. of inertia, 19. of load on beam, 58. of momentum, 21. of stability of body, 93. of torsive load, 53. Momentum, 20. Moment of velocity, 20. Mortar, adhesion of, 173, 187. common, 169, 172. hydraulic, 170. volume and thickness of, 183. Mortice and tenon joints, 135. Muirhead's cement (insulator), 175. Multiple conductor cables, 387. Muntz's metal, 252. Nails, description and application of, 131. 462 INDEX. Nails, holding power of, 131. Neutral axis in beams, 56. plane in beams, 55. Nippers, wire, 292. Nomenclature of circuits, 409. Obelisks for supporting wire, 184. Office arrangements, distribution of instruments, 406. arrangements, battery room, 407. arrangements for testing, 407. arrangements for distributing and collecting messages, 407. commutators and connection boards, 405. fittings, &c, 403. furniture, &c, 408. Offices, drawings of, 321. examples of, viz. :— America (Western Union), 405. Berlin, 404, 406. India, 405. London, 405, 407. Paris, 404, 405, 407. Offices, local lines and, 352. Office wires, arrangement of, 403. wires, leading in, 403. Oils, drying, 278. Ordinate (catenary), 96. Organisation, telegraph, 413. of labour, 373. Orthographic projection, 320. Oudroic, 279. Over-house wires, 381. Packing, distribution and transport of material, 372. Paint for wire ties, &c, 225. Painting, varnishing, polishing, 299. Paper drawing, 317. Parabola and catenary compared, 102. Paraffin, 277. Parallel forces, 11. Parallelogram of couples, 11. of forces, 4. Parallelepiped of forces, 5. Parameter (catenary), 95. Paris, central office at, 404, 405, 407. Parker's cement, 173. Parkes' process for vulcanising, 267. Partners (masts), 143. Perspective projection, 319. Pickets for guys, tackle, &c, 288. Picking up cable, 398. Pieces of structure defined, 74. Pike poles, 287. Pillars of different materials com- pared, 44. iron, strength of long and short, 40. Pitch of rivets, 219. Plan (surveying), 306. Plane joint, conditions of stability at, 92. joint, moment of stability at, 93. Plane table, 315. Plans of offices recorded, 408. scales for, 317. Plaster of Paris, 174. Pliability, co-efficient or modulus of, 29 Plinths' for poles, 183, 375. Plotting surveys, 318. Plumb rule, 295. Pointing, 187. Pole angle and tie, 78. fittings and fastenings, 66. holes, 326. holes, boring, 157. holes, digging, 153, 156, 374. holes, filling, 92, 159. roofs or rain caps, 348. selection of pattern, 325. Poles, angle contiguous on curves, 84. angle, loads on (table), 86. angle, pegging out, 366. arrangement of wires on, 338, 347. attachment of insulators to, 336. bamboo, 218, 326. box and lattice, 65. cast iron, 195. considered as beams, 64, 68. considered as struts, 44. coupled, or A, 66, 329. draw, 329. earthplates and cross-feet for, 327. erecting, 375. erecting on rock, 326. erecting on inclined ground, 377. examples of, 325. heights of, 327. high, built or compound, 329. hold on earth of, 92, 326. iron (malleable), 216. iron, strength of, 226. masonry plinths and cairns for, 374. metal, special patterns, 65. numbering of, 335i number per mile, 328. rake of, 330. sites for, 365. strength of iron and wooden in practice, 325. INDEX. 463 Poles, stmts for, 334. strutted and tied, 86. stays and ties, their application to, 331. terminal, 329. testing or control, 342. trussed, 86, 329. Polish, French, 300. Polishing, 299. Polygon, funicular, 84. of couples, 11. of forces, 5. Poncelet's or Mallet's co-efficient, 50. Porcelain, 274. Portland cement, 173. Position, stability of, 92. Potential energy, 22. Pozzolanas, 171. Pressure, atmospheric, 105. fluid, 104. resistance of materials to, 38. tests for cables, 402. to indent wood, 44. Pressures, line of (blockwork), 94. Pressure, wind, 105. Prismatic compass, 308. Projection, perspective, orthographic, and isometrical, 319. Proof load, 31, 32. load, beams, 56. load, cast iron, 194. load, malleable iron, 214. load, masonry and brickwork, 187. load, ropes, 281. load, timber, 131. strain, 34. Protection of cables in rivers, 403. of timber from rot and insects, 126. Protracting, 318. Prussian specification for wire, 346. Puddle, clay, 160. Puddling, 198. Punching, 51. Quarters (masts), 143. Radius (catenary), 96. Railway, distance of telegraph from, 323. crossings, 377. Eain caps or pole roofs, 348. Bake of masts and poles, 151, 330. Ramming earth round poles, &c, 92, 159. Ranging lines (setting out), 310. ■s, 293. Red