UC-NRLF fifiS LIBRARY , OF THE UNIVERSITY OF 'CALIFORNIA. MAY 5 1894 Accessions NoJ\>tTlJ5 . Class No. H m m : -'-' - ' 1 ' i m ' 1 m m /a THE ELECTRICIAN'S POCKET-BOOK THE ENGLISH EDITION OF HOSPITALIER'S i r "Formulaire Pratique de I'Electricien;" TEANSLATED, WITH ADDITIONS, BY GORDON WIGAN, M.A., BARRISTER-AT-LAW, MEMBER OF THE SOCIETY OF TELEGRAPH ENGINEERS AND ELECTRICIANS. CASSELL & COMPANY, LIMITED: LONDON, PARIS & NEW YORK. 1884. [ALL RIGHTS RESERVED.] TK' 5 AUTHOR'S PREFACE TO THE SECOND YEAR'S EDITION. THE favourable reception accorded to our FORMULAIRE, and the advice and encouragement which we have received, prove that we were not mistaken as to the purpose and utility of this little hook. We there- fore now hring it forward in the second year, with more confidence than in the first year of its issue. Each one of the numerous altera- tions to he found in this edition is an improvement, as it either fills up a gap, corrects an error, or gives some new information. Thus, in the first part, which is devoted to first principles, definitions, and general laws, we have remodelled the whole of the part on induc- tion, and given formulae for the galvanic field produced by a current of any given common geometric^, form. * J We have also modified some of the definitions of the units of mea- surement, in order to make them clearer and more precise ; we have given the " Thomson's bridge " method for the measurement of very small resistances, the formulae of Thomson's new voltmeters and am- meters, the formulae of the bifilar suspension, and the work produced by men and horses, etc. In the Fourth Part, devoted to applications of Electricity, although but few new inventions have appeared, we have, nevertheless, been enabled to add the results of tests of the new batteries of Skrivanow, Lalande, and Chaperon ; the Edison-Hopkinson, Schuckert, and Ferranti dynamos ; Ayrton and Perry's motors ; and the Grenoble ex- periments of Marcel Deprez on electrical transmission of power. We have completed the chapter on alternating current machines by giving the methods of Joubert and Potier, which enable the electro- motive force, current strength, and energy of such machines to be measured. The methods are fully given, so that either the efficiency of transformers or secondary generators, which are now receiving so much attention, or the high electromotive forces used in the trans- mission of energy, may be easily measured. In conclusion, we beg to thank our correspondents for their valuable co-operation. They will see that, as far as possible, we have taken advantage of their advice and information. We trust that they will kindly continue their friendly collaboration, and again, in the common interest, help us still further to improve this volume. E. H. Paris, February, 1884. TRANSLATOR'S PREFACE. IN common with many of those who have had to do with the modern development of electrical engineering, I had long desired some small portable book, in which it would be easy to find constants, formulae, methods, and other practical information in a concise form and without difficulty. The favourable reception accorded to M. Hospitalier's " Formulaire Pratique de 1'Electricien " by English electricians, has led me to hope that a similar book in English might be useful to electrical engineers. I have therefore prepared the present work, which consists principally of a translation of M. Hospitalier's " Formulaire." This, the main portion of it, has been carefully compared with M. Hospitalier's edition for 1884, and almost all the additional informa- tion contained in that edition has been added. During the progress of the work I have also added such new matter as my own reading or experience has suggested. My thanks are due to Prof. Fleeming Jenkin, F.R.S., and other friends, for valuable suggestions ; to Mr. W. H. Preece, F.R.S., and Mr. Kempe, of the Post Office, who have kindly allowed me to make use of some of the technical instructions of their department ; and also to Profs. Ayrton and Perry, and Messrs. Crompton and Kapp, for most valuable contributions. I trust, that though I may not have added very much in quantity to the information to be found in the French edition, the additions may yet be found of value, and that at all events I may have succeeded in producing a faithful and intelligible rendering of the original. It is intended, should the work meet with a favourable reception, to follow M. Hospitalier's example and republish it periodically, with such additions as may be desirable. I therefore venture to repeat his appeal, and to ask electricians generally to assist in such a task by forwarding to me, addressed to the publishers, corrections of any errors which may be found in this book, suggestions for its improve- ment, and, above all, the results of any new work, in the form of tables or formulae. In conclusion, I must express my great indebtedness to Mr. Alfred J. Frost, Librarian of the Society of Telegraph Engineers and Electricians, who, at a time when I was unable to attend to any business, undertook the somewhat formidable task of correcting the final proofs and seeing this work through the press. Q. -yy Dept. Mech. Bng. TABLE OP CONTENTS. (See also Index to Tables, page 315.) FIKST PAET. Definitions First Principles General Laws. PAGE Magnetism. Definitions Laws of magnetic actions Properties of lines of force Coefficient of induced magnetism Magnetic in- duction Terrestrial magnetism 1 Static electricity. Law of electrical attraction and repulsion Distribution of electrostatic charges Induction Specific induc- tive capacity ........... 5 Condensers. Capacity Charge Condensers arranged parallel and in cascade Energy in a condenser Contact electricity Volta's law 7 Dynamic electricity, or electricity in movement. Laics of currents. Ohm's law Kirchoff's laws Bosscha's corollaries Specific resistance Conductivity Resistance of conductors Resistance of derived shunt or parallel circuits ...... 9 Voltaic batteries. Laws of chemical actions Constants Energy of a battery Arrangement of cells Pollard's theorem . . .11 Electrolysis. Faraday's laws 14 Heating effect of currents. Joule's law 15 Work produced by currents . . . . . . . .16 Electro-dynamics. Electric or galvanic field Magnetic shell Sole- noid Mutual actions of two currents Rectilinear currents Plane rectangular circuits Action of two coils at a distance Ampere's law Action of the earth on currents Astatic conductors Sole- noids 18 Electro-magnetism. Fundamental principle Ampere's rules Multiplier Action of currents on magnets Electro-magnet Maxwell's rule Action of an element of a current on a magnet vi THE ELECTRICIAN'S POCKET-BOOK. PAGE pole Galvanic field 1 produced by an arc of a circle, a circle, an infinite rectilinear circuit, and a plane closed circuit Magneti- sation by currents Rule for finding the poles of electro-magnets . 20 Induction. Laws of induction Extra current Induction in a rectilinear circuit displaced so as to be parallel to itself in a uniform magnetic field Induction in a closed circuit Influence of the extra current on induced currents Lenz's law Conser- vation of energy in induction 24 SECOND PART. Units of Measurement. Fundamental units. C.G.S. system Multiples and sub-multiples Decimal notation Dimensions Derived units .... 29 Geometrical units. Length, area, volume Units of different countries 31 Mechanical units. Yelocity Acceleration Units of force and weight Units of work or energy Horse-power Watt . . 35 Magnetic units. Unit pole Unit magnetic field .... 40 Electro-magnetic units. C.G.S. units Practical units Units of current strength, quantity, electromotive force, resistance, and capacity ............ 41 Comparison of electrical units used by different physicists . . 43 Units used by the house of Siemens at Berlin 47 Electrostatic units 47 Various units.-^ Pressure Temperature Heat Mechanical equi- valent of heat Units of energy Photometric units ... 48 THIRD PART. Measuring Instruments and Methods of Measurement. Geometrical measurements. Micrometer gauge 53 Mechanical measurements. Velocity, force, and work ... 54 ELECTRICAL MEASUREMENTS. Resistance coils and resistance boxes. Standard B.A. unit Subdivi- sions of the ohm Combination of coils Post- Office bridge box TABLE OF CONTENTS. vii PAGE Cable-testing bridge box Dial resistance box Thomson and Varley's slide resistance box Precautions in using resistance coils "Wheatstone's bridge Slider bridge Thickness of wire for resistance coils ' 54 Standards of electromotive force. Post-office standard, Daniell Warren de la Rue's chloride of silver battery Latimer Clark's standard cell Zinc-cadmium couple Simple cell Reynier s standard cell 61 Standards of capacity. Condensers Construction of condensers . 64 Accessory instruments. Circuit breakers Commutators Reversing commutators Reversing keys Short - circuiting keys Dis- charging keys Double contact bridge key 66 General methods of measurement. Direct methods Opposition Substitution Comparison Indirect methods .... 68 MEASUREMENT OF CUEEENTS. I. GALVANOMETEES 69 Sine and tangent galvanometers Gaugain's galvanometer Post- Office tangent galvanometer Schwendler's galvanometer Siemens universal galvanometer Thomson's reflecting galvano- meter Thomson's astatic galvanometer 70 Lamp, scale, and mirror Hole, slot, and plane .... 75 Ship's galvanometer Dead-beat galvanometers of Thomson, Marcel Deprez, Ayrton and Perry, Marcel Deprez and d'Arsonval Torsion galvanometer of Siemens and Halske .... 76 Ammeters and voltmeters Ayrton and Perry's spring ammeter and voltmeter Lieut Cardew's ammeter Ayrton and Perry's spring and solenoid ammeter and voltmeter Crompton and Kapp's unchangeable constant ammeter and voltmeter ... 79 Thomson's new current and potential galvanometer Balistic galvanometer 80 Shunts and circuit resistance coils Multiplying power Compensa- tion resistance 87 Constant of a galvanometer Maximum sensibility Theorem of sensibility Formula of merit Circuit resistance coils Calibra- tion of a galvanometer Thickness and resistance of galvanometer wires Shape of coils 89 Measurement of a current in C.G.S. units by the tangent galva- nometerOscillation method 93 Indirect measurement of current strength. By Ohm's law By the voltmeter 94 Dept. Mech, Eng. viii THE ELECTRICIAN'S POCKET-BOOK. PAGE II. ELECTRO -DYNAMOMETERS of Weber, Joule, and Siemens and Halske 94 HI. VOLTMETERS 95 MEASUREMENT OP RESISTANCES. Resistance of conductors. By substitution By addition to a known circuit Wheatstone's bridge Eesistance of a conductor connected to earth Eesistance of overhead lines Ayrton and Perry's ohm- meter J. Carpentier's proportional galvanometer Specific con- ductivity Measurement of very high resistances Measurement of very low resistances : Thomson's bridge 96 Eesistance of galvanometers. By half deflection By equal deflection Thomson's method 100 Internal resistance of batteries. Thomson's half deflection method By the differential galvanometer Method when an even number of identical cells is at hand Mance's method Siemens' method Munro's method 102 Insulation of overhead lines. Ordinary method Determination of insulation per mile 105 MEASUREMENT OF POTENTIAL AND ELECTROMOTIVE FORCE. Electrometers. Electroscopes, repulsion electrometers Thomson's absolute electrometer Thomson's quadrant electrometer Idio- static and heterostatic methods Law of deflection of the quadrant electrometer Mascart's symmetrical electrometer Lippmann and Debrun's capillary electrometers Ayrton and Perry's spring electrometer 106 Indirect measurement of differences of potential. Voltmeters Opposition method Partial opposition method . . . .109 Electromotive force of batteries. Equal resistance methods Equal deflection methods of Wiedemann, Wheatstone, Lacoine and Poggendorff Clark's potentiometer Law's potentiometer By opposition 110 MEASUREMENT OF ELECTRICAL QUANTITY. Faraday's law Gas voltmeters Electrolytic cells Edison's electric meters Coulomb meters of Edison, Ayrton and Perry Integrating coulomb meter of Vernon Boys 116 MEASUREMENT OF CAPACITY. Electrostatic capacity of condensers 117 TABLE OF CONTENTS. IX MEASUREMENT OP ENERGY. PAGE Dynamometers. Absorption and transmission Simple dynamo- meter Ayrton and Perry's absorption dynamometer Revolution counters and speed indicators . . . . . . . .118 Measurement of electrical energy. Energy expended by an electrical apparatus Heat disengaged in a conductor through which a current is passing Energy metres of Ayrton and Perry, Marcel Deprez, and Vemon Boys 120 CABLE TESTING. Standard temperature Tank To insulate the end of a cable Instruments ........... 122 Resistance of the conductor. Bridge method False zero method Reproduced deflection method Resistance of earth plates . . 123 Electrostatic capacity Ratio of discharge Loss of charge Loss of half charge Total electrostatic capacity per mile or per knot Potential of two cables joined together Capacity of two cables joined together .......... 124 Insulation. Deflection method Differential galvanometer method By loss of charge Insulation of joints Calculation of insula- tion Speed of transmission Duration of transmission Weight of conductor and dielectric . 126 FOURTH PART. Practical Information. Applications. Experimental Results. Algebraic formula. Permutations and combinations Newton's binomial theorem . . . . . . . . . .130 Table of n \ 5 n2 5 Vw"; ^ 3 ; V ; -mi ; - j- ; of numbers from 1 to 100 and factors of it Progressions and logarithms .... 131 Table of decimal and Naperian logs from 1 to 100 . . . .135 Geometrical formula. Lengths, areas, volumes Apothemes, radii, and areas of regular inscribed polygons, in terms of the side . 137 Table of sines and tangents 139 Trigonometrical fonmila. Solution of triangles, etc. . . .140 Coins of different countries 144 Physical formula. Fall of bodies Moment of inertia Formula of the bifilar suspension Velocity of sound, light, wind, engine x THE ELECTRICIAN'S POCKET-BOOK. PAGE belts, armatures, and field magnets of dynamo machines "Work produced by men and horses ........ 144 Specific gravity of solids and liquids 148 Baume and Cartier and Gay-Lussac's scales for liquids lighter than water 149 Baume and Beck's scales for liquids heavier than water . . . 151 Specific gravities of solutions of sulphuric acid in water . . .152 Densities of solutions of nitric acid 153 Densities of solutions of zinc sulphate and common salt . . 153-4 Specific gravities of gases and vapours 154 Densities of solutions of copper sulphate 155 Barometer. Exact formula for the reduction of the height of the barometer to C. Mean height of barometer at different heights above sea level 155 Thermometer. Fahrenheit and Centigrade thermometer scales Determination of high temperatures 156 Linear coefficients of expansion of some solids Cubic coefficient of expansion of mercury 157 Melting and boiling points of common bodies Boiling points of liquids 158 Heat disengaged by the combination of one gramme of certain sub- stances with oxygen and chlorine 159 Heat disengaged or absorbed by chemical actions Combustion of common gas and electric light 160 Heat of liquefaction and vaporisation Specific heat . . . 160 RESISTANCE. List of common materials in order of decreasing conductivity . . 161 Resistance of common metals and alloys at C. . . . .162 Conductivity relative to pure copper of copper alloyed with other substances, and of different samples of copper . . . .163 Influence of temperature on the resistance of metals . . . 164 Besistance of carbon, selenium, phosphorus, and tellurium . . 165 Besistance and conductivity of liquids 166 Besistance of sulphuric and nitric acids Copper sulphate and zinc sulphate Mixtures of copper and zinc sulphates .... 167 Besistance of water, ice, and glass 168 Besistance of insulators, guttapercha and indiarubber . . .169 CONDUCTORS. Nature of conductors Bare conductors Covered wire . . .171 Birmingham gauges, " jauge carcasse " 172-3 TABLE OF CONTENTS. XI PAGE Copper, resistance of pure copper wire 174 Weight of silk covering of wires 175 Iron Galvanised wire Phosphor bronze Silicium bronze . . 175 Commercial types of conductors . . . . . . . .177 Mechanical tests for insulators 178 Specific inductive capacity. Capacities of condensers of common shapes in electrostatic units 179 MAGNETS. Power of magnets Supersaturation Influence of temperature Temper Compressed steel Experimental determination of the moment of inertia of a magnetised bar To bring an oscillating magnet to rest 179 Methods of magnetising. Single touch Divided touch Double touch Elias' process Magnetisation of a needle Armatures for magnetised bars 181 Terrestrial magnetism. Elements of terrestrial magnetism at Paris on Jan. 1st, 1879 At le Pare Saint-Maur on Jan. 30th, 1883 . 183 ELECTED - MAGNETS . Laws of electro -magnets Maximum attraction Action of a bar of iron in a solenoid Formulae for electro -magnets far from the saturation point Electro -magnets of telegraph instruments Construction of coils 183 Production and Applications of Electricity. Classification. Chemical, thermal, mechanical, and various actions 188 BATTEEIES. One-fimd cells without depolariser. Volta's battery and its varieties Batteries with carbon positive plates Cells of Smee, Walker, Maiche Cells with iron as the positive plate . . . .190 One-fiuid cells with solid depolariser. Warren de la Rue, Skri- vanow, Gaiffe, Marie-Davy, and Leclanche Oxide of copper cell of MM. Lalande and Chaperon 191 One-fiuid cells with liquid depolariser. Poggendorff, Delaurier, Chutaux, Dronier's salt, Trouve, Tissandier 193 Two-fiuid cells. Becquerel, Daniell, Meidinger, Callaud, E. Rey- nier, Grove, Bunsen, Archereau, d' Arsonval's depolarising liquid Carbons of Bunsen cells d' Arsonval's zinc carbon cell 194 xii THE ELECTRICIAN'S POCKET-BOOK. PAGE E. Eeynier's jacketed zinc cells Modifications of Grove's and Bunsen's cells Cells of Marie"-Davy, Duchemin, Delaurier Bichromate of potash Fuller, Cloris Baudet, d' Arsonval, Niaudet's chloride of lime battery Circulation, agitation, and aeration . 197 Thermo -chemical batteries. Becquerel, Jablochkoff, Dr. Brard . 199 E. m. f. of one-fluid batteries without depolariser, of Grove's cell, of amalgams of potassium and of zinc Metallodion cell . 199 E. m. fs. of some two-fluid cells Theoretical e. m. fs. . . 202 Theoretical conditions of a perfect battery Constants and work of some known cells Defects of batteries Choice of batteries according to the work they have to do Care and maintenance of batteries Battery testing .202 ACCUMULATORS. Of Gaston Plante and Faure Faure-Sellon-Volkmar accumulator Copper and zinc accumulators of E. Reynier Power of storage, and power of giving out of accumulators 208 CALCULATION OF ELECTEO- CHEMICAL DEPOSITS. Chemical and electro -chemical equivalents Calculation of the e. m. f . of polarisation in an electrolyte Electrolysis of water Calculation of the e. m. f. of cells Electrolysis without polarisation 211 ELECTRO-METALLURGY. Electrotyping. Copper Moulds General management of baths and currents Density of current Copper cliches or electrotypes . Electroplating. Coppering Brassing Gilding Silvering Sil- vering table plate Nickeling 215 THERMO-ELECTRICITY. Thermo-electric power Inversion Neutral point Formula . nd table for the calculation of thermo-electric power Bismuth -copper battery Noe"'s battery Clamond's battery 222 HEATING ACTION OF CUEEENTS. Loss of energy in a conductor Heat disengaged Limit of diameter of wires Heating of a conductor Heating of equal and similar coils Electric light. (See also page 260) 226 MECHANICAL GENERATOES OF ELECTRICITY. Definitions Work expended Electrical energy produced Avail- able electrical energy Heating of the machine Relation between the external and internal resistances ...... 228 TABLE OF CONTENTS. Xlll PAGE Classification of machines Methods of excitation Qualities Field magnets Armatures Conditions to be aimed at in a powerful machine Influence of speed on work absorbed Characteristic Critical speed Lead of brushes Use and influence of the iron ring Maintenance of the brushes and commutator Thickness of wire Working conditions 230 Continuous current machines. A Gramme, Heinrichs, Gulch er, Schukert, Siemens, Edison, Edison-Hopkinson, Biirgin, Brush, Elphinstone- Vincent 236 Alternating current machines. Siemens, Ferranti - Thomson, de Meritens 243 Measurement of current strength and e. m. f. of alternating cur- rent machines Methods of MM. Joubert and Potier . . . 245 ELECTROMOTOES. Alternating, pole-reversing, and continuous.current Electrical work Heating Mechanical work Motor driven by a battery Deprez's and Trouve's motors Gramme machine with permanent magnets Gramme and Siemens' dynamos Ayrton and Perry's motors 247 TRANSMISSION OF POWEB. Principle Theoretical case Practical case Electrical, mechanical, and commercial efficiency 251 Theoretical limit of the work transmitted by a line of given resistance 253 Gramme machines Marcel Deprez's experiments between Miesbach and Munich, and at the Gare du Nord at Paris, and at Grenoble . 255 Useful formulse 257 ELECTEIC LIGHT. Voltaic arc. Classification Monophotal and polyphotal lamps Hand apparatus Lamps regulated by current strength, by shunts, by differential action Various lamps Alternating and continuous currents 260 Eesistance of the arc Energy absorbed 262 Carbons, bare and plated ......... 262 Gramme machines and lamps used in the French navy . . . 264 Abdank-Abakanowicz and Gulcher lamps 265 Tests at the Paris Electrical Exhibition in 1881. Machines and lamps of Gramme, Jurgensen, Maxim, Siemens, Biirgin, Siemens, Weston, and Brush 265-7 Electric candles. Jablochkoff, Jamin, and Debrun .... 265 xiv THE ELECTRICIAN'S POCKET-BOOK. PAGE Sun lamp 268 Incandescence. Semi-incandescent lamps of Eeynier and Werder- mann 269 Pure incandescent lamps of Edison, Maxim, Swan, Lane-Fox, and Siemens and Halske High resistance lamps Low resistance lamps -Nothomb's lamp Bernstein lamp Small lamps, for electric jewels 270 TELEGRAPHY. Overhead lines. Conductors, joints, insulators Insulation Loss Office wires Earth and earth wires . . . . 274 Underground lines. Cables Berthoud and Borel's cables Brook's cable 279 Submarine lines. Table of details of the principal recently con- structed cables 280 Instruments. Classification Visual, acoustic, registering, printing, autographic, and speaking High speed instruments . . . 281 Electro-magnets Means of avoiding the extra current on break- ing circuit Strength of telegraphic currents in France and India . 283 Range of electro -magnetic receivers Sensibility Siemens relays Local sounders Portable sounder 285 Dial telegraph Morse instrument Signals of the Morse instrument 287 Hughes telegraph Wheatstone automatic instrument Speed of transmission of telegraphic instruments 288 TELEPHONY. Magnetic and battery transmitters Receivers Line Induction Losses on the line Distance of transmission Work of batteries in use with microphones System of simultaneous telegraphic and telephonic transmission of Van Rysselberghe .... 289 FIFTH PART. Recipes and Processes. Alloys and amalgams. Fusible alloys Instrument makers' alloys Aluminium -^bronze Silvering for curved mirrors Tombac Romilly's brass Nickel coins Alloys for soldering . . . 293 Slight metallic deposits. To give copper the appearance of platinum Platinisedfsilver Platinised carbon Platinised iron Amalga- mation of iron and zinc Silver black Gilt plumbago . . . 294 Various stores. Cyanide of potassium Chloride of gold Porous pots Morse paper Copper sulphate Chloride of ammonium TABLE OF CONTENTS. XV PAGE (sal-ammoniac) Dextrine Black oxide of manganese Commer- cial copper and zinc sulphates Purification of commercial sulphuric acid Gilder's verdigris Purification of graphite . . 296 Magnetic figures 298 Joints and soldering of wire ........ 299 Varnish and insulators, Red varnish Agglomeration of wires Coating of external wires of large electro-magnets Cement for induction coils Varnish for silk Varnish for insulating paper Insulating mixture for coils of electrical instruments Clark's and Chatterton's compounds ....:.... 300 Cements. For insulators, Muirhead's, black, Siemens' Marine glue Cement to resist heat and acids Waterproofing of wooden battery cells Gaston Plante's cement Cement for bone and ivory 302 Various. Ebonite Waterproofed vats for electro -plating Turner's cement Composition for rubbing the cushions of fric. tional electric machines Cleaning copper and its alloys Cleaning articles for nickel plating ........ 303 Deposition of copper on glass Temporary drills and tools Black bronze Green or antique bronze Medal bronze Bronzing iron Preparation of carbon for electric light Solution for paper of chemical telegraphs Translation of Morse signals into letters Fixing wires for electric house bells Spray producer Static in- duction machines Ink for writing on glass Ink for engraving on glass Coppering by simple immersion 306 BIBLIOGRAPHY 312 INDEX OF TABLES . , 315 Dept. Mech. Eng. THE ELECTRICIAN'S POCKET-BOOK. DEFINITIONS, PKINCIPLES, GENERAL EULES. THE physical phenomena, the study of which is included under the title of electricity and magnetism, can be subdivided into several groups, which, for want of a better classification, may be investigated in the fol- lowing order : (1) Magnetism. The action of magnets on magnetic bodies, and of one magnet upon another. (2) Static electricity. The action of electrical charges. (3) Dynamic electricity, or electricity in motion. Laws of currents, chemical action, and heating effects. (4) Electro-dynamics. Action of currents on each other. (5) Electro-magnetism. Magnetic actions produced by currents. (6) Induction. Currents produced in closed circuits by electrical or magnetic actions outside those circuits. We will adopt this order in the explanation of electrical laws, methods of measurement, and practical results. This classification does not, perhaps, present all necessary qualities from a scientific point of view, but it has the advantage of establishing convenient subdivisions, which facilitate research, and, to a certain extent, prevents confusion between the different subjects. MAGNETISM. The name magnet is given to all bodies capable of attracting iron. The properties of magnets, taken as a whole, and their investigation, constitute the science of magnetism. Magnets may be divided into three classes : (1) Natural magnets. Magnetic oxide of iron, or magnetite Ee 3 O4, or loadstone. B 2 DEFINITIONS, PRINCIPLES, LAWS. (2) Artificial maynets. Tempered or compressed steel. (3) Electro-magnets. More or less pure iron, magnetised by the action of a current. Artificial magnets are made, according to the purpose for which they are to be used, in the form of bars, needles, horse-shoes, and U's. A magnet has always at least two poles. The axial line, or magnetic axis, is the line joining the poles of the magnets ; the equatorial line is that which is perpendicular to it. In a magnetised needle, the pole which turns towards the north is called the north pole, austral pole, marked pole, or Airy's red pole. It is indicated by the letters N or A. The pole which turns towards the south is called the south pole, boreal pole, non-marked or Airy's blue pole. It is indicated by the letters 8 or B. Magnetic or paramagnetic bodies are those which, without magnetism of their own, are attracted by magnets. Liamagnetic bodies are, on the contrary, repelled by magnets. Of magnetic action. Two poles of the same name repel each other ; two poles of different names attract each other. The f o rce exerted between two magnetic poles m and m' is proportional to the product of their intensities, and inversely proportionate to the square of the distance (d) between them ; _ mm ~' The unit pole, or unit of magnetic quantity, is that which, at the unit distance from a similar pole, exercises an action equal to one unit of force. The portion of space which is under the influence of a magnet is called the magnetic field. The intensity of the magnetic field at a given point is equal to the force which the unit pole would exert at that point. The direction of the force is that in which a pole is urged by the magnetic field, or is that which a short magnetised needle, balanced and freely suspended, would take up when placed in the field. The space which surrounds a magnet, which is called the magnetic field, is found to be in a particular condition characterised by the presence of lines of force. This magnetic field is defined when we know the number of lines of force, their form, and their direction at each point of the field. These lines of force, in the simplest case (that of a magnetised bar) spread out in several directions, returning to the opposite end to that from which they started, and return through the interior of the mass of the bar. By defining a given line of force as the trajectory described by a north pole or marked pole moving freely under the influence of the magnet, the MAGNETISM. 6 direction of the line of force will be : From the north pole to the south pole in the magnetic field ; from the south pole to the north pole within the magnet. Fig. 1. Magnetic Field. The above sketch shows, roughly, the direction and form of the lines of force of a field produced by a magnetised bar. These lines of force have a real existence, as is shown by magnetic figures, and possess the following properties : Properties of the lines of force. (1) Lines of force tend to becomer shorter. (2) Lines of force which are parallel and in the same direction repel each other (Faraday) , (3) A line of force passing through a magnetic body may be considered as magnetically shorter than a line of force of the same length passing through air. The investigation of magnetic figures confirms these theories of Faraday's in every case, and explains the mutual attractions and repulsions of magnets. A uniform magnetic field is that of which the intensity is the same at all points, and in which the lines of force are straight, parallel, and equidistant. The magnetic action between two magnets, of which the lengths may be neglected as compared with the distance between them, is inversely proportional to the cube of the distance between them (Gauss). The magnetic action between a suspended magnet and a mass a cting upon it are proportional to the square of the number of oscillations which the magnet would make in a given time under their action alone, and inversely proportional to the square of the time which the magnet takes to make one complete oscillation (Coulomb}. Absolute moment or magnetic moment of a magnet. Let m be the in- tensity of one of the poles of a magnet, and I the distance between the poles, its moment is the product ml. Intensity of magnetisation. The intensity of magnetisation is the ratio of the magnetic moment of a magnet to its volume. The properties of a magnetic field may be expressed numerically by DEFINITIONS, PRINCIPLES, LAWS. showing the intensity of the field and the direction of the magnetic force at every point. By tracing the direction of the force at each point of the field lines of force are obtained, and by making the number of these lines of force proportional to the intensity of the field at each point, a graphic representation of the field is obtained which is very useful in the investiga- tion of magnetic actions and induction effects. This mode of represent- ing a magnetic field is due to Faraday. When a magnetised bar, whose moment is ml, is placed in a uniform magnetic field of intensity H perpendicularly to the lines of force, a couple G is produced proportional to the intensity of the field, to that of the poles m, and to the distance between them I. G = mlH. This couple tends to turn the needle round and cause its magnetic axis to take up a position parallel to the lines of force of the field. Magnetic induction. A magnetic body placed in a magnetic field is magnetised in the direction of the lines of force of the field. Its magnetism is called induced magnetism, and the action itself is called magnetic induction. The magnetism retained by a magnetic body after it has been withdrawn from the field is residual magnetism ; the unknown cause of the residual magnetism is called coercive force. Coefficient of induced magnetism, or magnet- ising 1 function. Let H be the intensity of a magnetic field, 7 the intensity of magnetisation ; the magnetising function k is given by the equation "H It is proportional for very small values of H ; beyond such values k is a function of H, which diminishes when H increases, and tends towards a final value, which is called the limit of magnetisation. TEKRESTRIAL MAGNETISM. When considering its magnetic action, the earth may be looked upon as a vast magnet, whose marked pole, or " north pole," is at the south. Magnetic meridian. A vertical plane passing through the magnetic axis of a magnetised needle, suspended by its centre of gravity. Declination. The angle which the magnetic meridian makes with the terrestrial meridian.* * Sailors sometimes call this angle the variation of the compass ; but this term is incorrect. STATIC ELECTRICITY. Inclination. The angle made by a magnetised needle with the horizon in the magnetic meridian. Intensity. The value of the terrestrial magnetic force which is resolved into horizontal intensity and vertical intensity. Isoclinic lines. The locus of the points of equal inclination. Magnetic equator, locus of points of no inclination. Magnetic poles, points where the inclination is 90. Isogonic lines, locus of the points of equal declination. Agonic lines, locus of the points of no decimation. Isodynamic lines, locus of points of equal intensity. Variations. Hourly, diurnal, annual, secular, etc., changes which occur in the value of the elements of terrestrial magnetism. Magnetometers and magnetographs. Apparatus by which the values and variations of terrestrial magnetism are measured and registered. To neutralise the directive action of the earth on a magnetic needle. (1) A magnetic bar is placed above the needle in the plane of the magnetic meridian, so as to act in a contrary direction to the earth. By varying its distance from the needle the action of the earth may be entirely, or in part, neutralised ; the oscillations of the needle become slower as the directing force diminishes. (2) By using astatic needles ; two needles nearly equally magnetised and mounted on the same pivot, with their contrary poles superimposed. (See their use in Third Part.) STATIC ELECTRICITY.* Statical electricity is manifested on electrified bodies under the form of a charge. The quantity of electrification of the body gives the measure of its charge, and the nature of this charge with respect to the surrounding space determines its sign. The production of a charge of a given sign on a body always determines the production of an equal charge of opposite sign on another body. By convention the charge taken by glass rubbed with silk is called vitreous electrification, positive (-}-), positive fluid, or positive electricity. The charge taken by resin, gum, indiarubber, or yellow amber rubbed with flannel is called resinous negative ( ), negative fluid, or negative electricity. Bodies which show no sign of electrification are said to be in a neutral state. * For a long time the name of f fictional electricity was given to a group of phenomena produced by electrical charges. This is an improper expression, because friction is only one means (it is true, that which is most employed) for producing electrical charges. Dept. Mech. Engf; O DEFINITIONS, PRINCIPLES, LAWS. Laws of electrical attraction and repulsion. Two bodies whose charges are of the same sign repel each other ; two bodies whose charges are of a contrary sign attract each other. The attraction or repulsion of two charged bodies is proportional to the product of the charges, and inversely proportional to the square of the distance (Coulomb'). Calling the charges qq', and the distance between them d, the force/ is given by the equation The sign -\- indicates an attraction ; the sign repulsion. Distribution of electrostatic charges. The charge of a conductor is on its surface. It is distributed uniformly over a sphere, and accumulates on points, edges, etc. The distribution of a charge is defined by the electrical density at each point ; that is to say, the quantity of electricity per unit of surface at each point. The potential of a charged body is the measure of its electrification. The electrostatic capacity of a body is measured by the quantity of electricity or charge which must be communicated to it to raise its potential by one unit. The following relation exists between the potential V of a body, its charge Q, and its capacity C. Q Electrostatic induction. The action exerted by a charged body on another body in the neutral state placed at a distance. In every body in the neutral condition induction precedes attraction. Induction depends on the nature of the medium which separates the two bodies, which is called the dielectric. This influence is a measure of the inductive capacity of the medium. Specific inductive capacity, or dielectric capacity. The ratio between the capacity of two condensers of the same dimensions, of which one is an air condenser and the other has for its dielectric the substance of which the specific inductive capacity is sought. The specific inductive capacity of dry air at C. and at a pressure of 76 centimetres of mercury (see figures in Fourth Part) is adopted as the unit. CONDENSERS. CONDENSEKS. Two conductors of any form separated by an insulator or dielectric, and having charges of opposite signs, form a condenser. The Leyden jar is a condenser, so is a submarine cable. The common condensers which are used in induction coils, and as standards of capacity, are in general composed of sheets of tinfoil separated by insulating sheets (of paper, mica, etc.). These tinfoil sheets act like the internal and external coatings of a Leyden jar. Capacity Of condensers. This capacity is measured by the quantity of electricity which the condenser contains when charged by the unit of potential. In the electrostatic system the units have been choeen so that the capacity of a spherical insulated conductor is numerically equal to its radius. The C.G.S. unit of electrostatic capacity is the capacity of an insulated spherical conductor of one centimetre radius. In the electro-magnetic system (the only one which is employed in practice) the unit is the farad, a condenser which, when charged to the potential of one volt, contains one coulomb of electricity. In practice the micro- farad is most commonly used. (See Second Part.) Charge Of a condenser .-^The charge Q taken by a con- denser is equal to the product of its capacity C by the e. nl. f . E by which it is charged. QrrCE. Example. A condenser of 0'5 of a microfarad charged to a potential of 150 volts would contain 0'5 x 150 = 75 microcoulombs of electricity. Charge taken by two condensers. Two condensers of capacity C and C', connected one to the (-{-) pole, the other to the ( ) pole of an insulated battery, their other armatures being to earth, take equal charges of a contrary sign (-f- q and q}. The relations between the charges, the capacities and potentials v and v', are the following, E being the e. m. f. of the battery : q =. cv q cV v v' E. EC' EC E <=^ *=;+} *=T7i c" 1 " c' Condensers joined tip for surface. Let ab c . . . be the individual capacity of each condenser, the total capacity C a -f- b 8 DEFINITIONS, PRINCIPLES, LAWS. If the condensers are charged separately with quantities, q ~ av ,C / r ' Intensity of the field produced by a circle of radius r on the perpen- dicular to its plane, passing through its centre at a distance d, Putting irr 2 =: S (area of circle of radius r) and r- -\- d? p 2 , we get, 2CS SOLENOID. 23 Solenoid. Intensity of the field on the axis. Let n be the number of turns of wire, r the radius, and 21 the length of the solenoid, and a the distance of the point M on the axis from the nearest end of the solenoid ; then, Fig. 5. Solenoid. irnC / a-}- 21 a I \ ^ r v _|_ ( a -f~27)2 ~ ^j^+a 2 Calling the angle AMO , and the angle BMO $>', TrnC _ /rr (cos <^> cos ). Intensity of the field at the centre. The intensity of the field is at a maximum at this point, 27rnC fc ~7^r-. ~"' Calling the diagonal of the solenoid 2c, Intensity of the field produced by an infinitely long rectilinear current. Let r be the distance of the point under consideration from the current, Intensity of the field produced by a plane closed circuit. First, at a point on the normal passing through the centre of gravity of the area of the closed circuit, and at distance d, ' 2SC f =~&' 8 being the area of the circuit. Dept. Mech, 24 INDUCTION : LAWS. Second, at a point in the plane of the circuit at distance d from its centre, /= sc - J d* on by currents. A wire traversed by a_ current possesses temporary magnetic properties. When an insulated wire is wound a great number of times round a piece of soft iron, the passage of a current develops a powerful magnetisation, which ceases when the current is interrupted, if the iron is very soft. This is an electro -may net, of which the power varies with the dimensions, the strength of the current, and the number of turns of wire, etc. (See Fourth Part.) When the iron is not perfectly soft, it retains some residuary magnetism when the current is interrupted. Rule for finding* the poles of an electro-magnet. When a current passes through the wire of the electro-magnet, if we look at the end of each pole, the south pole is that one at which the current circulates in the direction of the hands of a watch, and the north pole (marked pole) that at which the current circulates in the reverse direction. This is in accordance with Ampere's hypothesis of molecular currents. INDUCTION. Every relative displacement of a conductor and a magnetic or galvanic field produces an electromotive force in the conductor, and if the con- ductor form part of a closed circuit, an induced current is set up in it in consequence. A magnet producing a magnetic field is in this car 3 called a field magnet, and a circuit producing a galvanic field is called a primary circuit. The conductor in which the current is induced is called an armature if the induction be produced by a magnet, and a secondary circuit if the induction be produced by a current. Induced currents may be produced either by relative mechanical displacement of the inducing field and the conductor (magneto- and dynamo-electric machines) or by variation of the galvanic field produced by the current passing through the primary circuit (induction coils). The induction of a current on its own con- ductor is called self-induction, and the current induced in a conductor by making or breaking circuit is called the extra current. Induction produced in a rectilinear circuit displaced parallel to itself in a uniform mag- netic field. Electromotive force of induction. "Let e be the e. m. f . INDUCTION IN A CLOSED CIRCUIT. 