and cold shortness in iron, 190, 206. Refraction, correction for (survey- ing), 316. Repairs, checks on, 412. classified, 409. estimating for, 364. execution of, 411. materials and tools for, 411. Report of completion, 364. on telegraph project, 356. Repose, angles of, 26. Resilience or spring, its modulus, 33. strength and elasticity, moduli of, 36. Resin and ashes cement, 175. Resistance, centre of, of joint (frames), 76. centre of, plane joint, 92. fluid, 105. line of, in frame, 76. Resultant of couples defined, 11. of forces defined, 3. of force and couple, 12. of forces and couples, 13. of parallel forces, 13. Rigidity or stiffness defined, its mo- dulus, 29. in designing beams, &c, 72. of structure defined, 75. River cables, choice of site, 325, 371. cables, description of, 353. cables, protection of, 402. soundings for cable laying, 371. span, erecting, 379. span, terminating wire, 382. span, sites for masts, 324. Rivers, motion of water in, 106. stability of channels of, 107. Rock, erecting poles on, 326. foundations, 163. labour of boring, 161. Roman or Parker's cement, 173. Rope hemp, Manilla, 279. joints in, and knots, 283. proof strength, factors of safety, 282. strength of, 281. tarred, 280. tenacity when doubled, 49. twisting fibres into, 54. wire, splicing, &c, 223. Rot in timber, 127. Route for line, choice of, 323. Royal masts, 147. Rubble masonry, 183. Rule, plumb, 295. 464 INDEX. Run steel, 241, Sapwood, 118. Saws, 292. Scales for plans and sections) 317. Scarfed joints, 134. Scissors and shears, 290. Screw-drivers and spanners, 298. Screws, holding power of, 132. (ironwork), 220. Sealing-wax varnish, 300. Seasoning and drying timber, 117, 123. Section (levelling), 306. Sections, scales for, 317. Semi-steel or homogeneous metal, 243. Serving mallet, 297. Set, 30, 32. Setting out angles, 366. on inclines and hills, 368. overhead lines, 365. river spans, 370. river cables, 371. town lines (aerial), 369. underground lines, 369. Sextant box, 308. Shackle insulator, 344. Shafting, 53. Sharpening tools, 291. Shearing defined, 36. force of load in beam, 58. phenomenon of, 50. resistance to, of timber, 51. resistance compared with tenacity, 50. stress in beams, 60. stress in flanged beams, 61. stress, its distribution, 50. Shears or scissors, 290. hand, for lifting, 287. or shear legs, 287. Ships' masts, examples of, 147. and telegraph masts compared, 151. Shocks and vibration affecting tex- ture of iron, 207* Sickness amongst workmen, 420. Sights, fore and back (levelling), 315. Siticated asphalt for cables, 179. Silicon in steel, 243. Sinking, velocity of (cable), 106, 108. velocity of, longitudinally, 110. velocity of, transversely, 111. of new earthwork, 160. Sites for masts and river cables, 324. Skin on iron, 56, 191, 193, 200, 294. Slack allowed in laying cables, 395. Slopes of earthwork, 91, 153, 159. Smelting iron ore, 189. Soldering alloys, 302. alloys, melting points of, 302. description and conditions, 300. fluxes, 304. hard, 305. soft, 305. sources of heat for, 303. Sounding, 310, 316. rivers for cables, 371. Space, French units of, 2. Spanners, 298. Span wire, dip equation, 97. wire, limiting length, 98. Spar defined, 123. Specific conductivity of cable con- ductors, 385. Specifications for cable wire, 234 line wire, 230. line wire, Prussian, 346. telegraph work, 356. Spirit level, 295. Splicing cables, 399. wire rope, 223. Spring or resilience, its modulus, 33. Stability of blockwork, 92. earth, 26, 91, 153. friction, 26. frames, 84. river channels (table), 107, structure defined, 74. at foundation joint, 163. and position of centre of gravity, 95. Stalks, fixing insulator, 343. Statics and dynamics defined, &c, 1, 18. fundamental principles, 3. Statical measure of force, 2. Stations and station lines (survey- ing), 306. Stay defined, 77. Staying frames, 83. masts, 139, 149. Stays and ties, attachment to poles, 330, 376. attachment to masonry, 332. anchors for, 332. appliances for tightening, 334. ereotion of, 333. Stays, cross, 330. Steel-appearances of fractured sur- faces, &c, 243. applications, tools, &c, 246. INDEX. 465 Steel, Bessemer, 198, 240. blister, cementation, 240. cast, 241. co-efficient of expansion, 242. composition of, 243. corrosion of, 246. deflection permitted in practice, 72. density, &c, 242. effects of manganese in, 243. effects of silicon in, 243. hardening, 241. joining, 246. mechanical properties, 243. production of, 240. punching, 246. run, 241. semi, steely iron, or homogeneous metal, 241, 243. shear, 241. strength and selection of, 243. tempering, 241. tenacity, 244. in telegraph construction, 248. welding, 243. welding to iron, 247. wire and its application, 244, 248, 345. working load on, 246. Stiffness, 33. or rigidity denned, its modulus, 29 torsive, 53, Stirrups, 133. Stones, shaping, dressing, and facing, 181. Stoppers for line wires, 297. rope, 283. Stores or materials, estimates for, 359. Storing cables, 402. Stowage of cables on shipboard, 392. Strain defined and expressed, 29. and load, their relation, 31. proof, and shock producing it, 34. and stress, transverse, 55. Straining tackle, 283. up line wires, 283, 378. Stranded wire, its uses, 236, 345. Straps for joining timber, 133. Strength, elasticity, and resilience, their moduli, 36. of cables, 389. and elasticity of cable core, 386. of iron and wooden poles in prac- tice, 325. relative, of large and small masses, 34. Strength, relative to internal struc- ture, 36, 118. of struts, 40. of structure defined, 74. of timber, 118, 129. Stress in beams, 56, 60. defined, its intensity, 29. distribution, 75. in frames. 75. horizontal, in frame, 82. open frame, 82. Stretching or winding insulators, 342. Structure defined, 74. strength, stability, and rigidity of, 74. of wood (organised), 118. Structures, conditions of, their effi- ciency and durability, 74. Strut defined, 40. equilibrium, unstable, 76. generally inferior to tie, 77. and tie frame, 78. Struts of different materials com- pared, 44. frame of two, 77. iron, 223. joints for lengthening (timber), 135. long and short, strength of, 40. long, and beams compared, 44. oblique meeting beam, post, or tie, 136. poles considered as, 44. for poles, 334. timber, formulse for, 41 . Strutted and tied poles, 86. Sulphur cements, 175. Superintendence estimate, 363. Surface protection of timber, 126. Surveying by angular measurements, 315. corrections for refraction and cur- vature, 316. with chain, 313. defined, 306. with plane table, 315. and levelling instruments, 307. Surveys, checking, 313. plotting, 318. Swinging insulator, 341. Tackle for straining wires, &c, 283. Tangent (catenary), 96. Taper in cables, 388. Tar and clay cement or luting, 179. Tarred ropes, 279. 466 INDEX. Technical terms, carpentry, 122. brickwork and masonry, 179. Telegraph masts, heights attained, 148. masts, examples of, 148. and ships' masts compared, 151. Telescopic level, 309. Temper of tools, 294. Temperature and elasticity, 35. affecting tenacity, 48. and strength (ca"st iron), 193. Temporary wires, straining up, 382. Tenacity affected by structure or texture, 46. form of section, 47. temperature, 48. shocks, 48, 49. annealing, 49. of chains and rods compared, 49. of doubled rope, 49. modulus of, 47. resistance to crushing, and trans- verse strength, relative, 56. Tenon and mortice joint (timber), 135. shouldered joint, 135. Tension on cable at ship, 112. on cable, paying out stopped, 114 on cable being raised, 115. on bight and grapnel rope, 115. phenomena of fracture by, 45. on wire, 97. on wire, effect of elasticity, 100. on wire, effect of change of tem- perature, 100. on wire from inclination at insu- lator, 115. Tents, 418. Terminal poles, 329. Terminating wires, 381. at river crossings, 381. Testing arrangements in offices, 407. balls, 343. cables by pressure, 402. chains, 215. cast iron, 196. or control poles, 342. iron work, 214. materials, 32. ropes, 282. Theodolite, 308. Thrust, horizontal, of frame, 82. Tie defined, 47. efficiency of, 78. equilibrium stable, 76. and strut (angle pole), 78. Tie and strut compared, 77. Tied and strutted poles, 86. Ties, frame of two, 77. iron, 224 iron, paint for, 225. joints for lengthening timber, 133. and stays, anchors for, 332. and stays attaching to masonry, 188, 332. and stays, appliances for tighten- ing, 334 and stays, erection of, 333. and stays, &c fitting of, 376. and stays, making and applying, 330. Timber (see Wood). beams, deflection, 72. beams, strength constants, 131. defined and classified, 122. durability of, 129. examination and testing of, 121. factors of safety, 131. hot air seasoning, 124. joining, 131. resistance to shearing, 51. seasoning and drying, 117, 123. steaming and boiling, 125. strength arid elasticity. 