25 due to induction, H the intensity of the magnetic field, I the length of the rectilinear circuit, v its velocity, a the angle made by the conductor with the direction of the lines of force, ^ the angle between the direction of motion and the direction of the force exerted between the magnet field and the circuit ; then, e =1 ~S.lv sin a cos . If the conductor be moved in the direction of the force, <(> =r o .'. cos <> 1, and e ~H.lv sin o. Energy of induction. Let t be the time in which the displacement takes place, and W the energy of induction, _ H 2 V f 2 1 sin?acos2. CM Oi i-H Oi O O Tfi 'iffl pnooas ami osay s. 00 * TH CM CO CO CM CM no r-l S.KOSKOHJ, ei co co' i>l 06 oi o i-! . CO E S S 4fi S d3 N Q a a rH | 1 | | "^ M i i -4J O t? S 1 I I i M" g a 1 1 M 1 2 "i s ^ PH O ^ i 1 I i i g & & 2 .2 g 00 03 O 15 -c"ondenf e r ^ so as to vary the capacity and facilitate measurements. Fig. 16 shows the upper part of a condenser of one microfarad divided into five parts as follows : 05 -03 -2 -2 -5, CONDENSERS. 65 Construction of one - microfarad condenser (Culley). Requires 37 sheets of good tinfoil, 184 millimetres by 152, separated from each other by two leaves of very thin hot-pressed paper, such as is used for bank notes. The two series are composed respectively of eighteen and nineteen sheets of tinfoil. The one with nineteen leaves forms the exterior of the condenser, and is connected to earth. The Fig. 16. One Microfarad divided into Five Parts. additional leaf has the effect of neutralising the effects of the induction of neighbouring objects. Tho paper should be thoroughly dried, and soaked in paraffin, either by immersing it in a bath of melted paraffin or painting it over with a camel-hair pencil. In order to construct this condenser a plate of sheet iron is taken, a little larger than the sheets of paper, and mounted on four legs, so that it may be heated from below by means of a gas jet. Its surface ought to be plain, and polished, with a groove round the edge to receive the excess of paraffin. The paper is cut out in sheets large enough to stick out beyond the sheets of tinfoil about 25 millimetres all round. The two upper corners of each sheet are turned up, one of the corners of the metallic sheets is also turned down. They are spread out with care, and joined into two series, one of eighteen and the other of nineteen sheets, by soldering together the corners which are not turned up opposite to the turned up corners of the same side of the sheets, so as to make two distinct books of them. A sheet of the paper is laid on the warm plate of sheet iron ; it is covered with melted paraffin with a very silky camel-hair pencil ; on this is laid the first tinfoil sheet of the book containing nineteen sheets. This sheet is then covered with varnish ; on it is placed two sheets of the paraffined paper. On this paper is placed the first sheet of the series of eighteen sheets, so that the soldered corners correspond to the turned up corners of the paper, and are opposite to the soldered corners of the other seiies. A coat of varnish and two sheets of paper are then added as before ; the second sheet of the series of nineteen is then spread out, taking care to smooth each leaf carefully as it is put 66 METHODS OF MEASUREMENT. into its plao3. When the apparatus is constructed it is placed between two hot metal plates and submitted to a pressure of 400 kilogrammes to squeeze out the excess of paraffin and make the whole compact. By this means the alteration in the capacity of a condenser is avoided, which would be produced by any alteration in the distance between the metal plates. Two thicknesses of paper are used in order to ensure good insulat on, which might be destroyed if there were any small hole or break in the paper. Care must be taken to arrange a battery of one to ten elements, and a galvanometer between the two series of metallic plates so as to observe whether the insulation remains perfect whilst the con- denser is being built up. "When the condenser has become quite cold its capacity is verified by some suitable method. If the capacity is too small it is increased by applying pressure. If this method is insufficient more tinfoil leaves must be added ; if, on the other hand, the capacity is too large, a few tinfoil leaves are removed. When the operation is finished, the condenser is placed between two wooden mounts joined by two wooden screws, which keep up an invariable pressure ; the whole is then placed in a box carrying two binding screws connected to the two armatures of the condenser. The same method is employed for mica condensers, but the elasticity of this substance causes their capacities to vary with the pressure to which they are subjected. For equal volume a mica condenser has a larger capacity than a condenser with paraffined paper, because the inductive capacity or inductive power of mica is greater than that of paper. ACCESSOEY APPARATUS FOR ELECTRICAL MEASUREMENTS. Circuit breakers and commutators are used to make and break electrical connection between the different measuring Fig. 17. Plug Circuit Breaker. Fig. 18. Battery Commutator. apparatus. They are made both with keys and with plugs, and for one or more directions as may be required. The form known under the name COMMUTATORS KEYS. 6T of battery commutator is a very convenient form when it is necessary to vary the number of elements in circuit rapidly. Reversing Commutators. The simplest form is composed of four thick brass quadrants screwed to a plate of ebonite, and not touching each other, having semicircular slots cut out in them, in which brass plugs may be introduced to make electrical contact between the quadrants. Fig. 19. Plug Reversing Commutator. Fig. 20. Reversing Key. Reversing keys are used to connect the galvanometer to other measuring apparatus. The contacts are so arranged that when one of the springs is pressed down, the current flows in one direction, and when the other is pressed down, in the reverse direction. Two other keys enable the springs to be wedged, so that permanent contact can be maintained when necessary. Short-circuit key Or tapper is connected between the terminals of the galvanometer, to prevent cur- rents of too great strength accidentally passing through the coils. In its normal condition the spring presses against a platinum contact; and when pressed down, against an ebonite contact. A mov- able stop enables the key to be kept down permanently when it is necessary. Fig. 21. Short-Circuit Key or Tapper. 68 METHODS OF MEASUREMENT. Discharging key, used in measurements with condensers. The most commonly used is Sabine's. It has three keys. The first puts the condenser in circuit ; the second insulates the condenser ; the third connects the condenser and the galvanometer. Fig. 22. Sabine's Discharging Key. Double Contact key is used in bridge measurements with ordinary bridge boxes. The connections are so arranged that the first contact closes the battery circuit, and the second the galvanometer circuit almost immediately one after the other, and this is effected by pressing down one key only. GENEEAL METHODS OF MEASUREMENT. Methods of measurement may be divided into two great classes : (1) Direct methods, in which a quantity to be measured is compared to a quantity of the same kind by one of the three following methods : a. By opposition. b. By substitution. c. By comparison. (2) Indirect methods, in which the magnitude of the quantity to be measured is deduced from the value of two or more other known quantities by means of a known relation. (Example : Heat disengaged in a voltaic arc, resistance of a conductor, when the strength of a current passing through it and the difference of potential between its two ex- tremities are known.) MEASUREMENTS OF CURRENTS. 69 a. Differential, zero, equilibrium or balance, opposition methods. These consist in opposing the unknown magnitude by a known magnitude and reducing to zero, or compensating the effect of the unknown magnitude by variations of the known magni- tude. When equilibrium is established, the equality of the magnitudes is shown by the equality of the effects. In this case we have to observe the non-existence of a phenomenon. The instrument does not require a scale, but a variable standard or graduated standards are necessary. The type of this method is the ordinary process of weighing. In electrical methods, we may take the Wheatstone bridge method as a type. In this it is only necessary to be satisfied of the equality of potential between two given points ; for this purpose galvanoscopes, galvanometers, electrometers, etc. , may be employed. The accuracy of the measurement depends upon the sensibility of the instrument which shows the equality of the potential between the two points under con- sideration. b. Substitution methods. The effect produced by the quantity to be measured is noted, and a known magnitude, capable of producing the same effect, is substituted for it. The instrument of observation must be graduated. The graduation may be arbitrary, but again it is necessary to have a variable standard or graduated standards. Sometimes one or both of the two effects is reduced in a known propor- tion, so as to bring the indications within the limits of the scale, or to that part of the scale at which the instrument is most sensitive. e. Comparison methods. First of all, the effect is measured of a known fixed magnitude, then that of an unknown magnitude. The ratio of these magnitudes is deduced from the ratio of their effects. A calibrated measuring instrument is necessary, or a fixed standard, but these are not necessary if we know the constant of the instrument, and the relation which connects the magnitude to be measured with the readings of the instruments. (Example : Sine galvanometer, tangent galvanometer, etc.) MEASUREMENT OF CURRENTS. Currents are measured by their electro-magnetic, electro -dynamic, or electro -chemical actions. There are these three classes of measuring instruments : (1) Galvanometers, based on electro -magnetic action. 70 METHODS OF MEASUREMENT. (2) Electro-dynamometers, based on the action of currents or electro- dynamic action. (3) Voltmeters, based on chemical action. (1) GALVANOMETEBS. Every apparatus in which a magnetised needle is deflected by a current forms a galvanometer. A galvanometer is a galvanoscope when it indicates the passage of a current without measuring it. In zero methods galvanometers act as galvanoscopes. Galvanometers are based on a discovery made by (Ersted, in 1819, and on Schweigger's multiplier. The application of astatic needles to galvanometers is due to Nobili, and that of the reflecting mirror to Sir Wm. Thomson. Galvanometers vary almost infinitely both in form and arrangement. We will only describe those most in use, but we will first point out the general principles which have been applied to them, and which, when they have a considerable importance, give the name of the instrument. Absolute galvanometer. Enables the strength of a current to be directly measured in terms of the dimensions of the galvanometer and of the horizontal component of terrestrial magnetism. Astatic galvanometers. The directive force of the earth is diminished, so as to increase the sensibility of the instrument, either by means of a directing magnet or by a pair of needles forming an astatic system. Balistic galvanometer. The measurement is made by the impulse on the needle produced by the action of a momentary current. Calibrated galvanometer. The graduation of the scale is made, not in degrees, but in terms of the strength of the current, or the ordinary gradation in degrees is accompanied by a reduction table. Current galvanometers. A galvanometer in a circuit which measures directly the strength of the current passing. Dead-beat galvanometer. The needle goes to its position of equilibrium almost without vibrating. Differential galvanometers measure the difference of the action of two currents on a magnetised needle. E. m.f. galvanometer. A galvanometer formed of relatively fine wire, placed as a shunt between two points of a circuit, the difference of potential between which is to be measured (indirect measurement) . Fine wire or tension galvanometer. These are unscientific names expressing the nature of the wire with which the coils are wound. This nomenclature is disappearing and giving place to the indication of the resistance of the galvanometer in ohms. Mirror galvanometer, or reflecting galvanometers. The index is formed by a. ray of light. GALVANOMETERS. 71 Quantity galvanometers have thick wire. Sine galvanometer. The law of deflection is connected with the sine of the angle of deflection. Tangent galvanometers. The law of deflection is connected with the tangent of the angle of deflection. Torsion galvanometer. The action of the current is balanced and measured by the torsion of a rod or wire. It may be seen by this enumeration that the name of a galvanometer only defines its principal property, and that any given galvanometer may present several different properties to the same degree. The choice of an instrument to be used depends upon the nature of the measurements to be performed, the desired degree of accuracy, and the kind of people who have to make use of it, etc. Galvanometers are also sometimes called multipliers or rheometers, but these terms are disappearing. Sine galvanometer is composed of a vertical galvanometer coil, in the centre of which is placed a magnetised needle, free to turn in a horizontal plane. The plane of the coil is placed in the plane of the magnetic meridian, i.e. parallel to the needle. The current is then passed through the coil ; the needle is deflected ; the coil is then turned in the direction of the deflection until the needle again becomes parallel to the coil. The strength of the current is proportional to the sine of the angle through which the galvanometer coil has been turned, whatever may be the relative dimensions of the needle and the coil, and whatever may be the shape of the coil. Sine galvanometers are very sensitive, because the coil may be very close to the needle, but the observations require more time than those made with other instruments ; each move- ment of the coil producing a deflection of the needle, some time is re- quired in order to get the needle and coil parallel. The sensibility increases with the deflection. Tangent galvanometer. When a very small magnetised needle is placed in the centre of a circular galvanometer coil of very large dimensions, and the axis of the needle is in the plane of the coil, it may be shown that the tangent of the angle of deflection is sensibly proportional to the strength of the current passing. The maximum sensibility is at O 3 ; the sensibility disappears at a deflection of 90. It is necessary, therefore, to measure very small angles, and to compensate for the smallness of the deflection by the accuracy of its measurement, or by the employment of Thomson's reflecting galvanometer (page 73). Gaugain's conical multiplier. A galvanometer coil 72 METHODS OF MEASUREMENT. forming a short frustum of a right cone, at the apex of which the needle is placed ; the height of the cone is equal to half the radius of the base. Helmholtz has shown that the effect is doubled by having two coils placed symmetrically on each side of the needle ; this forms the tangent galvanometer which approaches most nearly to the theoretical conditions. For a galvanometer with one coil we have : C represents the strength of the current ; 8 the angle of deflection ; a the radius of the base ; n the number of turns in the coil ; H the horizontal component of the earth's magnetism. In order to get an absolutely uniform magnetic field at the centre of the needle, three vertical parallel coils must be used, the centre one larger than the other two, so that all three lie on the surface of a sphere of which the small needle occupies the centre. Post-office tangent galvanometer, for telegraphic measurements, is formed of a circular ring of brass 15 centimetres in diameter, on which the coils are wound ; the needle is about 18 milli- metres long, which practically gives sufficient accuracy. The needle carries, at right angles to its axis, an index 12 centimetres long, which moves above a scale with two graduations, one in degrees on one side of the ring, the other in tangents on the other side. To prevent errors of parallax in reading, a piece of looking-glass is placed in the plane of the graduated ring, which reflects the index ; when a reading is taken, the image of the index must be concealed by the index itself. The ring carries three coils, one composed of only three turns of thick wire, the other two have each a resistance of 25 ohms. At pleasure any one of the coils may be used separately, or two coils in series, or two coils parallel, according to the nature of the currents to be measured. Schwendler's tangent galvanometer, used in the Indian telegraph service. This is a tangent galvanometer with two coils, one of 1 ohm and the other of 100 ohms. The one- ohm coil is accom- panied by two resistances of 20 and 200 ohms, which may be added to the circuit. The one -hundred ohm coil has also two similar resistance coils of 1,000 and 2,000 ohms. The instrument has also a reversing key, so that readings may be taken on both sides of the scale ; two plugs to introduce one or the other of the coils into the circuit, and two terminals for the attachment of the wires. For the measurement of very powerful currents the copper ring which supports the coils is cut in two, and its extremities connected to two other terminals, and thus forms a third coil. GALVANOMETERS. 73 The length of the needle is not more than one -fifth of the diameter of the coil. This needle carries an aluminium index fixed at right angles to its axis, and provided with wings of the same metal to check its oscillation. The whole is enclosed in a cubical box of 15 centimetres side. The closing of the box automatically raises the needle, and disengages it from the pivot. With one DanielPs cell the 100 ohms coil and 2,000 ohms resistance in the circuit, the deflection is 5; one half of the scale is graduated in degrees, the other half in tangents. Ofoaeh'S galvanometer. A tangent galvanometer, the coils of which can be inclined from the vertical position. When the coils are inclined at an angle 0, if 5 be the deflection, the current is proportional to tan 8 sec 0. The angle through which the coils are turned is read on a divided quadrant by means of a vernier. The instrument is provided with one coil of very low resistance, and one of very high resistance, so that it can be used both as an ''ammeter," and a "voltmeter"; the power of varying the constant of the instrument by inclining the coils gives it a very wide range of utility, enabling both small and large currents and differences of potential to be measured by one and the same instrument. , Siemens' universal galvanometer. An instrument in which a set of resistance coils, a wire Wheatstone-bridge, and a galvanometer with movable coils, which forms a sine galvanometer, are included in one piece of apparatus. All telegraphic measurements of resistance of e. m. f . and current strength can thus be performed with the same piece of apparatus, the wire bridge being convertible into a Clark's potentiometer. Sir William Thomson's reflecting galvano- meter. This is the most sensitive apparatus known for measuring small currents and high resistances. It varies very much in form, but in principle it is composed of a light magnetic needle suspended in the centre of a large coil of wire ; and of a reflecting system which enables the deflections of the needle to be amplified. A long index is formed by a ray of light reflected upon a divided scale by a little mirror, which is attached to the magnetic needle. The deflections always being very small, and the coil relatively large, the deflections are always sensibly proportional to the strengths of the current. It is constructed either astatic, dead-beat, or differential, etc. In the non-astatic form it is composed of four little magnets from 4 to 5 millimetres in length, cemented to a small mirror. The diameter of the 74: METHODS OF MEASUREMENT. mirror is about 6 millimetres, and the total weight of the mirror and needle together is not more than 7 centigrammes. The object of multi- plying the number of needles is to obtain the maximum of magnetisation with the minimum of mass, because the needle comes more readily to zero as its magnetisation is greater. The mirror is suspended by a cocoon fibre, and placed in the centre of a coil enclosed in a cylinder of brass. The front face is closed by a plate of glass. The cylinder is supported on a tripod with levelling screws, by which the instrument can be levelled. A slightly curved directing magnet, supported by a vertical rod fixed on the case of the instrument, forms an artificial meridian, of which the strength and direction can be varied by causing it to slide up or down, or turn round on the rod, so as to act with more or less force upon the suspended magnet, and so vary the sensibility of the instrument. Regulation of the sensibility of the galvanometer. When the poles of the directing magnet are arranged like those of the terrestrial magnet (the marked pole to the south) its directive force is added to that of the earth, and the sensibility of the apparatus diminishes. By turning this magnet through 180, its directive force is opposed to that of the earth, and the sensibility increases. To get the maximum of sensibility the magnet is lowered until the two actions neutralise each other, then it is slightly raised so as to preserve a slight directive force to bring the luminous index back to zero. Thomson's astatic galvanometer. The astatic system is only employed in instruments wound with a very long wire, each needle separately being surrounded by a coil, and the current passing in opposite directions in each coil. As the whole system is rather hea v y the lower needle has attached to it a small lozenge-shaped plate of aluminium to damp its vibrations ; the adjustment of the position of the directing magnet is con- trolled by means of a tangent screw. The square or cylindrical box enclosing the apparatus has an opening to contain a thermometer and is also provided with a spirit level, which enables the system to be put in a perfectly vertical position. Each of the coils is composed of two parts separated by a vertical plane. The astatic system can thus be withdrawn for adjustment or repair of the cocoon fibre, etc. There are thus really four distinct coils, which are in connection with eight terminals placed on the foot plate. According to the way in which these terminals are connected the coils may be grouped in series, parallel, or with two coils parallel, and the two systems of two coils in series, so that the resistance of the galvano- meter can be varied according to the measurements which have to be made. The shunts which accompany a galvanometer always correspond to GALVANOMETERS. 75 the arrangement of the coils in series. The cocoon fibre is attached to a knob which can be raised or lowered at pleasure. When it is lowered the needles rest on the coils, and the instrument may then be removed without risk of breaking the fibre. The readings of the deflections of the galvanometer are made by means of a lamp, divided scale, and mov- able mirror. The arrangements being the same for all reflecting apparatus we will describe it once for all. Lamp, scale, and mirror. An arrangement devised by Sir "William Thomson for observing and measuring very small angular de- flections, which is applied to all reflecting apparatus, galvanometers, electrometers, etc., and in which a ray of light acts as a long index without weight, and therefore without inertia. A movable mirror is fixed to the apparatus of which the deflections are to be measured, a lamp and scale are placed before it at a variable distance, generally 60 to 80 centimetres, the light of the lamp passes through a narrow slit cut in the base of the scale, falls on the movable mirror, is reflected from it, and returns, forming a small luminous image on the upper part of the scale ; the least movement of the mirror displaces the image along the scale. The distance passed over is equal to that which an index of double the length of the distance from the mirror to the scale would pass over.* The opening is sometimes a slit, the movable image is then a luminous vertical line ; sometimes a circular hole crossed by a very fine platinum wire, stretched vertically, when the image is an illuminated circle crossed by a thin black vertical line. If the mirror is plain the light is converged so as to come to a focus on the scale by means of a lens. Sometimes the mirror is concave, which does away with the necessity for a lens. The concave mirrors being very expensive, a thin disc of silvered glass, and a lens are more often used ; microscopic covering glass answers very well for this purpose. The scale is generally divided into millimetres, and printed in black on white glazed paper ; sometimes it is formed of ground glass, and the deflections are read on the other side of the scale. When a petroleum lamp with a flat wick is used, the wick ought to be placed with its edge turned towards the slit. An incandescent electric lamp gives a very sharp image with a slit. Hole, Slot, and plane. An arrangement devised by Sir * In accurate scientific measurements this distance is sometimes 6 metres, so the deflections read upon the scale are equal to those of an index 12 inches long. The deflections being infinitely small, the strengths are exactly proper, tional to the divisions of the scale. 76 METHODS OF MEASUREMENT. W. Thomson, by which any piece of apparatus, galvanometer, electrono- meter, etc., which rests on a table by means of three levelling screws, can be removed and always replaced in the same position. The three legs are numbered 1, 2, and 3. Foot No. 1 is placed in a small hole made in the table ; foot No. 2 in a short slot, whose axis, when prolonged, passes through the hole ; foot No. 3 on the plane of the table. All error is thus avoided when the instrument is replaced after being moved. The advantage of having a slot instead of a second hole is that the arrange- ment allows of more than one instrument being used in the same place, independently of the dimensions of the instruments, if the feet of the levelling screws be all of the same diameter. By this method, therefore, one lamp and scale will answer for several instruments. Sir William Thomson's ship's galvanometer. For cable testing on board ship. The mirror and needle are attached to a stretched wire fastened at both ends, and passing through the centre of gravity of the system to prevent oscillations caused by the rolling and pitching of the ship. The apparatus is further surrounded by a thick iron cage in order to preserve the instrument from disturbances produced by external magnetic forces; a strong directing magnet of horse -shoe shape embraces the coils and directs the needles. The spot of light is brought exactly to zero by means of a small regulating magnet worked by a rack, pinion, and milled head placed behind the galvanometer. Dead-beat galvanometer. A galvanometer is called dead- beat when it rapidly takes up its position of equilibrium under the action of a current, and comes rapidly to zero when the current is interrupted. This result is obtained by many details of construction. These are the most used : (1) Surrounding the needle with a mass of copper, which damps the vibrations by the effect of the induced currents which the movement of the needle produces in its mass ( Weber) . (2) The needle is provided with a light vane, which moves in water or in air, and resists sudden movements. (3) The needle has a very small mass, and strong magnetisation, and very large directive force is applied. Sir 'William Thomson's dead-beat galvano- meter. The numerous oscillations of the mirror in ordinary galvano- meters often cause precious time to be lost in making measurements. Sir W. Thomson's dead-beat galvanometer gets over this difficulty. It is a modification of the ordinary non-astatic reflecting galvanometer. The GALVANOMETERS. 77 centre of the coil is occupied by a brass tube A, of such length that the part ab is in the middle of its length, the tube a is closed by a small plate of glass, it is tapped at one end, on which a small ring c is screwed, into which a third part of the tube, also closed by a plate of glass, is screwed so as to form a completely closed air-chamber. A small mirror m, carrying a small magnetised needle, is placed in the centre of the tube c ; the mirror is very nearly of the same diameter as the tube, only j ust having clearance. It is suspended by an extremely short cocoon fibre ; the space ab, closed by a small glass plate, is just deep enough to enable the mirror to give a good deflection on the scale. By this arrange- ment all violent movement by the action of the current is prevented ; Fig. 23. Sir W. Thomson's Dead-Beat Reflecting Galvanometer. instead of passing the point of rest, and coming back again, the spot of light travels slowly to its proper position, and stops there without passing it. When the current is interrupted the spot of light comes back to zero. The suspension being a very short fibre, the mirror does not move so freely as in the ordinary galvanometer, its sensibility is therefore not so great, but it is nevertheless quite sufficient for most purposes. It is easy to replace the fibre when it is broken. One end of the fibre being fastened to the mirror, the other end is passed through a little hole bored in c. The fibre is then stretched until the mirror is suspended, and does not touch the sides of the tube. A drop of varnish is then let fall upon the hole, which is thus closed, and the fibre fixed (Kempe). Marcel Deprez' dead-beat galvanometer. A very light soft-iron needle placed between the two poles of a strong horse- shoe magnet. The index is made of straw, hair, or aluminium. The deflections are produced by two coils of coarse or fine wire, according to the currents to be measured, placed on each side of the needle. The mathematical expression of the law, which connects the current strengths with the deflections, is not known. In some arrangements the deflections of the needle are amplified by a cord and pulley arrangement. Ayrton and Perry's dead-beat galvanometer. Something like the preceding apparatus, but the shape of the coils and 78 METHODS OF MEASUREMENT. the form of the pole pieces of the magnet are so calculated that the deflections are proportional to the current strengths up to an angle of about 40. These instruments are wound both with coarse and fine wire, so as to form ammeters or voltmeters. The wire is in some cases made up into a cable, the strands of which can be arranged either parallel or in series, by means of a special commutator ; when the wires are parallel the constant of the instrument is one -tenth of the constant when the wires are in series. Those instruments which have this arrange- ment are also provided with a resistance coil, which can be thrown into the circuit by removing a plug. The ammeter is thus calibrated ; the instrument is arranged with the wires in series, and put in circuit with a standard Daniell's cell ; a deflection a is thus obtained ; the resistance coil (in this case 1 ohm) is then unplugged, and a second deflection b is obtained ; then ~~ E (a - b) where E is the e. m. f. of the Daniell's cell (1'079 volts), when the wires are again put parallel. . ab *. I ~~E(-i) lb' The forms without commutators are calibrated by comparison with other instruments, Siemens' dynamometer being generally used. Dead-beat galvanometer of Messrs. Deprez and D'Arsonval. Intended for the measurement of very small currents. A galvanometer coil is suspended between the branches of a vertical horse-shoe electro-magnet by two platinum wires, which bring the current to it, and form an elastic torsion couple. A tube of iron placed in the interior of the coil between the branches of the magnet concentrates the magnetic field. The readings are made by means of Sir W. Thomson's system of lamp, scale, and mirror. When the terminals are connected by a short circuit the apparatus comes to zero without os- cillation. This property makes the apparatus very useful in zero methods. It indicates a current of one -tenth micro -ampere very clearly. Siemens and Halske's torsion galvanometer. Intended for commercial use as a voltmeter ; composed of a bell- magnet in the shape of a thimble split longitudinally along two generators diametrically opposite to each other. The poles of the VOLTMETERS AND AMMETERS. 79 magnet are formed by the two arms thus made. The magnet is fixed on a vertical axis, and turns between two coils of fine wire, through which the current passes. The action of the current is balanced by a bifilar suspension or a spiral spring placed at the upper part. One Daniell's cell produces a torsion of 15 ; a resistance coil enables the instrument to measure up to 100 volts. A graduated table gives the number of volts corresponding to each angle of torsion. Ampere-meter, amperometer, or ammeter. The name given to commercial graduated instruments, which enable the value in amperes of a current passing through them to be known by direct reading. Voltmeter. A galvanometer with a long fine coil, which gives by direct reading the value in volts of the differences of potential between two points of a circuit between which it is inserted as a shunt. In reality a voltmeter also measures the strength of the current which passes through it, but as its resistance is very great as compared with the other parts of the circuit, we may consider that its introduction as a shunt between two given points of a system does not change the con- ditions. The differences of potential are thus proportional to the strength of the current passing through the instrument. It is necessary to give very high resistances to voltmeters, so as to prevent the heating of the wire, which would have the effect of causing the instrument to give too small deflections. It is well, in order to avoid this heating, not to allow the current to pass continuously. A small key is generally placed on the apparatus by which the circuit can be closed at the moment of taking a reading. Precautions to be taken in the nse of volt- meters and ammeters containing permanent magnets. These apparatus must be frequently calibrated, because of the variation in the power of the magnets. It is well to put the armatures on their magnets when they are not in use, but the armature must be removed before taking a reading. A simple plan of ensuring their removal is to fasten a plate to the armature so as to hide the scale when the armature is on the magnet ; any mistake thus becomes impossible. It has lately been found that the constant taking off and putting on of the armature is destructive of the magnetism of permanent magnets. Instruments which are in constant use should not have their armatures replaced. Only when an instrument is to be laid by for some weeks should the armature be put on. 80 METHODS OF MEASUREMENT. Ayrton and Perry's spring ammeter. A soft iron needle, placed almost at right angles with the axis of the coil and attached to a spiral spring. The action of the current is balanced by that of the spring. Deflections proportional to the currents can be obtained up to an angle of 45. This apparatus acts with alternating currents. With a fine wire coil and a special graduation, the spring ammeter becomes a voltmeter. These instruments are provided with a toothed wheel and pinion arrangement, by which the deflections of the needle are amplified. Both wheel and pinion are fitted with a spiral spring. This not only tends to prevent " back-lash " when both springs are in action, but also enables the constant of the instrument to be varied to a known extent by throwing one of the springs out of action. This mechanism has been applied to the ohmmeter and arc horse -power meter of the same inventors. These instruments are not yet in practical use. Sir Wm. Thomson's absolute galvanometer (1882). For commercial use. Consists of a magnetometer, which is movable along a horizontal graduated scale, and a directing magnet, the magnetic moment of which in C. G. S. units is known. The sensibility is varied by using or removing the directing magnet, and by placing the magnetometer closer to, or removing it farther from, the vertical coil through which the current passes. A potential galvanometer enables measurements to be made from ^ of a v lt U P to 1,000 volts without the use of auxiliary coils. The current galvanometer from of an ampere LOO up to -100 amperes without using shunts, the correctness of which is always doubtful. The resistance of the first instrument is more than u,000 ohms ; that of the other almost nothing. They may be set up on any circuit that has to be measured without disturbing it, and the measured quantities de- termined in volts and amperes by a simple arithmetical operation. The magnetic moment of the directing magnet should be frequently verified, and great care be exercised to keep it from shocks, jars, or vibrations, and far from the magnetic fields of dynamos, etc. Let H be the horizontal intensity of the magnetic field in C.G.S. units (either with or without the magnet), d the number of divisions on the magnetometer scale, n the number of divisions on the platform scale, E the difference of potential at the terminals of the instrument. The gradu- ations are so arranged that E = H volts. GALVANOMETERS. 81 TT In taking a series of readings the magnetometer is fixed, and cal- culated once for all. Then, by multiplying d by this ratio E is obtained. BalistiC galvanometer. When a certain quantity of electricity is instantaneously discharged through a galvanometer, if the resistance of the air to the movement of the needle be neglected, the quantity of electricity passing is proportional to the sine of half the angle of oscillation. The resistance of the air is reduced as much as possible in the balistic galvanometer. Ayrton and Perry have given it the following form: A high resistance Thomson's reflecting galvanometer has its needles removed and replaced by the following arrangement : Forty little magnets of different lengths are prepared, and after they have been magnetised to saturation, two little spheres are constructed with them, in each one of which all the magnets are arranged in the same direction. The spheres are built up of segments cut out of a little hollow ball of lead. Both spheres are joined together by a rigid rod, so as to form an astatic combination, which is suspended in the usual way. With this arrangement great sensibility is obtained, and the air only offers a very small resistance to the movement of the needles. It has been shown that the ratio of the first oscillation to the second is only one to 1*1695, which is sufficiently close to unity to enable us to take account of the damping effect produced by the air by a very simple correction. The extreme limit of an oscillation is called its elongation. Approximate correction for the resistance of the air. Let a' be the first elongation, a" the second elongation, on the same side of zero, the approximate arc o which would have been obtained without the resistance of the air is : a' - a" a = a -f Captain Cardew's ammeter. This instrument consists in principle of two coils wound in opposite directions; one, of many turns of fine wife, the other, of one or two turns of thick wire, acting in opposite directions on a magnetised needle, which is brought to zero by means of a directing bar magnet placed on the top of the coils. The fine wire coil is of some thousands of ohms resistance ; the coarse wire coil of about -02 to -03 ohm. The current to be measured is passed through the thick wire. The fine wire is put in circuit with a resistance box and from one to three standard Daniell's cells. The resistance box is then un- plugged, until the needle is brought to zero. Then, if G METHODS OF MEASUREMENT. C = current strength to be measured, r = resistance of fine wire coil, B =2 resistance unplugged in resistance box, n =. number of Daniell's cells, K=z constant of the instrument, To find K, the two coils, with a resistance box in circuit with each, are arranged in parallel arc in circuit with a dynamo or battery of very low Internal resistance. A small resistance is unplugged in the thick wirQ circuit, and the resistance box in the fine wire circuit is unplugged, until the needle is brought to zero. Then : If r =^*esistance of fine wire coil, R resistance unplugged in fine wire coil circuit, r' rz resistance of thick wire coil, B/ =r resistance unplugged in thick wire coil circuit, In addition to the two or three turns of thick wire, these instruments are provided with a rectangle of thick copper bars, which acts as a coil for measuring very large currents. The fine wire coil and the needle move together in a groove, so as to be nearer or farther from this rectangle, the distance being observed on a divided scale. The value of K is de- termined for each division of the scale. This sliding action is but little used. This instrument has the advantage of not changing its constant, which also can be readily determined at any time. If the Daniell's cells be carefully put up, its indications are very trustworthy, and may be taken as true within one or two per cent. Its disadvantages are the length of time necessary to take a reading, and its want of portability, owing to the use of Daniell's cells. With care, however, it may be used as a convenient instrument for the calibration of others. Crompton and Kapp's current and potential indicators. To avoid the trouble of constant re -calibration, neces- sary where permanent steel magnets or springs are employed as the balancing force in electrical measuring instruments, Messrs. Crompton and Kapp have devised their potential and current indicators, in which electro -magnets saturated by the current which is to be measured, replace the permanent steel magnets. Both these instruments consist essentially of a coil of wire traversed by the current, and capable of CURRENT AND POTENTIAL INDICATORS. 