129. struts, formulae for, 42. surface, protection of, 126. testing for faults, 121. warping of, 126. Tin, 251. Tinning and galvanising, 204. Tools, abrading, 293. application to iron, 294 boring, 292. construction, 355. cutting, 289. earthwork, 154. hints on, 421. percussive, 294. for repairs, 411. sharpening, 291. temper of, 294. wire nippers, 292. Topgallant and royal masts, 147. Topmasts described, 147. Torsion defined, 51. resistance to, 51. Torsive moment of load, 52. strength, tables of, 53. Toughened cast iron, 192, 194, 243. Town lines, setting out, 3G9. Traction, angle of, 26. Transport /estimate), 360. INDEX. 467 Transport, 372. Transverse crushing and tensile strengths, their relation, 56. load, strain, and stress (see beam), 55. strength of tubes, 64. Trees, ages at maturity, 122. felling, season for, 120. felling, modes of, 123. heights of, 120. Trestle trees, 144. Triangle of forces, 4. Triangles, chaining, 313. ill-conditioned, 313. Trigonometrical formuls?, 311. Truss defined and described, 82. Trussed poles, 87. coupled, and A poles (their use), 329. Tubes, transverse, strength of, 64. for underground lines (laying), 382. Tubular masts, joints in, 65. Turpentine varnish, 300. Twisting wires and fibres, 54. Ultimate strength defined, 31. Underground lines, 349. in asphalt, 178. flush or draw-boxes, 382. inserting wire, 383. laying tubes, 382. sizes of wire used, 382. Unguents, lubricants, 24. Unit force British, 2. „ „ defined, 2. „ „ French, 2. „ ,, Gauss' absolute, 2. „ ,, gravity, 2. ,, mass, 2. Units force compared, 2. force in practice, 2. of mass, time, and space, 2. of work (gravity and absolute), 23. Varnishing and galvanising wire, 349. and painting, 299. Varnish, turpentine, 300. Velocities, composition and resolu- tion of, 20. graphical representation of, 20. Velocity defined, 19. of falling bodies, 2. moment of, 20. of sinking cable, 108. uniform and accelerated, 20. Vibration and impact, effects of, 33. and shocks, influence on texture and strength, 50, 207. Vulcanite and ebonite, 268. Vulcanised gutta-percha, 261. Vulcanising processes, 266. Warping of timber, 126. Water, fresh and salt, heaviness, 104. level, 309. motion in rivers, &c, 106. seasoning (timber), 125. Web in flanged beams, its functions, 58, 61. Wedges and keys in ironwork, 221. and joggles in carpentry, 132. Weight of copper wire, formulae, 250. of iron wire, bars, and plates, formulae, 202. Welding, strength of joints, 202. iron and steel together, 247. steel, 243. Whitworth's wire gauge, 235. Wind pressure, 105. Winding or stretching insulators, 342. Wire across river, erecting, 379. attachment to insulators, 342, 346, 382. compound (American), 250. copper, for cable core, 249, 385. copper, formulas for weight of, 250. corrosion in railway tunnels, 345. covering with gutta-percha, 256. covering with india-rubber, 270. curve, use of set curves, 1 02. drawing and tenacity, 46, 209. dip of, 101. effects of ligature on, 46. erection on high masts, 382. eyebolts, 296. eye on single, 223. gauges, 234, 296. guards at angles, 344. iron, weight formula, 202. joints in, 223, 300, 346, 377. killing, 379. lead-coated gutta-percha covered (joints), 352. length of (catenary), 100. limiting length of, 97. nippers, 292. paying out, jointing, 377. rope, splicing, 223. sizes used for lines, 344, 382.' span, formulas for dip, tc, 95. specifications, 230, 346. 468 INDEX, Wire, steel, applications, 248, 345. steel, tenacity, 244. stoppers for lines, 297. straining up line, 283, 378, 382. stranded, its use, 236, 345. surface protection of, 349. suspended in water (catenary), 99. tension and dip affected by tem- perature and elasticity, 100. ties, strength of, 215. ties of parallel wires, 225. Wires, arrangement on poles, 347. inside offices, 403, 405. leading into offices, 403. lightning and contact, 347. straining, in pairs, 380. straining, overhouse, 381. straining, temporary, 382. terminating, 381. terminating at river crossings, 382. twisting into ropes, 54. underground, sizes used, 382. tenacity of ordinary and telegraph, 209. Wood (see Timber). characteristics of good, 120. endogenous, 118. and iron construction compared, 238. pressure required to indent, 44. sap and heart, 118. seasoning, dry, 117. structure of, 117. structure and strength related, 118. Work, 21. done against gravity, &c. , 21. of rotating a body, 24. units, 23. Working drawings, 321. load defined, 31. load, deflection under, 72. load, iron, 215. load, steel, 246. load, timber, 131. Wray's compound, 273. Wrought, iron (see Iron). Zinc, 251. BELL AND BAIN, PRINTERS, MITCHELL STREET, GLASGOW. CATALOGUE OF STANDARD WORKS Published by CHARLES GRIFFIN & COMPANY. 