83 deflecting a magnetic needle against the force of an electro-magnet. In order that an electro -magnet may suitably replace a permanent one, it is necessary that its iron core should be saturated with all the varying strengths of current for which the instrument is to be used, and also that the magnetic effect due to its coils alone should be neutralised. Fig. 24. Plan of Field Magnets and Strip of Copper carrying the Current in the Current Indicator. The first of these conditions is fulfilled by making the amount of iron in the magnets very small in comparison with that of the copper wire, and the second by setting the deflecting coil at such an angle with the line joining the poles of the electro-magnet, that while one component of the force due to it is employed to deflect the needle, the other more than neutralises the magnetic effect of the coils. As a result of this, the strength of the field actually falls off when high currents are being 84 METHODS OF MEASUREMENT. measured, thus allowing the increment of the angle of deflection to be comparatively large, even for high currents. The potential indicator has a pivoted needle, swinging within a brass tube, which thus acts as a damper, rendering the instrument almost dead beat, and mounted at the lower end of a steel axle, to the upper end of Fig. 25. Plan of Potential Indicator, showing the two slightly inclined Deflecting Coils. which is fastened a light aluminium pointer. The electro -magnet is of horse-shoe form, fastened to a central tubular stand, which also serves to support the two deflecting coils, one on each side ; the tube within which the needle swings being inserted into the stand. The electro- magnets and deflecting coils are wound with from 50 to 100 ohms of high- resistance copper wire, and an additional resistance of German silver, nine times as great, is added. This can, however, be short-circuited by depressing a key when the instrument has to be used for measuring low electromotive forces ; in this case, the value indicated by the pointer AYRTON AND PERRY'S AM- AND VOLTMETERS. 85 must be divided by 10. For very low readings it is preferable to read with the key depressed, as, otherwise, the very low currents produced would be insufficient to saturate the iron. A commutator allows the current to enter in the right direction, so as to bring the pointer over the scale, the handle of the commutator then points to the positive terminal. The current indicators may have either pivoted or suspended needles. For measuring currents of 10 amperes and upwards, the deflecting coil is replaced by a single copper strip. The current entering by one of the flat electrodes splits into two parts, each part passing round the cores (wound with low-resistance wire) of an electro-magnet of horse-shoe form, the similar poles of which point towards each other. The current then unites again, and, after passing through the metal slip close under the needle, leaves the instrument by the second electrode, which is separated from the first by a narrow sheet of insulating fibre. The upper electrode is marked so as to allow the direction of the current to be easily determined. Both instruments should be placed in such a position that the north pole of the needle points to the north, though the error caused by neglect- ing this is inconsiderable. The deflections in both instruments are very nearly proportional to the currents, and as re -calibration is never required, the scale of the potential indicator is divided directly into volts, and that of the current indicator into amperes. For alternating currents, the magnetised steel needle is replaced by a needle made of soft iron. Ayrton and Perry's spring: proportional am- aild voltmeters. These instruments also depend on the saturation of a small piece of soft iron by a smaller current than that likely to be measured. The directive force is obtained by a spring of peculiar form, formed of a flat ribbon of very thin metal, looking not at all unlike a very regular shaving cut in a lathe. This form of spring, when proper di- mensions are given to it as regards thickness of material, length of strap, and diameter of cylinder round which it is wound, rotates through a large angle for a very small axial extension without permanent set, and the angle of rotation is directly proportional to the force tending to extend the spring. In the simplest form both am- and voltmeter consist of a hollow light iron tube closed at the bottom ; this tube is suspended by the spring, the lower end of which is attached to the bottom of the tube. The tube is guided top and bottom, and to its upper edge is fastened a pointer; the whole is inserted in a coil of wire forming a sucking solenoid, the pull of the solenoid on the iron tube being proportional to the strength of the current passing (as soon as the iron tube is saturated) , provided the iron core has the position determined by the inventors, 86 METHODS OF MEASUREMENT. and the angle of rotation of the spring, and therefore of the pointer, being proportional to the pull on the tube, the scale over which the pointer moves may (after the first few degrees) be made to show amperes and volts directly, and the same deflection will indicate one ampere or one Fig. 26. Unshielded Form of Ammeter and Voltn>-?ter. AA, tbin soft iron tube carrying pointer p ; G, spring attached to bottom of tube, and to glass c >ver ; FF, solenoid. The figure shows the guiding pins at top and boituiu ol' the tube. volt at all parts of the scale. In order to avoid the labour of gradua- ting each instrument separately, a regulating coil is provided outside the solenoid, by which the instrument can be adjusted. As soon as the adjustment is made by the maker, the coil is immovably cemented in its place. The ammeter is wound with copper strip of the same width as the reel on which it is wound, the separate layers being divided from each other by a layer of varnished fabric. The scale of these instruments is very open, the readings being accurately proportional, between about 7 and 270. The instruments are found to be but little affected by the magnetic field of dynamo machines, SHUNTS AND CIRCUIT RESISTANCE COILS. 87 etc., and may, indeed, be used nearer to such disturbing fields than the permanent magnet instruments of the same inventors. In cases in which it is required to have instruments perfectly shielded from surrounding magnetic influences, Messrs. Ayrton and Perry have constructed am- meters and voltmeters depending on the action of the same kind of spring as that described above, but in these instruments the solenoid is replaced by a peculiar form of tubular magnet. So perfectly shielded are these Fig. 27. Shielded form of Ammeter and Voltmeter. AA, Iron tube suspended by spring ; GG. guiding pins : P, pointer ; BB, soft iron tube, parted at D by brass or othi-r non-magnetic metal ; the wire is coiled on BB, DD, KK ; c, outer soft mm tube ; xxxx, soft irn plates connecting inner and outer soft iron tubes ; KK, adjustable soft iron plug for adjustment. instruments, that, according to the inventors, they may be used standing on the field magnets of a powerful dynamo machine without introducing any appreciable error. The scale is not proportional, the divisions getting wider apart as the deflection increases, nor is the range so wide as in the solenoid form. The adjustment in these instruments is effected by a screwed soft-iron plug at the bottom of the tubular magnet. SHUNTS AND CIECUIT BESISTANCE COILS. Shunting* the galvanometer. A circuit placed between the poles of a galvanometer, for the purpose of reducing its sensibility in 88 METHODS OF MEASUREMENT. a certain known proportion, and to bring its deflections within the limits of the gradation, is called a shunt. To reduce the current to - of its n value, the resistance of the shunt S ought to be : G n-1 G being the resistance of the galvanometer. Generally galvanometers are provided with a shunt box containing three shunts, which reduce its sensibility to the 10th, to the 100th, to the 1,000th, and of which the respective resistances are : G G . G 9 ' 00 ' 999* The shunts are enclosed in a separate box ; Fig. 28 shows the arrangement generally used. Multiplying power of a shunt. The ratio of the current which traverses the galvanometer without a shunt to that which traverses the galvanometer with a shunt, the current traversing the whole circuit remaining the same. Calling this ratio m, Fig. 28. Galvanometer S Shunt BJX. Resistance of a shunted galvanometer.- Calling this G l5 then the law of derived currents gives GS When a galvanometer is shunted the value G! then comes into the calculations if no compensating resistance be used. Compensating resistance. When a galvanometer is shunted its resistance decreases, hence the current increases in strength ; to bring back the current to its former strength resistance must be inserted in the circuit, which is called compensating resistance, and of which the value B c is given by the formula GALVANOMETERS. 89 G-f-S A galvanometer of resistance G, with its shunt and its compensating resistance, may be considered as a galvanometer of the same resistance, but smaller sensibility. Constant Of a galvanometer in French nomenclature is the deflection produced by one DanielPs cell in a circuit of which the total resistance is equal to one megohm. By shunting the galvanometer to the , if r is the internal resistance of the Daniell's cell, GI that of the shunted galvanometer, E a resistance introduced into the circuit, such that 1,000,000 the deflection of the galvanometer will be the constant.* In England the constant of a galvanometer means the number by which its indica- tions must be multiplied to reduce them to amperes, milliamperes, or microamperes, as the case may be. Maximum sensibility. With a tangent galvanometer the maximum sensibility is at 45. In measurements by the equal deflection method, the deflections must therefore be made about 45. In half deflection methods the best angles are 35 and 55, for which the tangents, and consequently the strengths of the currents, are one the double of the other. In any kind of galvanometer it is as well to mark upon the instrument this angle of maximum sensibility. Theorem of sensibility (It. r. Picou).The relation between a physical action y, and the reading on a graduated scale x, may be written in the general form A being a constant, and/(#) a function which depends on the mathe- matical theory of the apparatus. The sensibility of the apparatus S is * It would be more scientific and more practical to define the constant of a galvanometer as the deflection produced by a current of one micro- ampere. The calculation of current strengths would be much simplified by this method, especially with tangent galvanometers, in which the deflections are proportional to the current strengths. 90 METHODS OF MEASUREMENT. equal at each instant to the ratio of f(x} to its differential coefficient The maximum point of sensibility is arrived at by considering the function S, and particularly by taking the value of x, which gives the value zero to the differential coefficient of the function S. This theorem when applied to the tangent galvanometer indicates that its maximum sensibility is at 45; for the sine galvanometer the sensibility increases infinitely, the maximum is at 90. Formula of merit of a galvanometer. This is the resistance of a circuit through which one DanielFs element will produce unit deflection on the graduated scale of a galvanometer. The circuit is formed of one Daniell's cell of resistance r, a rheostat E, galvanometer G, and shunt S : a deflection of d divisions is obtained. The resistance of the shunted galvanometer is Gi. Gi _ GS the multiplying power m of the shunt is : mi=. J ' . Formula of merit md (r -f- E -J- Gj). The formula of merit is larger as the galvanometer is more sensitive. Circuit resistance COilS. Resistance coils, which are placed in the circuit of a calibrated voltmeter to increase the range of its indica- tions; they have generally a resistance equal to 1, 2, 3 ... times that of the voltmeter to which they belong. The readings made 011 the apparatus must therefore be multiplied by 2, 3, 4 ... n -j- 1, in order to obtain the value of the quantity measured. The sensibility diminishes in proportion to the number of coils introduced. These resistances, and the wire of the galvanometer, ought never to be allowed to heat, because the deflections would be reduced on account of the increase of resistance produced by heating. Calibration of a galvanometer. This operation consists in tracing out a gradation proportional to the strengths of the currents which pass through the galvanometer. With a tangent or sine galvanometer calibration is not required ; it is only useful for appa- ratus for which the law of deflection is unknown. With any galvano- meter of resistance G the operation is as follows : First of all shunts are prepared for the galvanometer of , g, ^, etc,, and corresponding GALVANOMETERS. 91 compensating resistances. A circuit is then formed composed of the galvanometer, a constant battery, and a resistance box. First of all a shunt , and corresponding compensating resistance, is inserted. Sufficient resistance is then added to bring the deflection to a suitable value ; for example, 1. The shunt and the compensating resistance is then removed, the current passing through the galvanometer is thus doubled; the deflection obtained corresponds to a double strength. The shunt g, and its compensating resistance, is then inserted. The resistance box is then adjusted to bring the deflection back to the original value, say 1. The shunt, and its compensating resistance, is then removed ; the current is thus tripled ; the deflection obtained corresponds to three times the strength, and so on. The deflections are marked on the galvanometer itself, or on a reduction table. To bring these deflections within the limits of the scale, a resistance may be inserted in the circuit, or the galvanometer may be shunted, or the battery may be shunted ; but this last method makes the currents too large, and disturbs the constancy of the battery. Absolute calibration of* a galvanometer. This operation consists in marking on the graduation of the instrument the current strengths in amperes corresponding to each deflection ; it is especially used in commercial apparatus. The methods vary infinitely. One of them, based on electrolytic action, consists in causing a given current to pass through a decomposition cell, and the galvanometer to be calibrated for a certain length of time, t (seconds) ; keeping the deflection constant during the experiment, the quantity of electricity Q in coulombs which has passed through the decomposition cell, and the galvanometer deduced from the chemical action, enables us to calculate C from the relation : C amperes. Another method consists of introducing a perfectly fixed and known resistance E into the circuit of the galvanometer. The difference of potential between the two extremities of this resistance is measured by any suitable method, and C is deduced by Ohm's law. It is well to verify the calibration of a galvanometer often, as the calibration may change from moment to moment by the action of external or internal causes. This verification is made by the same means used for the original calibration. Thickness and resistance of galvanometer Wire ; Shape Of the COllS. For very strong currents one 92 METHODS OF MEASUREMENT. single turn of very thick wire is often used ; for thermo-electric currents twenty to thirty of wire of one millimetre in diameter ; the resistance is about a quarter of an ohm. Galvanometers of high resistance (Thomson's, etc.) have from 5,000 to 10,000 ohms resistance ; the diameter of the wire is not more than one -tenth or two -tenths of a millimetre, and its length may be as great as 4,000 metres. Some galvanometers wound with German silver wire have as much as 50,000 ohms resistance ; they give a deflection of 200 divisions of the scale with a single Daniell's cell, and 20 megohms in the circuit. The use of German silver is advantageous, especially in differential galvanometers, because of the small variation of resistance produced by changes of temperature. Resistance is always a dis- advantage, but it is impossible to have a great number of turns of wire in a small space without a large resistance. All contact between the wires must be avoided, as it would prevent the action of the whole part interposed between the points of contact. Bad insulation of the wire disturbs the true value of the shunts, Fig. 29. Form of the Coil in the Reflecting Galvanometer. Fig. 30. Graded Galvanometer. and renders the instrument useless for exact measurements. Copper wire ought to be carefully covered with white silk, ani well dried before it is coiled ; after a few layers have been coiled the coil ought to be again dried, and steeped in pure paraffin. The resistance of the wire as it is coiled ought to be frequently GALVANOMETERS. 93 compared with its calculated resistance. For a given length and thickness of wire there is a special form of coil which gives the maximum effect. Sir William Thomson has calculated this form for the reflecting galvanometer ; a transverse section of this form is given by the equation #2 (tfly) 5 - ?/2. x being the ordinate in the direction parallel to the axis of the coil, a the distance B ; O, the origin of the co-ordinates, the centre of the coil ; Fig. 29 shows the theoretical curve and its practical form. Part of the wire must necessarily be removed from the centre to allow space for the magnet. The thickness of the wire ought not to be the same in all the layers. The sectional area ought to increase proportionally to the diameter at each point in order to give the best results. In practice three or four different thicknesses answer the purpose. In Sir William Thomson's graded galvanometer, one, two, three, or four parts of the wire can be used according to need, the necessary connections being made by means of a key ac, which turns about the point c (Fig. 30). Measurement of currents in . O. 8. units by the tangent galvanometer. In the case of a galvanometer with a circular coil of which the needle is so short that the tangents of the angles of deflection are proportional to the current strengths : r the radius of the coil in centimetres ; n number of turns of wire ; H horizontal component of terrestrial magnetism (in dynes) ; C strength of current in C. G. S. units ; 5 angle of deflection. Then, C= X H 1 an J.G.S. units. 2irn And as 1 ampere = C.G.S. units, C = X H tan 8 X 10 amperes. In England the ratio - is called the constant of the galvanometer.* Zirn * Here again we find ambiguity in consequence of badly defined expres- sions, as in France the constant of a galvanometer is the deflection produced by one Daniell's cell through a total resistance of one megohm. 94 METHODS OF MEASUREMENT. Comparison of current strengths by the method Of oscillations (Latimer Clark} is carried out by means of a galvanometer or galvanoscope with a single needle. The galvanometer coil is placed at right angles with the magnetic meridian, the needle is made to oscillate, and the number m of oscillations performed under the action of terrestrial magnetism in a given time (one minute, for example) is counted. A current of strength c is passed through the coil, and the number of oscillations n during the same time is noted. The number of oscillations N is then counted with another current C. We have then the relation : If the horizontal component of the earth's magnetism H be known, the first two experiments are sufficient, and we have, Indirect measurement of current strength. (1) By Ohm's law. The difference of potential E between two points of the circuit separated by a known resistance E is measured, and Ohm's law is applied : C== E' This method is particularly suitable for the measurement of very strong currents which do not permit of a galvanometer being placed directly in the circuit. (2) By the voltmeter. The current to be measured is caused to pass through a voltmeter or decomposition cell for n seconds. The volume of gas is observed or the deposit is weighed, and the number of coulombs Q is calculated by the electro -chemical equivalents. The current strength C is then given by the formula, C= Q -. ft II. ELECTRO-DYNAMOMETERS. Electro-dynamometers depend on the mutual attractions and repul- sions of currents. They give indications proportional to the square of the current strengths, and consequently independent of the direction of ELECTRO-DYNAMOMETERS. 95 these currents. They are thus suitable for the measurement of alter- nating currents. As they contain no magnet, it is easy to make their indications independent of terrestrial magnetism. Weber's electro-dynamometer is composed of a fixed coil and an interior concentric movable coil, of which the axis is at right angles to that of the fixed coil. It is supported by a wire bifilar sus- pension, the wires of which conduct the current, and their torsion balances the mutual action of the coils. The deflection is read by means of a lamp, scale, and mirror. Joule's electro-dynamometer. The movable coil is suspended from a scale beam. It is horizontal, and is free to move' vertically. The fixed coil is below it. The planes of the turns of the two coils are parallel. The force exerted between the two coils is measured by the weight, which must be added to or taken from the scale pan suspended to the other end of the beam, and balancing the movable coil. Siemens and Halske's electro-dynamometer, intended for practical work. The action of the current is balanced by the torsion of a bifilar suspension, hair or spiral spring. It is com- posed of a fixed coil, and a movable coil outside the fixed coil, and having only one single turn of wire. The directive action of the earth upon the movable coil may then be entirely neglected ; that of the fixed coil is proportional to the number of turns of wire. At each measurement the two coils are brought back into a position at right angles to each other, and the angle of torsion, which may be as much as 270, measures the current. The sensibility increases with the current strength, since the torsions are proportional to the squares of the current strengths. The most complete form of this instrument has two fixed coils. One of the coils made of a thick wire is used for currents of from ten to sixty amperes ; the other coil for currents of from one-half to ten amperes. III. VOLTMETERS. Up to the present time the measurement of current strengths by the voltmeter has been but little applied. This method is based on Faraday's law. A constant current of unknown strength C is caused to pass through a voltmeter or decomposition cell for t seconds. The volume of gas disengaged is measured, or the deposit produced by the passage of the current is weighed by means of the electro -chemical equivalents. The quantity of electricity Q in coulombs which has 96 METHODS OF MEASUREMENT. passed through the voltmeter is calculated. The value of C is then deduced from the formula : 0=4 This method is principally employed for the calibration of gal- vanometers. (See Measurement of electrical quantities.) MEASUREMENT OF RESISTANCES The methods of measuring resistances are very numerous, and vary with the kind of instrument at hand, the accuracy which it is desired to obtain, and the nature of the resistance to be measured. We will point out here the most simple and most commonly used methods. RESISTANCE OF CONDUCTORS. Substitution method. A constant battery, a galvanometer G and the resistance to be measured x, are arranged in circuit. The deflection of the galvanometer is noted, and a resistance box is substi- tuted for x. The box is unplugged until the deflection is the same as at first. If E be the resistance unplugged, we have x = B. The accuracy depends on the sensibility of the galvanometer, the accuracy of the box, and the constancy of the battery. By addition to a known circuit. A circuit of total re- sistance E, made up of a battery, a galvanometer, and a resistance box, gives a deflection 5. The resistance to be measured x is introduced, and the deflection becomes 5'. We have then, g' E Whence _S-5' * - T R 8 and 8' are not the angles, but the current strengths, corresponding to the deflections. They may be expressed in any arbitrary units. This method requires a calibrated galvanometer and a constant battery. Wheat* tone's bridge. The most convenient form for ordi- nary resistances is the Post- Office bridge box. When suitable resistances WHEATSTONE'S BRIDGE. 97 have been unplugged between AB and BC, the battery key is pressed down, resistances are unplugged in the box which nearly correspond to equilibrium, and the left-hand key, which corresponds to the galvanometer, is pressed down. The plugs are then taken out or put in, as may be required, until the needle of the galvanometer remains at zero. If the galvanometer is very sensitive, it must at first be shunted, and very quick blows be given on the keys, so as not to risk breaking the suspending filament. When equilibrium is obtained, the shunt may be removed from the galvanometer, and the circuit kept closed for a longer time. The figure below shows the arrangement of the circuits; K x is the battery key (the right-hand key in the box), K 2 the galvanometer key (the left-hand key in the box), x .the resistance to be measured, and AD the resistance box. According to the resistance of the galvanometer and the value of the resistances to be measured, different arrangements may be adopted for the ratio of the arms of the bridge, or the galvanometer may be placed where the battery usually is, and the battery in place of the galvanometer. Fig. 31. Diagram of Wheatstone's Bridge. Resistance of galvanometer for maximum sensibility (Schwendler) . The resistance G of the galvanometer which gives the greatest sensibility for a given arrangement of the bridge is : - 98 METHODS OF MEASUREMENT. This formula allows a suitable galvanometer to be chosen when we know the sort cf resistances to be measured. Measurement of the resistance of a conductor Which is put to earth. The point D of the bridge is connected to earth ; one of the ends of the resistance x is connected to the point C, the other to earth. One of the poles of the battery is also connected to earth. Generally two different values are found, R' and R", according to whether a positive or negative current has been used, because of the in- fluence of the earth couple on the resistance to be measured. If the readings are taken quickly, we may take it that _R' + R" 2 The resistance x then includes that of the conductor and the sum of the earth resistances. Resistance of overhead lines. When three lines are available. Let r lf r 2 , and r 3 be the resistances of the three lines to be measured. They are joined up successively, two by two, in circuit, and the combined resistances measured : ri + r 2 = RI ; ri + r 3 = R 2 ; ra + r 3 = R 3 ; We then have for the respective values of r\, r 2 , r 3 : _ RX -fr- H. 2 - R 3 . Tl ~ 2 Ayrton and Perry's ohmmeter. Founded on Ohm's law and the measurement of R by the ratio ^-' Two coils fixed at right angles act on one and the same needle. One of the coils, which is wound with thick wire, is placed in the main circuit ; the other, wound with fine wire., as a shunt between the two extremities of the resistance to be mea- sured. By making the coils and the needle of suitable proportions, the deflections are proportional to the resistances, and the measurement is MEASUREMENT OF RESISTANCES. 99 made by a reading on the graduated dial. The ohmmeter does away with the necessity for a galvanometer and a resistance box, and enables a con- ductor traversed by currents to be measured when hot without stopping the machines. J. Carpentier's proportional galvanometer. Two coils arranged at right angles, and wound with the same number of tums of wire. In the centre a small needle and mirror. These coils are connected up in parallel arc. A known resistance being placed in the circuit of one of them, and the resistance x to be measured in the circuit of the other, the deflection of the needle read by means of the mirror shows the resistance directly. Measurement of the specific conductivity of a Conductor.* Is used especially for copper, of which the true con- ductivity at is represented by 1. In order to find the specific con- ductivity of a given sample, the real resistance of this sample is measured, and the resistance from its dimensions which it ought to have at the temperature of the experiment, if it were pure, is calculated. Let B TO be the measured resistance and E c the calculated resistance ; then, T? Conductivity = -Km The number given by the formula is always smaller than 1. Measurement of very large resistances. (1) A current from a battery of e. m. f. E is passed through a resistance x so great that the resistance of the battery and galvanometer may be neglected in comparison with it. A deflection 8 is obtained so that =! If the constant of the galvanometer is d^ we have : x zr E megohms. 8 (2) n elements of e. m. f. E, the resistance to be measured x, and the galvanometer G, are arranged in circuit. A certain deflection 8 ia * Conductivities are often expressed by taking the conductivity of pure copper at 100. In this case the number which represents the conductivity relatively to pure copper taken as unity, must be multiplied by 100. 100 METHODS OF MEASUREMENT. obtained. The same deflection is then obtained with n' elements, and a rheostat, the galvanometer being shunted to the Then: If -. = 100 and m = 1,000, x = 100,000 E. Tl This method is used for the measurement of the insulation of tele- graph lines. Measurement of very low resistances. "With very low resistances, bad contact affects the result in the usual methods. For these measurements Thomson'' s bridge is used. In the figure, x is the Pig. 32. Measurement of very Low Resistances. resistance to be measured between the points M and N ; Us a graduated wire of which the resistance is known, a and a two equal resistances, b and b two equal resistances, G is a sensitive galvanometer, J the battery. The points P and Q are shifted until the galvanometer comes to zero, then x=.l RESISTANCE OF GALVANOMETERS. Hall deflection method. A constant battery of small resistance is used. A resistance box, battery, and galvanometer of re- sistance G are placed in the same circuit. A resistance E is introduced into the circuit, and this resistance is increased up to a value Ej, such that the current strength is reduced to one-half ; we have then, G = E! - 2E. This method requires a calibrated galvanometer. RESISTANCE OF GALVANOMETERS. 101 Equal deflection method. With a low resistance con- stant battery and non- calibrated galvanometer. The galvanometer Gr, the battery E, and shunt S, and resistance box R are arranged as shown Fig. 33. Equal Deflection Method. in the figure. The resistance R gives a certain deflection of the galvano- meter ; the shunt is removed, and the resistance R is increased up to a value R 1( such that the deflection becomes the same as in the first case. Then: \ R ' Sir William Thomson's method, which is independent n Fig. 34. Thomson's Method. of the resistance of the battery. The Wheatstone bridge is arranged as shown in the figure. The resistance box R is then varied until the 102 METHODS OF MEASUREMENT. deflection of G does not change, when the short circuit key between B and D is closed, then '- INTERNAL RESISTANCE OF BATTERIES. Half deflection method. Applicable to batteries without sensible polarisation. The battery of unknown resistance r, a galvano- meter of resistance G, and a resistance box are arranged in one circuit ; a resistance R is unplugged, giving a deflection a, this resistance is then diminished until the deflection is 2a. If R' is this second resistance, r = R - (2E/ + G). a and 2o must be replaced by their corresponding sines or tangents, according to the kind of galvanometer used. Sir William Thomson's method. Applicable to bat- teries without sensible polarisation. The battery of resistance r, galvanometer G, and resistance box are placed in circuit; such a resistance R is then unplugged as will give a deflection easy to be read, and at the point of good sensibility of the galvanometer. A shunt of resistance S is then put between the poles of the battery, and the galvanometer is brought back to the same deflection by diminishing the resistance in the box to a value RI, then This method may be used with a non- calibrated galvanometer. Differential galvanometer method (Latimer Clark'). Galvanometer with a short thick wire. The current passes through one of the coils of resistance G, the needle is deflected through an angle a, and the current is then passed through both circuits, and the galvano- meter is brought back to the same deflection by the introduction into the circuit of a resistance R, then r = H. This method can only be applied to constant batteries. Measurement of internal resistance of batteries when an even number of absolutely identical ele- ments is at hand. They are put up in two series groups, with the same number of cells in each group. These groups are then connected in INTERNAL RESISTANCE OF BATTERIES. 103 opposition. The e. m. fs. balance each other, and then the total resis- tance is measured in the same way as that of an ordinary conductor by any known method. (Substitution, Wheatstone's bridge, etc.) Method by means of the electrometer, con- denser, or galvanometer of very high resistance. The electrometer, the condenser, or the high resistance galvanometer is connected to the two poles of the battery, which is otherwise on open circuit, so as to measure the difference of potential either by a discharge method or by a direct reading ; the system is then shunted by a known resistance until the difference of potential is reduced to one half, the resistance of the shunt is then equal to that of the battery. Only applicable to constant batteries. Mance's method, one of the best, as it only requires the battery to be constant during the short interval during which the key is closed. A Wheatstone bridge being arranged, as shewn in the figure, with a Fig. 35. Mance's Method. short circuit key between B and D, the arm AD is adjusted, until on pressing down the key the deflection of the galvanometer does not change, then If the arms a and b are equal, the formula is simplified, and becomes Siemens' method requires a continuous rheostat, or a sliding 104 METHODS OF MEASUREMENT. contact resistance box. Two points B and Bi, in the resistance AC, are found such that the deflection of G does not change ; in this case r = G -f b - a. The galvanometer ought to be of smaller resistance than the battery, and Fig. 36. Siemens' Method. sufficiently sensitive to allow R to be made fairly small without reducing the deflection too much. method. B is a battery of which the internal r is to be measured, C a condenser from ^ to 1 microfarad, S a shunt, and Fig. 37.-Munro's Method. G the galvanometer ; K x and Ka keys. KI is pressed down, and the deflection of the galvanometer dj is observed ; keeping the key Ki pressed down, K 2 is pressed down, and the deflection dz in the opposite direction is observed ; then d, This method is one of the best in practice, as it is applicable to all batteries. INSULATION OF OVERHEAD LINES. 105 INSULATION OF OVERHEAD LINES. General measurement. A tangent galvanometer of resis- tance Gr, a battery, and a fixed resistance of say 1,000 ohms, are put up in circuit ; the deflection S is observed ; this is taking the constant of the galvanometer; then the resistance box is removed, and the free pole of the battery is connected to earth, and one of the ends of the line to the galvanometer, the other end remaining insulated. A second deflec- tion 8' is thus obtained ; the insulation resistance of the line E is then Ei = 1000 X I' I In order to make the influence of the earth current negligible it is as well to use from thirty to forty Daniell elements in series. Insulation per mile. If the line is n miles long, the insu- lation per mile is EfW. In good conditions the insulation per mile ought not to be less than 300,000 ohms. (See Fourth Part.) This method of calculating the insulation per mile is not very correct, because it supposes that the leakage is identical at every point of the line. The measurement may be made more correctly by taking into account the resistance Gr of the galvanometer, and resistance r of the battery; * the formula is then When a great number of lines have to be measured at once it is useful to arrange a double entry table, in which is noted the insulation resistance for all values of 8 and 8'. MEASUREMENT OF POTENTIALS AND ELECTROMOTIVE FORCES. The difference of potential between two points of an electrified circuit is measured directly or indirectly. The direct measurement is obtained by a special class instrument, the electrometer. There are a great number of indirect methods which enable these measurements to be made. All galvanometers, for example, which in reality only measure current strength, may also be used for the measurement of potentials or electro- motive forces. * r is the resistance of the whole battery, not that of one elemeut. 106 METHODS OF MEASUREMENT. ELECTROMETERS. Electrometers belong to two classes, according as they are based upon (1) electrostatic actions, or (2) electro -capillary actions. When they only show differences of potential they act as electroscopes ; when they measure these differences they are electrometers. Electroscopes. The best known is the gold-leaf electroscope. It is composed of two strips of gold leaf from 8 to 10 centimetres long by 2 broad, suspended in a glass globe by a rod of metal terminated by a plate of brass, which, when it is electrified, causes the gold leaves to diverge ; in Eohnenberger's electroscope there is only one gold leaf sus- pended between two bodies ; one charged with positive and the other with negative electricity. These instruments are very sensitive, but are not much used for the purposes of measurement. Repulsion electrometers. Cavendish's (1771-1781) and Lane's (1772) may be used for rough measurements ; the first true electro- meter is Coulomb's torsion balance (1785). In Milner's and Peltier's electro- meters the torsion thread is replaced by a magnetised needle which produces the directive force ; the same device is used in Kohlrausche 's apparatus. These instruments are not much used now, being replaced by Sir W. Thomson's absolute and quadrant electrometers. Sir William Thomson's absolute electrometer. Based upon the attraction of two electrified discs arranged parallel to each other. One of the discs of known dimensions is surrounded by a guard ring, which causes the charge upon the disc to be uniformly distributed as if it had no edges. One of the discs :'j suspended by springs ; a micrometer screw is so regulated that the disc remains suspended a little above the guard ring when no part of the apparatus is electrified. Idiostatic method. The two plates are connected with the two bodies, the difference of potential between which is to be measured. The movable plate is then raised up until it takes up its original position, which is observed by means of a stretched hair and two fixed marks. At this moment the force of the springs and the attraction between the two discs balance. Calling V the potential of one of the plates, and V that of the other, the difference of potential is given by the formula ELECTROMETERS. 107 D, distance between the plates. F, electrical attraction equal to the effort of the springs which balance it. A, mean area between the surface of the suspended disc and the opening of the guard ring. This method of using the absolute electrometer is an idiostatic method, because no external charge is introduced. It is necessary that the exact distance D between the two discs should be known. Heterostatic method. In this method the two plates are insulated ; the upper one is charged to a high and constant potential. The constancy is verified by the aid of an accessory electrometer or gauge, and this constancy is maintained by means of a replenisher, which re-charges the disc. The lower plate is alternately connected to the earth and to the body of which the potential is to be measured. The difference of attraction in the two cases gives the difference of potential between the body and the earth, that is to say, the potential of the body. The formula then becomes, V - V' is the difference of potential between the earth and the electrified body ; D - D' the difference of the readings of the screw of the lower plate, which may be observed with perfect accuracy without introducing the absolute distance between the plates ; very great correct- ness is thus obtained. Sir William Thomson's quadrant electrometer is composed of a needle in the shape of a figure 8 suspended by means of a bifilar suspension between four horizontal metallic quadrants, which are electrically connected together diagonally two by two. The needle is kept positively charged by means of a Leyden jar, and its charge is kept constant. (See Heterostatic method, Gauge, and Replenishes ) One of the pairs of quadrants is connected to earth (potential =. by definition), the other is connected to the body, of which the potential is to be measured. The deflection is a function of the difference of potential. According to the form of the needle, and the relative dimensions of the quadrants and the needle, the deflections measured in degrees are proportional to the differences of potential up to 3 in general, and up to 10 when the instrument is well constructed, and is used under good conditions. The readings are made on a curved scale by means of a lamp and mirror. The best type, besides the gauge and replenisher, is furnished with an arrange- ment by which the directive force can be varied, and by which it may be 108 METHODS OF MEASUREMENT. observed whether this force remains constant after it has been adjusted ; and an induction plate, which diminishes the sensitiveness of the instru- ment. In measuring high potentials the induction plate is connected to the electrified body. The potential induced by this plate, which is small and far from the quadrants, is thus measured. Law of deflection of the quadrant electrometer (CkrJc- Maxwell). M = K(A-B)[C-|(A+B)]. M, moment of the couple which turns the needle. A and B, respective potentials of the two pairs of quadrants. C, potential of the needle. K, constant of the instrument. If A and B are equal potentials of contrary signs, the electrometer becomes symmetrical, and the equation is reduced to M = K (A - B) C. Mascart's symmetrical electrometer. A simplified form of Thomson's quadrant electrometer. It is used by the heterostatic method. The needle is connected to the body of which the potential is to be measured ; each pair of quadrants to one of the poles of a chloride of silver battery of twenty to forty elements, of which the middle is con- nected to earth in order to give equal charges of contrary signs to the quadrants ; the apparatus is then symmetrical. This method is used for observing the atmospheric electricity at the observatory of Montsouris. In the arrangement adopted by M. Mascart the moment M which turns the needle is nothing when Lippmann's capillary electrometer. A very sensitive instrument intended for the measurement of very small e. m. f s. , based on the variations which the capillary depression of mercury undergoes under the influence of an e. m. f. In the latest form designed by M. Lippmann the depression caused by the e. m. f. is balanced by a pressure exerted on the mercury by means of a pneumatic arrangement. The height of the mercury is read by means of a microscope, and is brought back to the same point at each experiment. The value of the pressure exerted measured by a mercury pressure-gauge gives the e. m. f. The instrument is most sensitive between zero and one half Daniell. It will show voioo of a Daniell. Its indications are very quick, and enable DIFFERENCES OF POTENTIAL. 