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Com- plete in One Volume, fcap. 8vo., cloth, 6/- Twelfth Edition. Or, in Three Parts : Part I. Bucolics and Georoics . . . . 2/6 Part II. The jEneid, Books I.— VI 2/6 Part III. The ^neid, Books VII.— XII. .. 2/6 " Contains the pith of what has been written by the best scholars on the subject* The notes comprise everything that the student can want."— A thmteum. " The most complete, as well as elegant and correct, edition of Virgil ever published) in this country." — Educational Times. " The best commentary on Virgil which a student can obtain." — Scotsman. COBBETT (William) : ENGLISH GRAMMAR in a Series of Letters, intended for the use of Schools and Young Per- sons in general. With an additional Chapter on Pronunciation, by the Author's Son, James Paul Cobbett. Fcap. 8vo. Cloth, 1/6. (The only correct and authorized Edition), "A new and cheapened edition of that most excellent of all English Grammars,, William Cobbett's. 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Cloth, 2/- Ninth Edition. 20 CHARLES GRIFFIN & COMPANY'S CRAIK' S ENGLISH LITERATURE. A COMPENDIOUS HISTORY OF ENGLISH LITERATURE AND OF THE ENGLISH LANGUAGE from the Norman Conquest. With numerous specimens. By George Lillie Craik, LL.D., late Professor of History and English Literature, Queen's College, Belfast. In two vols. Royal 8vo. Handsomely bound in cloth, 25/- ; full calf, gilt edges, 37/6. New Edition. .G.ENE.RA.L CONTENTS. Introductory. 1. — The Norman Period — The Conquest. II. — Second English — commonly called Semi-'Saxon. III. — Third English — Mixed, or Compound English. IV. — Middle and Latter Part of the Seventeenth Century. V. — The Century between the English Revolution and the French Revolution. VI. — The Latter Part of the Fighteenth Century. VII. — The Nineteenth Century : (a) The Last Age of the Georges. (6) The Victorian Age. With numerous Excerpts and Specimens of Style. ". Anyone whO'Will take the trouble to ascertain the fact, will find how completely even our great poets and other writers of the last generation have already faded from .the view of the present with the most numerous class of the educated and reading .public. Scarcely anything is generally rtad except the publications of the day. Yet .-NOTHING IS MORE CERTAIN THAN THAT NO TRUE CULTIVATION CAN BE SO ACQUIRED. This is the extreme case of that entire ignorance of history which' has been affirmed, not with more point than truth, to leave a person always a child '"The ipresent 'worjc • combines the History of the Literature with the His- tory op the Language. The scheme of the course and revolutions of the Lan- guage which is followed here is extremely simple, and resting not upon arbitrary, but upon natural or real distinctions, -gives. us the only view of tke subject that can claim to be regarded as of a scientific character." — Extract from the Author's Preface. '".Professor Craik's book going, as it does, through, the whole history of the language, probably takes a place quite by itself. The great 'VAlue of the book is its thorough comprehensiveness. It is always clear and straightforward, and deals not in theories but in facts." — Saturday Review. CRAIK (Prof.): A MANUAL OF ENGLISH LITERATURE, for the Use of Colleges, Schools and Civil Service 'Examinations. ^S , electe d' from the larger worlc, by Dr. Craik. Crown tSvo. Cloth, 7/6. Seventh Edition. "A Manual -of English Literature from so experienced and well-read a scholar as Professor Craik needs no other recommendation than the mention of its existence." — Spectator. " This augmented elfort' will bci'-we -ttotfbt ntit.'-received with decided -approbation by those who are entitled to judge, and studied with much profit by those who want to fleam. .... .If our COMPANY'S HENRY MAYHEW'S CELEBRATED WORK ON THE STREET-FOLK OF LONDON. LONDON LABOUR AND THE LONDON POOR : A Cyclopaedia of the Condition and Earnings of those that will work and those that cannot work. By Henry Mayhew. With many full-page Illustrations from Photographs. In three vols. Demy 8vo. Cloth, 4/6 each. " Every page of the work is full of valuable information, laid down in so interesting a manner that the reader can never live"— Illustrated News. ""Mr. Henry' MaJ?hew's famous record of the habits, earnings, and sufferings of the London poor."— -Lloyd's Weekly London Newspaper. "Thisremarkable book, in which Mr. Mayhew gave the better classes their first real insight into the habits, modes oi livelihood, and current of thought of the London poor." — The Patriot. The Extra Volume. LONDON LABOUR AND THE LONDON POOR : Those that will not work. Comprising the Non-workers, by Henry Mayhew; Prostitutes, by Bracebridce Hemyng; Thieves, by John Binny ; Beggars, by Andrew Halliday. 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Conte-nts : — General View of London, its Population, Size and Contrasts — Professional London — Criminal London — Pentonville Prison — The Hulks at Woolwich — Millbank Prison — The Middlesex House of Detention — Coldbath Fields— The Middlesex House of Correction, Tot- hill Fields — The Surrey House of Correction, Wandsworth — Newgate — Horsemonger Lane — Clerkenwell. "This volume concludes Mr, Henry Mayhew's account of his -researches into the crime and poverty df 'London. The amount of labour of one kind or other, which the whole series of his publications represents, is something almost in- calculable." — Literary Budget. *** This celebrated Record of Investigations into the condition of the Ppor of the Metropolis, undertaken from philanthropic motives by Mr, Henry Mayhew, first gave the wealthier classes of England some idea of the state of Heathenism, Degradation, and Misery, in which multitudes of their poorer brethren languished. His revelations created, at the time of their appearance, universal horror and excitement — that a nation, proies- sedly Christian, should have' in its midst a vast population, so sunk in ignorance, vice, and very hatred of Religion, was deemed incredible, until further examination established the truth of the statements advanced. The result is well known. The London of Mr. Mayhew will, happily, soon exist only in his pages. To those who would appreciate the ettorts already made among the ranks which recruit our "dangerous" classes; and who would learn what yet remains to be done, the work will afford enlightenment, not unminglea wiin surprise. GENERAL PUBLICATIONS. 33 MILLER (Thomas, Author of " Pleasures of a Country Life," &c.) : THE LANGUAGE OF FLOWERS. With Eight beautifully-col- oured Floral Plates. Fcap. 8vo. Cloth, gilt edges, 3/6. Fourteenth Thousand. " A book In which thou wilt find many a lovely saying About the leaves and. flowers." — Heats. 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New Edition. * # * This unique Edition of the great dramatist is admirably suited for home use ; while objection-able phrases have been expurgated, no rash liberties have been taken with thetext* "It is quite undeniable that, there are many passages in Shakspeare which a father could not read aloud to his'cHiUdren— a brother to His sister — or a gentleman to a lady ; and every one almost must have felt or witnessed the extreme awkwardness, and even distress, that arises from suddenly stumbling upon such expressions Those who recoilect such scenes must all rejoice that Mr. Bowdler has provided a security against their recurrence This purification has been accomplished with surprisingly little loss, either of weight or value ; the base alloy in the pure metal of Shakspeare has been found to amount to an inconceivably small proportion It has in general been found easy to extirpate the offensive expressions of our great poet without any injury to'the context, or any visible scar or blank irr the composition! 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SOUTHGATE (Henry) : MANY THOUGHTS OF MANY MINDS : being a Treasury of Reference, consisting of , Selections from the Writings of the most celebrated Authors, compiled and analytically arranged by Henry Southgate. Toned paper, square 8vo. Cloth gilt, elegant, 12/6 ; Library Edition, half Roxburgh, 14/- ; morocco antique, 21/- Twenty-eighth Edition. " The produce of years of research." — Examiner. " Destined to take a high place among books of this class." — Notes and Queries. " A treasure to every reader who may be fortunate enough to possess it.' — English Journal of Education. " The accumulation of treasures truly wonderful." — Morning Herald. 1 This is a wondrous book." — Daily News. " Worth its weight in gold to literary men."