109 the variations of an electrical phenomenon of short duration and varying with time to be observed (loss of charge of a condenser of a secondary battery, etc.). Its great sensitiveness enables it to be used in all zero methods (Wheatstone's bridge, etc.). Debrun's capillary electrometer. The essential part is a capillary tube one millimetre in diameter, arranged almost horizontally, in which the mercury is displaced under electrical action ; it is sensitive enough to show the ^7^77 f a volt. I* & graduated by means of zinc- cadmium elements, of which the e. m. f. is '281 volt. Ayrton and Perry's cylindrical spring electro- meter. For the measurement of potentials above 500 volts. On the same principle as the quadrant electrometer. In this instrument the quadrants are quarters of an elongated cylinder, and the needle, two cylindrical plates attached to a vertical axis ; a spiral spring balances the torsion produced by the attractions due to the charges of the two pairs of quadrants which are joined to the two points, the difference of potential between which is to be measured. The torsion of the spring measures the difference of potential. It is used by the idiostatic method, by joining the movable cy Under to one of the pairs of quadrants. It enables the e. m. f. of alternating current machines to be measured, which cannot easily be done by electro -dynamometers, because of self-induction. The instrument is portable and fairly dead-beat, the movable cylinder having a small moment of inertia. INDIRECT MEASUREMENT OF DIFFERENCES OF POTENTIAL. We will go over the principal indirect methods of measuring the differ- ence of potential D between two points A and B. Graduated galvanometers or voltmeters. If we have a galvanometer, of which the function which connects current strengths to the deflections is known, and of so high a resistance, that if it is connected as a shunt between the points A and B, so small a current only passes through it that the flow of the current in the rest of the system is not sensibly altered ; Ohm's law enables us to deduce at each instant the difference of potential between the points A and B from the strength of the current which passes through the galvanometer. In practice voltmeters are constructed with a resistance of several thousand ohms, and they are graduated directly in volts. Measurement is thus reduced to a direct reading. The galvanometers of Sir William Thomson, 110 METHODS OP MEASUREMENT. Marcel Deprez, Ayrton and Perry, etc., are thus constructed, and are used in practical measurements of machines, motors, and lamps. Opposition method. A sensitive galvanometer, and n ele- ments of e. m. f. E in series, are arranged between the points A and b, so as to send a current in the opposite direction to that which would flow through a conductor connected to the two points A and B ; n is then varied until the galvanometer comes to zero, or the deflection changes signs according as there are n or n -}- 1 elements. Then, The error cannot be greater than -g-, which is generally sufficient in practice. Partial opposition method. Two resistance boxes, E and B/ (Fig. 38), of so high a resistance as not sensibly to alter the difference Fig. 38. Partial Opposition Method. of potential, are placed between A and B. A galvanometer G- and a battery wE are arranged as shown in the diagram. B and B' are then varied until the galvanometer comes to zero. Then, The opposition methods have the advantage of not polarising the standard battery, thus giving more exact measurements, the galvano- meter only acting as a galvanoscope. Condenser method. This method is identical with that employed in measuring the e. m. f . of batteries, which we will describe later on. E. M. F. OF BATTERIES. The e. m. f. of a battery is equal to the difference of potential between its poles when the battery is on open circuit. For want of DIFFERENCES OF POTENTIAL. Ill a standard of e. m. f., the e. m. f. of a battery is measured by comparison with that of another battery taken as a unit ; it is then expressed in practical units or volts by multiplying the result by the e. m. f. of the standard which has been used. Equal resistance method. A battery of internal resis- tance r, of which the e. m. f. is to be measured, a galvanometer Q- and a resistance box E, are arranged in circuit. E is varied so as to obtain a deflection within the limits of the graduation of G, the strength of the current is then C. The battery is replaced by the standard, and E is so varied as to make the total resistance of the circuit the same as in the first case ; the current strength is then C', whence, E_C E' ~~ 0'* According to the nature of the galvanometer C and C' are expressed by the tangents or the sines of the deflections. When the resistance of the galvanometer, together with the resistance E, is very large compared with the internal resistance of the batteries to be measured, there is no necessity to equalise the total resistance in the two experiments. This is the case, for example, when the total resistance of the galvanometer and the box exceeds from 20,000 to 25,000 ohms. Equal deflection method is used when the galvanometer is not calibrated ; the standard E, galvanometer G, and the box are arranged in circuit; the box is adjusted so as to have a convenient reading on the galvanometer. Let E be the total resistance ; the standard is replaced by the battery to be measured E', and the galvanometer is brought back to the same deflection ; the total new resistance is E, whence, EE The internal resistance of the elements may be neglected in comparison with that of the galvanometer G, and the resistances E and E' introduced into the circuit when these resistances are large; the formula then becomes, E_E-fG E' ~~ E' -f- G-' Wiedemann's method. Let E be the e. m. f . of the standard battery and E' that of the battery to be measured. The two batteries, a galvanometer, and the resistance box are placed in circuit. Let d be the 112 METHODS OF MEASUREMENT. deflection on the tangent galvanometer due to the sum of the two e. m. fs. The weaker of the two batteries is then reversed so as only to have the current due to the difference of the e. m. fs. Let d\ be the new de- flection ; then, E' ~~ d di WheatStone's method. A battery of e. m. f . E is introduced into the circuit of a galvanometer G- and resistance box E, a certain de- flection a is then obtained, then a new resistance p is introduced so as to obtain a smaller deflection B. The battery is then withdrawn, a battery of e. m. 1 E' is substituted for it, the resistance box is adjusted so as to bring the deflection back to the value a, obtained by the first battery. A resistance p' is then added so as to bring the deflection back to the value B ; then, This method does not require a calibrated galvanometer, and is indepen- dent of the internal resistance of the elements. method. Two batteries of e. m. f . E and E' are arranged in series, and a galvanometer Gr (Fig. 39) arranged as a shunt a B * Fig. 39. Lacoine's Method. between the points A and B. Between E and the point B a certain resistance E is introduced, and the resistance B' is adjusted until the galvanometer comes to zero ; then, E E supposing the resistance of the batteries to be negligible as compared with E and B'. When these resistances are so large that they must be taken into account the method is thus modified : DIFFERENCES OF POTENTIAL. 113 A first experiment is made with the resistances R and R', then R is changed by giving it a smaller value JR l5 and R' is adjusted so as to bring the galvanometer back to zero, the new value of R' is R'i ; then, E R - R! If the internal resistance of the elements is known this second operation is not needed. Calling the internal resistances r and r' the formula then becomes, E_R-fR E' ~~ R' + / Poggendorff'S method. A zero method. The batteries of Fig. 40. Poggendorif' s Method. e. m. f . E and E' are arranged as in Fig. 40 ; R and R' are adjusted until there is equilibrium ; then, E _ R -f- R' -f r E'~~ R In this method of measurement the battery E' produces no current, and does not polarise. The battery E ought to be constant, and be formed of a sufficient number of, say, Dauiell elements, that E may be greater than E'. The internal resistance r of the battery E comes into the above equation. It may be eliminated by making two experiments, the first with the resistances R and R', and secondly with smaller resistances Ri and R\ ; the formula then becomes, E __ (R - RQ 4- (R'_-- R'O E' ~~ R - R! Clark's potentiometer. Requires two galvanometers and three batteries, the standard, the battery to be measured, and an auxi- liary battery. It has the advantage that the standard and the battery to be measured are compared under the same conditions, no current I METHODS OF MEASUREMENT. passing through either of them. Thus errors produced by polarisation which are introduced into most other methods, are avoided. In the above diagram E is a coil of bare wire, made of platinum and iridium alloy of 40 ohms resistance, making 100 turns round an ebonite cylinder, turning on an axle like a Wheatstone's rheostat. The two ends of the wire are attached to the extremities A and B, which serve as pivots. ririrv^rnrrrT~TvHprY^nnj - STV I* Fig. 41. Clark's Potentiometer. P is a battery of a few elements joined also to the blocks A and B, which sends a continuous current through E ; the rheostat enables the total resistance in this circuit to be varied. The standard is at E joined to the points A and B with a galvanometer interposed at G, which must be brought to zero ; this may be easily done by varying the rheostat. The battery E' is joined to the point A by one of its poles, the other pole is joined to a second galvanometer G', and a contact n, which slides on the resistance. The point of contact n is moved along the resistance E until the galvanometer G' comes to zero. Calling the two parts of the resistance E on each side of the contact a and 3, when G' is at zero, we have, E 04- b E The resistance E being graduated, the ratio is read directly on the scale. The error in this method is less than the i.ooo.ouoflb. of a volt. When the battery to be measured is stronger than the standard they are interchanged, the standard is put at E' the battery at E, and the experi- ment is made as before. It is only necessary to substitute the letters one for another in the formula when the elements have been exchanged. Prof. Adams has justly remarked that the galvanometer G' is useless, because the galvanometer G being at zero for a certain value of the rheostat, its equilibrium would be disturbed if the slider n were in any other position than that for whieh the galvanometer G comes to zero. DIFFERENCES OF POTENTIAL. 115 method. One and the same condenser is charged suc- cessively by the two batteries which are to be compared ; the ratio of the charges shows the ratio of the e. m. fs. The charges are measured by means of a balistic galvanometer, or a galvanometer with a suspended needle. The angle of impulse is almost proportional to the e. m. f., or, more exactly, the e. m. f . is proportional to the sine of half the angle of impulse, but when the deflection is not too great the e. m. f. is practically proportional to the angle. By shunting the galvanometer the e. m. f . of a whole battery may be obtained in terms of a single standard element. In this case the impulse produced by the standard element is observed, and the galvanometer is shunted until the whole battery gives the same impulse ; then, if S be the resistance of the shunt, If the angles of impulse are not equal, calling that produced by the standard 5, and that produced by the battery 5', we have or more correctly, 1 / sm -5 Correction for the resistance of the air, After having observed the first impulse the scale is carefully watched, and the point to which the spot of light comes on the second swing is also observed. One quarter of the difference between the two readings is added to the first reading in order to correct for the resistance of the air. Opposition method. elements of known e. m. f. E are opposed to ri elements of unknown e. m. f., E' interposing a galvano- meter, n and n' are then varied until the galvanometer comes to zero ; then, riE = n'W. If n elements give a deflection 5 on a galvanometer on one side of zero, and n -j- 1 elements a deflection 5' on the opposite side, then, From which the value of E' may be found. 116 METHODS OF MEASUREMENT. MEASUREMENT OF EL.ECTRICAI, QUANTITY. Faraday's law. If C be the strength of the current, t the time during which it is passing, the quantity of electricity Q given by the current during the time t is Q = Ct. Taking C in amperes and t in seconds, we get the value Q in coulombs. This is the method used for calculating the elements of dynamos which are to be used for electro -metallurgic operations ; it is an indirect method. Direct methods, based on the chemical or mechanical actions of the current, are carried out by means of voltmeters, coulomb meters, or electricity meters. Voltmeters. On account of the tendency of the gases to dissolve in acidulated water and other secondary phenomena, the gas voltmeter is not very correct, and is but very little used, and we only notice it for the sake of completeness. Electrolytic cells. The metal deposited by a current in a given time is weighed, and the number of coulombs is deduced by the electro -chemical equivalent. The solutions most used are sulphate of copper, sulphate of zinc, and nitrate of silver. M. Mascart has made some experiments with a 15 per cent, solution of nitrate of silver and a 10 per cent, solution of sulphate of copper. Edison's meters. Sulphate of copper was used in the first ; in the later ones, sulphate of zinc. It is set up in a derived circuit, so that only y^th or T ^ T ^th of the total current passes through it. The zinc solution contains 90 parts by weight of pure sulphate of zinc dis- solved in 100 parts of distilled water ; its density at 18 P ought to be 1 '33 (Francis JehF). The zinc plates are weighed once a month, and the number of coulombs is deduced from this weight by remembering that I ampere hour deposits 1,228 milligrammes of zinc. In another instrument of Edison's weighing is dispensed with. An automatic arrangement causes the plates to tip over as soon as they have gained a weight exceeding a certain weight ; the connections are changed, the plate which was the cathode becomes the anode, and reciprocally until the apparatus tips over the other way. A counter registers the number of movements produced during a given time. The total number of coulombs is deduced from this number by a very simple calculation. The apparatus is rather complicated. MEASUREMENT OF CAPACITY. 117 Edison's and Ayrton and Perry's coulomb meter. The principle of this instrument is to use an electromotor so arranged that its speed is proportional to the strength of the current passing through it. This motor turns a fan immersed in liquid. The resistance to the movement being thus also proportional to the speed, if the number of revolutions performed by the apparatus during a given time be registered, the number of coulombs which have passed through it can be found. It has not yet been used in practice. Vernon-Boys' integrating meter. This apparatus is an integrator which gives directly for any time t by a simple reading : fCdt. It has not yet been used in practice. MEASUREMENT OF CAPACITY. Capacities are measured by comparing them to those of standards, which in general vary between I and 1 microfarad. In practice these measurements are only applied to submarine cables, so we will only point out here a general method, reserving the explanation of special methods for the sections on cable measurements. Electrostatic capacity of condensers. A standard condenser of known capacity c is charged by means of a battery of given e. in. f., and discharged through a balistic galvanometer. Let a be the deflection. A condenser of capacity Cj is then charged with the same battery. It is discharged, and a second deflection o x is obtained ; then, " When shunts S and Si are used so as to make the two deflections equal, then, Si It is convenient to use Sabine's key in these measurements, taking care to adopt a uniform time of charging and a certain interval before discharging. For capacities varying between $ and 1 microfarad, Dr. Muir- head recommends to charge for 15 seconds, and to allow an interval of 1 118 METHODS OF MEASUREMENT. seconds between the charge and discharge. A cable of 1,000 knots requires a charge of 5 minutes and an interval of 10 minutes. MEASUREMENT OF ENERGY. Energy is measured in different ways, according to the nature of the phenomena to which it gives rise and the forms' under which it manifests itself. There are many classes of instruments, which are called : Calorimeters, when the energy appears under the form of heat. Dynamometers, when it appears under the form of mechanical work. Erameters, when it appears under the form of an electric current. The electrician has very seldom to use calorimetric methods, but it is as well to describe one method here for observing the heat produced in a wire through which a current is passing. A vessel is taken which contains a known weight of oil (in grammes) , it is carefully closed and enveloped in several thicknesses of flannel or felt, to prevent loss of heat by radiation, the wire is placed in the vessel, and being immersed in oil it is insulated ; the temperature t- of the oil is observed, the vessel is closed and placed in its envelopes and the current allowed to pass for a time T ; the vessel is then opened, and the temperature of the oil t% rapidly observed ; then if s be the specific heat of the oil, the total quantity of heat H produced in the time T is H = ( 2 ti)s calories (g.-d.), if ti and h be observed in centigrade degrees. DYNAMOMETERS. Classification. Under the name of dynamometers are included all apparatus which measure the work produced or absorbed by a machine ; hence there are two distinct classes: (1) Absorption dynamometers or dynamometer breaks, which measure the work produced ; (2) transmission dynamometers, which are interposed between the motor and the machine which it drives, and which measure the work expended. These instru- ments are interesting to the electrician on account of their importance in testing dynamo machines and electromotors. We will describe the forms of apparatus most generally used. Absorption dynamometers. The simplest and best known and most used is the Prony break. It has been improved by Appoldt, Kretz, Easton and Anderson, Amos, Emery, Brauer, Marcel Deprez, J. Carpentier, N. Raffard, Bramwell, etc. , who have made the apparatus easier to handle, and enabled us to obtain a certain propor- tionality between the coefficient of friction and the resistance, i.e. an DYNAMOMETERS. 119 automatic regulation of the instrument. There are several simple forms : A cord may be passed over a pulley and attached to the ground at one end by a spring balance, the other end carrying a scale pan, the reading on the balance minus the weight in the pan multiplied by the radius of the pulley, its circumference and the speed, gives the energy. Let E be the radius in feet, W the reading on the balance, W the weight in the scale pan in pounds, and S the speed in revolutions per minute, then Activity = (W - W) 2irrS foot-pounds per minute. Ayrton and Perry use two scale pans, the cord passing over the pulley being partly of thin smooth cord and partly of thick rough cord spliced together, the heavier weight being suspended from the thin cord, so that if the heavier weight tends to rise, the thinner cord comes on to the pulley, and thus diminishes the friction, and thus prevents the weight from being thrown over the pulley. The varying quantities of thick and thin cord form a sensitive self -adjustment of considerable range. Transmission dynamometers. There are a great number of these based on different principles. (1) The difference of tension of the two parts of the belt driving the machine is measured, and its speed of rotation. From this the work is deduced, after corrections for friction, slipping, elongation of the strap, etc. This class includes the dynamometers of Froude, Parsons, Tatham, Farcot, etc. (2) The difference of rigidity of the two parts of the strap is measured, and from it the difference of tension is deduced. The typical instrument of this class is that of Hefner- Alt eneck, and the modifications of it intro- duced by Briggs, Elihu Thomson, and Hopkinson. (3) The motive effort is transmitted to the machine directly by means of a spring, and the value of the effort is measured, which, multiplied by the speed, gives the work. These instruments are some- times supplied with a counter which registers the sum of the work produced during a given time. The instruments of the Agricultural Society of London, Meyy, J. Morin, Bourry, Taurines, etc. The tension of the springs is sometimes measured by an optical method, as in the Latchinoff's dynamometer, sometimes by an index, as in Ayrton and Perry 's instrument. Others act through a weight like the instru- ments of Darwin, Eaffard, the German dynamometer, King's, Whyte's, etc. (4) The work is measured by the tension of the moving axle, as in Sim's pandynamometer and Carlo Resio's apparatus. 