— Builder. SOUTHGATE (Henry) : MANY THOUGHTS OF MANY MINDS. Second Series. Square 8vo, toned paper. Cloth gilt, elegant, 12/6; Library Edition, half Roxburgh, 14/-; mo- rocco antique, 21/- Fifth Edition. " We are not surprised that a Second Series of this work should have been called for. Preachers and Public Speakers will find that it has special uses for them."— Edinburgh Daily Review. " Fully sustains the deserved reputation of the First Series." — John Bull. THE SHILLING MANUALS. By JOHN TIMBS, F.S.A., Author of " The Curiosities of London," &c. A Series of Hand-Books, containing Facts and Anecdotes interesting to all Readers. Fcap. 8vo. Neat cloth, one shilling each. Second Edition. I.— CHARACTERISTICS OF EMINENT MEN. ' By John Timbs. Bound in neat cloth, price 1/- " It is impossible to dip into this booklet without finding something that is new or that will bear repeating."— Sheffield Daily Telegraph. XL— CURIOSITIES OF ANIMAL AND VEGETABLE LIFE. By John Timbs. Neat cloth, price 1/- " Has the charm of freshness, besides containing much curious information." — Sheffield Telegraph. III.— ODDITIES OF HISTORY AND STRANGE STORIES FOR ALL CLASSES. Selected and compiled by John Timbs. 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" Will be found abundant in much out of the way information on almost every conceivable topic, where the popular mind is for the most part in error." — Evening Standard. VI.— THOUGHTS FOR TIMES AND SEASONS. Selected and com- piled by John Timbs. Neat cloth, price i/- " Contains a very* great amount and variety of out-of-the-way extracts from modern and old writings." — Mechanic's Magazine. " In a neat and concise form, are brought together striking and beautiful passages from the works of the most eminent divines and moralists, and political and scientific writers oi acknowledged ability."— Edinburgh Daily Review Opinions of the Press on the Series. " It is difficult to determine which of these volumes is the most attractive. WiH be found equally enjoyable on a railway journey, or by the fireside."— Mining Journal, " These additions to the Library, produced by Mr. Timbs* industry and ability, are useful, and in his pages many a hint and suggestion, and many a fact of importance, is stored up that would otherwise have been lost to the public."— Builder. " Capital little books of about a hundred pages each, wherein the indefatigable Author is seen at his best."— Mechanics' Magazine. " Extremely interesting volumes."— Evening Standard. "Amusing, instructive, and interesting As food for thought and pleasant reading, we can heartily recommend the ' Shilling Manuals.'"— Birmingham Daily (rosette* TIMBS (John, F.S.A.): PLEASANT HALF- HOURS FOR THE FAMILY CIRCLE. Containing Popular Sci- ence, Thoughts for Times and Seasons, Oddities of History, Charac- teristics of Great Men, and Curiosities of Animal and Vegetable Life. Fcap. 8vo. Cloth gilt, and gilt edges, 5/- Second Edition. " Contains a wealth of useful reading of the greatest possible variety."— Plymouth Mercury. VOICES OF THE YEAR (The) ; Or, the Poet's Kalendar. Containing the choicest Pastorals in our Language. Pro- fusely Illustrated by the best Artists. In bevelled boards, elaborately ornamented and gilt, 12/6. WANDERINGS IN EVERY CLIME; Or, Voyages, Travels, and Adventures All Round the World. Edited by W. F. Ainswoeth, F.R.G.S., F.S.A., &c, and embellished with up- wards of Two Hundred Illustrations by the first Artists, including several from the master pencil of Gustave Dore. Demy 410, 800 pages. Cloth and gold, bevelled boards, 21/- FIRST SERIES.— TW?*'' rv VTrtv T T ? ^riTTTDN. SECOND SERI MANY THOUGHTS OF MANY MINDS : A Treasury of Keference, consisting of Selections from the Writings of the most Celebrated Authors. FIEST & SECOND SEEIES. Compiled & Analytically Arranged By HENRY SOUTHGATE. In Square 8vo., elegantly printed on toned paper. Presentation Edition, Cloth and Gold ... 12s. 6dL each volume. Library Edition, Half Bound, Koxburghe ... 14a. „ Do., Morocco Antique 21s. „ Each Series is complete m itself, and sold separately. ** 'MANY Thoughts," Sic, are evidently the pro- dace of years of research. We look up any subject under the sun, and are pretty sure to find something that has been said— generally well said— upon it."— Examiner. " Many beautiful examples of thought and style are to be found among the selections."— Leader. "There can be little doubt that it is destined to take a high place among books of this class. "—Notes ■and Queries. " A treasure to every reader who may be fortunate enough to possess it. Its perusal is like inhaling essences ; we have the cream only of the great authors quoted. Here all are seeds or gems." — English Journal of Education. "Mr. Southgate's reading will be found to extend over nearly the whole known field of literature, ancient and modern. *' — Gentleman's Magazine. " Here is matter suited to all tastes, and illustrative of all opinions ; morals, politics, philosophy, and solid Information. We have no hesitation in pronouncing it one of the most important books of the season. Credit is due to the publishers for the elegance with which the work is got up, and for the extreme beauty and correctness of the typography."— Morning Chronicle. " Of the numerous volumes of the kind, we do not remember having met with one in which the selection was more judicious, or the accumulation of treasures eo truly wonderful." — Morning Herald. "Mr. Southgate appears to have ransacked every nook and corner for gems of thought."— Allen's Indian Mmt. " The selection of the extracts has been made with tosto, judgment, and critical nicety." — Morning Post. "This is a wondrous book, and contains a great many gems of thought." — Daily Hews. '■ As a work of reference, it will be an acquisition to any man's library."— Publisher's Circular. " This, volume contains more gems of thought, re- fined sentiments, noble axioms, and extract able sen tences, than have ever before been brought together iu our language.*'-— The Field. " Will be found to be worth its weight in gold by literary men."— The Builder. " All that the poet has described of the beautiful in nature and art; all the wit that has flashed from pregnant minds ; all the axioms of experience, the collected wisdom of philosopher and sage, art- garnered into one heap of useful and well-arranged instruction *&d amusement."— The Era. " The mind of almost all nations and ages of the world is recorded here." — John Bull. "This is not a law-book; but, departing from our usual practice, we notice it because it is likely to be very useful to lawyers." — Law Times. "The collection will prove a mine, rich and inex- haustible, to those in search of a quotation."— Art- Journal, t* " There is not, as we have reason to know, a single trashy sentence in this volume. Open where we may, every page is laden with the wealth of profonndest thought, and all aglow with the loftiest inspirations of genius. To take this book into our hands is like sitting down to a grand conversazione with the greatest thinkers of aU ages." — Star. "The work of Mr. Southgate far outstrips all others of its kind. To the clergyman, the author, the artist, and the essayist, 'Many Thoughts of Many Minds' cannot fail to render almost incalculable service,"— Edinburgh Mercury. "We have no hesitation whatever In describing Mr. Southgate's as the very best book of the class. There is positively nothing of the kind in the language that will bear a moment's comparison with it."— Manchester Weekly Advertiser. "There is no mood in which we can take it up without deriving from it instruction, consolation, and amusement. We heartily thank Mr. Southgate for a book which we shall regard as one of our best friends and companions." — Cambridge Chronicle. " This work possesses the merit of being a magni- ficent gift-book, appropriate to all times and seasons ; a book calculated to be of use to the scholar, the divine, or the public man." — Freemason's Magazine. " It is not so much a book as a library of quota- tions." — Patriot. " The quotations abound in that thought which is themainspring of mental exercise." — LiverpoolCourier. " For purposes of apposite quotation, it cannot be surpassed."- Bristol Times. "It is impossible to pick out a single passage in the work which does not, upon the face of it, justify its selection by its intrinsic merit."— Dorset Chronicle. ** We are not surprised that a Second Series of this work should have been called for. Mr. Southgate has the catholic tastes desirable in a good Editor. Preachers and public speakers will find that it has special uses for them." — Edinburgh Daily Review. " rhe Second Series fully sustains the deserved reputation of the First."— John Bull. London; CHAELE