120 METHODS OF MEASUREMENT. REVOLUTION COUNTERS AND SPEED INDICATORS. In all dynamometrical measurements it is necessary to know the speed of rotation of the machines. This speed of rotation is measured by means of two classes of instruments which enable us to know the number of revo- lutions per minute, most commonly represented by the symbol n. (1) Revolution counters show the mean speed of the machine during the time the experiment lasts, generally half a minute. In France Sainte's and Deschieri's counters are used. When the speed does not exceeed 80 to 100 revolutions per minute it is easy to count them directly without an instrument if a visible mark is made on some point of the revolving apparatus. (2) Speed indicators show the speed of a machine at each instant, and this enables its regularity to be judged of. They are fixed on the axle itself or to a special transmitter. The most used are Jims' tachymeters, and Jacquemier's indicator, based on centrifugal force. Marcel Deprez has also constructed one based on electro -magnetic actions. MEASUREMENT OF ELECTRICAL ENERGY. The measurement of the energy consumed or produced by an electrical apparatus is generally made by an indirect method which consists in the measurement of two elements which concur in the production of this energy, and introducing them into a formula which gives the result sought for. There are, however, some instruments which give this result directly. We will rapidly scan the direct and indirect methods which are most used. Energy expended by an electrical apparatus. If C be the strength of the current which passes through the apparatus, and E the difference of potential between the terminals, the work ab- sorbed W then is, PTf OE W = kilogrammes per second foot-pounds per second. 9'81 I'ooo This formula enables us to calculate the energy absorbed by an electric lamp, a motor, a resistance, etc. It springs directly from Ohm's and Joule's laws. Expressing W in horse -power, CE CE , W =. horse-power, or W -_ chevaux-vapeur. 746 7u6 AYRTON AND PERRY'S ERGMETER. 121 Heat produced in a conductor through which a current passes. If R is the resistance of the conductor (at the temperature of the experiment), E the difference of potential at the extremities of this resistance, C the strength of the current passing through it, the energy W, produced in the conductor in the form of heat, is calculated by one of the following formulae : QfJ CE _ C3E _ E2 M W = 9^81 - 9-81 - ~9^ Mogrammes per second ; CE _ C2R _ E2 or in calories (g.-d.) by the formulas : 4-16 4-16 4-16 R or W = -2405 CE = -2405 C 2 R = calories (g.-d.) per second. Ayrton and Perry's ergmeter. A movable light coil of fine wire with small moment of inertia free to move round an axis parallel to its length, is suspended by a bifilar suspension in a fixed coil of thick wire. The fine wire is arranged as a shunt, and the thick wire in the main circuit. The deflection is a measure of the product. Marcel Dcprez published a few years ago an analogous ergmeter, in which the action of the currents was balanced by a weight, but the indications of this instrument can only be correct if there be no relative displacement of the two circuits. It is easier in general to measure E and C separately and take their product, so that electrical ergmeters have not yet come into practical use. Recently Vernon-Boys has invented integrating erg- meters. These instruments show the sum of the energy absorbed by an electrical apparatus during a given time, they add up the number of kilogrammetres expended ; but as yet they are rather complicated, which prevents their immediate application, therefore we only mention them. Ayrton and Perry have devised a simple form of recording ergmeter intended to show the quantity of power used by a consumer from a public system of electrical supply. It consists of a fairly good clock ; the pendu- lum bob is replaced by a flat coil of fine wire, so connected that it can be arranged as a shunt between the supply poles. Close to this coil, but fixed to the clock case, is another flat coil of very stout wire, included in the main circuit. According to the relative directions of the currents in 122 METHODS OF MEASUEEMENT. these coils the rate of the clock is accelerated or retarded when the current is passing. This acceleration or retardation is proportional to C E, and there- fore to the energy which has passed in any time. By arranging the instru- ment so that the loss or gain due to the passing of the currents is very much larger than the mean rate of the clock, the instrument may be made sufficiently accurate for practical purposes. Say the clock is found at the end of a month to have gained or lost five hours, a table will at once give the number of volt-amperes, or ergs, or horse-powers per hour, or foot- pounds, or kilogrammetres, which have passed through the instrument during the month. CABLE MEASUREMENTS. The measurement of submarine cables forms one of the most important branches of the applications of electricity ; the methods employed are for the most part special. For this reason we thought it better to separate them from the general methods, and form a separate chapter for them. We will only indicate the most important methods, leaving out the question of localising faults, which would require too much detail, and for which the reader ought to consult special works. He will find a list of suitable books in the bibliography at the end of the volume. Special arrangements. The difficulties in carrying out the measurement of submarine cables, and the necessary precision, make it necessary to perform these measurements under special conditions which are not found in other branches of applied electricity. We will point out here the most important arrangements. Standard temperature. On account of the influence of temperature on the properties of the dielectric substances which are used in the con- struction of submarine cables, all results are reduced by calculation to a certain standard of temperature ; by usage 75 Fahrenheit is adopted as the standard, which corresponds with 24 Centigrade. Tank. For measuring capacity and insulation the cable is placed in a tank of cast or sheet iron perfectly connected to the earth either by gas and water-pipes, or on board ship through the hull. In the case of submerged cables the cable communicates with the earth by its external metallic envelope. The cable ought to be discharged before the tests are made by connecting it to earth for some hours. It is better to bring the ends of the cable into the testing room than to use auxiliary wires. To insulate the end of a cable. The core is uncovered for about 40 to 50 centimetres ; it is cleared of the hemp and iron wires. If the core is of indiarubber the felt is removed, and the conductor is laid bare CABLE MEASUREMENTS. 123 for a length of about 3 centimetres. The conductor and the dielectric are then covered with paraffin for a total length of about 5 centimetres, and the end is kept suspended in the air. Instruments. Complete measurements require a battery of 500 elements, a reflecting galvanometer and its shunts, a condenser, reversing keys, short circuit keys, charging and discharging keys, commutators, a Wheatstone's bridge, and resistance boxes. EESISTANCE OF THE CONDUCTOR. method. Wheatstone's bridge is generally used, especially when both ends of the cable of which the resistance is to be measured can be got at. It is then measured like an ordinary resistance. Fig. 42 shows the arrangement of the instrument. Fig. 42. Diagram of Connections for Bridge Test of Conductor of a Cable. False zero method* The connections are arranged as if for a measurement by Wheatstone's bridge. The short circuit key of the galvanometer is pressed ; the galvanometer deflects under the action 134 METHODS OF MEASUREMENT. of the earth current, and the deflection is observed. The reversing key is then pressed down, and the resistance box is rapidly unplugged until the same deflection is reproduced; the resistance is then read. This method can only be used when the earth current is constant. Reproduced deflection method (Frank Jacob'). The cable, of which the far end is to earth, is joined to a galvanometer suitably shunted, a battery, a reversing key, and to earth ; a series of readings is taken as rapidly as possible, reversing the current each time. Then a resistance box is substituted for the cable, and varied until the same deflections are reproduced. The resistances thus obtained are equal to the apparent resistances of the cable. The harmonic mean of the results of positive and negative currents gives the true resistance of the conductor. This method is very quick, and enables the variations caused by the earth currents to be easily eliminated. A battery of from 4 to 10 elements is used. Resistance Of earth plates. A galvanometer, one battery element, a large resistance, and the earth plates are arranged in circuit, and the deflection is read. The wires are then joined directly together without the plates. The deflection ought not to change if the earths are good ; if the earths have too high a resistance it may be remedied by watering the earth round the plates. ELECTROSTATIC OR INDUCTIVE CAPACITY is measured by the charge which a cable receives with unit potential the volt ; it is expressed in microfarads. The charge of a cable or condenser is proportional to the potential and the length of the cable, and inversely to the distar ce between the inducing surfaces. The rate of discharge or time necessary for a cable to lose a given part of its charge is independent of the potential. With guttapercha at 24 C. the loss during the first minute is 7 per cent. ; in the second minute 7 per cent, of the remaining charge, and so on to infinity. Lv/l + 6'9^. SPEED OF SIGNALLING. 129 Speed of signalling through cables is proportional to A _L PC r PCr S is the specific conductivity of the copper ; C the capacity per knot ; I length of the cable ; r the resistance of the conductor. The absolute speed in number of words per minute is, with a reflecting galvanometer, Hooper's indiarubber cable . . 1193'5 -J- (log D - kg d). W. Smith's guttapercha . . 968 75 (log D - log d). Common guttapercha . . . 903 '65 ~ (log D - log i). The maximum speed obtained is 50 per cent, higher than the above figures. Time of transmission of a signal (J2. Sabine).ThQ time in seconds t for a signal to be produced at the extremity of the cable is, With the Morse instrument . . . t ^ Cr seconds. Hughes . . . t = ^ Cr reflecting . . . t = -^ Cr C total capacity of the cable in microfarads; r resistance of the conductor in ohms. The speed depends both on the inertia of the instrument and the retardation produced by the cable. Weight of the conductor and of the dielectric. Expressing diameters D and d in millimetres, the weights in kilogrammes will be given by the formulae : Conductor. Weight per Weight per knot. kilometre. Solid copper .... 1278 d* 6-889 da. Stranded copper .... 10 d 5-399 d 2 . Dielectric. Hooper's indiarubber . 175(D-d*) 945 (D - d 2 ). Guttapercha .... 1-43 (D 2 - d 2 ) 771 (D - d*). 130 jfmtrti) PRACTICAL INFORMATION. APPLICATIONS. EXPERIMENTAL RESULTS. ALGEBRAIC FORMULA. Permutations and combinations. The different groups which can be made of n things each out of m things are called the combinations of n out of m things. Amongst these combinations are (1) the different products in which each group differs from the others only by one term without reckoning their order ; (2) the different permu- tations in which two groups may be considered distinct only by the order of the n things which compose them. The number of permutations of m letters n by n is equal to (in n + 1 ) (m n + 2) . . . . (m 1) m. The number of distinct products of m things n by n is equal to 1.2.3. . . . (m 1) m 1.2.3. . . . n . 1.2.3. .. . (m ri) The number of different permutations of m letters is equal to 1.2.3 (m 1) m. Newton's binomial theorem. This is so often used that we reproduce it in its most general form : (x -f- ) n * n + ax > - 1 + a 2 - - #-2 -f . . . . n ( 1) . . . . (n - NUMBERS AND THEIR RECIPROCALS, ETC. 131 TABLE OF NUMBERS (n); THEIR RECIPROCALS/,-- \; SQUARES (n 2 ) ; SQUARE ROOTS (A/TI) CUBES (n 3 ) ; CUBE ROOT ( A/) ; CIRCUMFERENCES (7m) ; AND AREAS OF CIRCLES C^?-)- WHERE n is THE DIAMETER. n 1 n ?l2 v/ Ti,3 S~* irn 7rn2 ~4~ I 1 1 1- 1 1- 3-14 79 2 5 4 1-414 8 1-259 6-28 3-14 3 3333 9 1-732 27 1-442 9-42 7'07 4 25 16 2- 64 1-587 12-57 12-57 5 2 25 2-336 125 1-709 15-71 19-63 6 1667 36 2-449 216 1-817 Iv85 28-27 7 1429 49 2-635 343 1-912 21-99 38-48 8 1?50 64 2-828 512 2' 25-13 50-27 9 1111 81 3- 729 2-08 28-27 63-62 10 1 100 3162 1,000 2-154 31-42 78-54 11 0909 121 3-316 1,331 2-223 34-56 95-03 12 0833 144 3-464 1,728 2-289 37-7 113-1 13 0769 169 3-605 2,179 2-351 40-84 132-73 14 0714 196 3741 2,744 2-41 43-98 153-94 15 0667 225 3-872 3,375 2-466 47-12 176-71 16 0625 256 4- 4,096 2-519 50-27 201-06 17 0588 289 4-123 4,913 2-571 53-41 226-98 18 0556 324 4-242 5,832 2-62 56-55 254-47 19 0526 361 4-358 6,859 2-668 59-69 283-53 20 05 400 4-472 8,000 2-714 62-83 314-16 21 0476 441 4-582 9,261 2-758 65-97 346-36 22 0455 484 4-69 10,648 2-802 69-11 380-13 23 0435 529 4-795 12,167 2-843 72-26 415-48 24 0417 576 4-898 13,824 2-884 75-4 452-39 25 04 625 5- 15,625 2-924 78-54 490-87 26 0385 676 5-099 17,576 2-962 81-68 530-93 27 037 729 5-196 19,683 3' 84-82 572-56 28 0357 784 5291 21,952 3-036 87-96 615-75 29 0345 841 5-381 24,389 3-072 91-11 660-52 30 0333 900 5-477 27,000 3-107 94-25 706-86 31 0323 961 5-567 29,791 3-141 97-39 754-77 32 0313 1,024 5-656 32,768 3-174 100-53 804-25 33 0303 1.089 5-744 35,937 3-207 103-67 855-30 31 0: J 94 1,156 5-830 39,304 3-239 106-81 907-92 35 0286 1,225 5-916 42,875 3-271 109-96 962-11 132 PRACTICAL INFORMATION. 11 1 ii M * v 7 " 7TH 4 36 0278 1,296 6- 46,656 3-391 113-1 1,017-88 37 0270 1,369 6-082 50,6,53 3-332 116-24 1,075-21 38 0263 1,444 6-164 54,872 3-361 119-38 1,134-11 39 0256 1,521 6-244 59,319 3-391 122-52 1,194-59 40 025 1,600 6-324 64,000 3-419 125-66 1,256-64 41 0244 1,681 6-403 68,921 3-448 128-8 1,320-25 42 0238 1,764 6-48 74,088 3-476 131-95 1,385-44 43 0233 1,849 6-557 79,507 3-503 135-09 1,452-2 44 0227 1,935 6-633 85,184 3-530 138-23 1,520-53 45 0222 2,025 6-708 91,125 3-556 141-37 1,520-43 46 0217 2,116 6782 97,333 3-583 144-51 1,661-9 47 0213 2,209 6-855 103,823 3-608 147-65 1,734-94 48 0208 2,334 6-928 110,592 3-634 150-8 1,809-56 49 0204 2,401 7- 117,649 3-659 153-94 1,885-74 50 02 2,500 7-071 125,000 3-684 157'OS 1,963-49 51 0196 2,601 7-141 132,651 3708 160-22 2,042-82 52 0192 2,704 7-211 140,608 3-732 163-36 2.12372 53 0189 2,809 7-28 148,877 3-756 166-5 2,206-18 54 0185 2,916 7-348 157,464 3-779 169-65 2,290-21 55 0182 3,025 7-416 166,375 3-802 172-79 2,375-83 56 0179 3,136 7-483 175,616 3-825 175-93 2,463-01 57 0175 3,249 7-549 185,193 3-848 179-07 2,551-76 58 0172 3,354 7-615 195,112 3-87 Ib2-21 2,642-08 59 0169 3,481 7-681 205,379 3-892 185-35 2,733-97 60 0167 3,600 7.745 216,000 3-914 188-5 2,827-43 61 0164 3,721 7-81 226,981 3-936 191-64 2,922-47 62 0161 3,844 7-874 238,328 3-957 194-78 3,019-07 63 0159 3,969 7-937 250,047 3-979 197-92 3,117-24 64 0156 4,096 8- 262,144 4' 201-06 3,216-99 65 0154 4,225 8-062 274,625 4-02 204-2 3,318-31 66 0152 4,356 8-124 287,496 4-041 207-34 3,421-19 67 0149 4,489 8-185 300,763 4-051 210-49 3,525-65 68 0147 4,624 8-246 314,432 4-081 213-63 3,631-68 69 0145 4,761 8-306 328,509 4-101 21677 3,739-28 70 0143 4,900 8-366 343,000 4-121 219-91 3,848-45 71 0141 5,041 8-426 357,911 4-14 223-05 3,959-19 72 0139 5,184 8-485 373,248 4-16 226-19 4 071-5 73 0137 5,329 8-544 389,017 4-179 229-34 4,185-39 74 0135 5,476 8-602 405,224 4-198 232-48 4,300-84 75 0133 5,625 8-66 421,875 4-217 235-62 4,417-86 76 0132 5,776 8-717 438,976 4-235 23876 4,536-46 77 013 5,929 8774 456,533 4-254 241-9 4,656-62 78 0128 6,084 8-831 474,552 4-272 245-04 4,778-36 79 0127 6,241 8-888 493,039 4-29 248-19 4,901-67 80 0125 6,400 8-944 512,000 4-308 251-33 5,026-55 81 0123 6,561 9' 53 ',441 4-326 254-47 5,153- 82 0122 6,724 9-055 551,368 4-344 257-61 5,281-02 83 012 6,889 9-11 571,787 4-362 260-75 5,410-61 ARITHMETICAL PROGRESSION. 133 71 71 n 2 v/ iit & irn jrn* 4 84 0119 7,056 9-165 592,704 4-379 263-89 5,54177 85 0118 7,225 9-219 614,125 4-396 267-03 5,674-5 86 0116 7,396 9-273 636,056 4-414 270-18 5,808-8 87 0115 7,569 9-327 656,503 4-431 273-32 5,944-68 88 0114 7,744 9-386 681,472 4-447 276-46 6,082-12 89 0112 7,921 9-433 704,969 4-464 279-6 6,221-14 90 0111 8,100 9-486 729,000 4-481 282-74 6,361-72 91 on 8,281 9-539 7^3,571 4-497 285-88 6,503-88 92 0109 8,464 9-591 778,688 4-514 289-03 6,647-61 93 0108 8,649 9-643 804,357 4-530 292-17 6,792-91 94 0106 8,836 9-695 830,584 4-546 295-31 6,939-78 95 0105 9,025 9746 857,375 4-562 298-45 7,088-22 96 0104 9,216 9-797 884,736 4-578 301-59 7,238-23 97 0103 9,409 9-848 912,673 4-594 304-73 7,389-81 98 0102 : 9,604 9-899 941,192 4-61 307-88 7,542-96 99 0101 ! 9,801 9-949 970,229 4-626 311-02 7,697-69 100 01 10,000 10- 1,000,000 4-642 314-16 7,853-98 and functions of IT. n = 3-1415926536. 1 = 0-3183098862. 7T 2 = 7r3 =31-0063. '1 = 0-56419. log TT = 1-4971498727. log * = 1-5028501273. 7T V /;T= 177245385. /7r~= 1-4646. Diameter of circle of which the circumference is one metre = 31'83 cm. Length of arc of 1 and radius 1 = '017452. Eadian angle of which the arc is equal to the radius (the unit of circular measure) = 57 15'. Arithmetical progression. Let a be the first term ; rthe difference between any two terms ; b the last term ; and n the number of terms. 134 PRACTICAL INFORMATION. [2* -f ( 1) r] a + /; Sum of first terms = -*-r - = --~ Sum of first n numbers from 1 to n - - -- Sum of first n odd number from 1 to (2 n 1) =. n". Oeometrical progression. Let a be the first term, b the last term, and q the ratio of any term to the next. Then, Sum of the first n terms = a -- - (7 1 Logarithms. If there be three numbers a, b, x, such that a=*, is called the logarithm of the number b to the base a, and we write : x log b. The number b is the antilogarithm. The collection of logarithms of the different numbers to one and the same base form a system of logarithms. Only two systems are now used in practice. 1st. Common or decimal logarithms, of which the base is 10. 2nd. Natural, Naperian, or hyperbolic logarithms, of which the base is e. e = 2-71828. Common logarithms are indicated by the symbol (log) ; natural logarithms by (log e ). LOGARITHM?. .135 TABLE OF DECIMAL (log) AND NAPERIAN (loge) LOGARITHMS OF NUMBERS FROM 1 TO 100. NUMBEKS. LOGARITHMS. NUMBERS. 1 LOGARITHMS. DECIMAL. NAPERIAN. DECIMAL. NAPERIAN. 1 o- o- 36 1-55630 3-58351 2 30103 69314 37 1-56820 3-61091 3 47712 1-09861 38 1-57978 3-63758 4 60206 1-38629 39 1-59106 3-66356 5 69897 1-60943 40 1-60206 3-68887 6 7-815 179175 7 84510 1-94591 41 1-61278 3-71357 8 90309 2-07944 42 1-62325 3-73766 9 95424 2-19722 43 1-63347 3-76120 10 1-00000 2-30258 44 1-64345 3-78418 45 1-65321 3-80666 11 1-04139 2-39789 46 1-66276 3-82864 12 1 1-07918 2-48490 47 1-67210 3-85014 13 1-11394 2-56494 48 1-68124 3-87120 14 1-14613 2-63905 49 1-69020 3-89182 15 1-17609 2-70805 50 1-69897 3-91202 16 1-20412 2-77^58 17 1-23045 2-83321 51 1-70757 3-93182 18 1-25527 2-89037 52 1-71600 3-95124 19 1-27875 2-94413 53 1-72428 3-97029 20 1-30103 2-99573 54 1-732:39 3-98898 55 1-74036 4-00733 21 1-32222 3-04452 56 1-74819 4-02535 85) 1-34242 3-09104 57 1-75587 4-04305 23 1-36173 3-13549 58 1-76343 4-06044 24 1-38021 3-17805 59 1-77085 4-07753 25 1-39791 3-21887 60 1-77815 4-09434 26 1-41497 3-25809 27 1-43136 3-29583 61 1-78533 4-11087 28 1-44716 3-33220 62 1-79239 4-12713 29 i 1-46240 3-36729 63 1-79934 4-14313 30 i 1-47712 3-40119 64 1-80618 4-15888 65 1-81201 4-17439 31 1-49136 3-43398 66 1-81954 4-18965 34 1-50515 3-46573 67 1-82607 4-20469 33 1-51851 3-49650 68 1-83251 4-21951 31 1-5:5148 3-52636 69 1-83885 4-23411 35 1-541-. 7 3-55534 70 1-84510 4-24850 136 PRACTICAL INFORMATION. 1 LOGARITHMS. i LOGARITHMS. g 1 DECIMAL. NAPERIAN. s N DECIMAL. NAPERIAN. 71 1-85126 4-2o268 8<5 1-93450 4-45435 72 1-85733 4-27667 87 1-93952 4-46591 73 1-86332 4-29046 88 1-94448 4-47734 74 1-86923 4-30407 89 1-94939 4-48864 75 1-87506 4-31749 90 1-95424 4-49981 76 1-88081 4 33073 77 1-88649 4-34381 91 1-95904 4-51086 78 1-89209 4-35671 92 1-96379 4-52170 79 1-89763 4-36945 93 1-96848 4-53260 80 1-90309 4-38203 94 1-97313 4-54329 95 1-97772 4-55388 81 1-90849 4-39445 96 1-98227 4-55435 82 1-91381 4-40672 97 1-98677 4-50471 *-3 1-91908 4-41884 98 1-99123 4-58497 84 1-92428 4-43032 99 1-99564 4-59512 85 1-92942 4-44265 KO 2-00000 4-60517 Knowing the log of a number n in the one system, its log in the other system is obtained by the following formula : loge n = 2-3025851 log . log n 0-434294482 log,, Properties of logs. Those which are most generally used are set out in the following table : log ab ~ log a -}- log b. log - =i log a log b. log aP in b log a. i>/- log a log Va = --. Interest. Simple interest. Let i be the rate (sum brought in by one pound during one year expressed as a fraction of a pound), A the sum placed at interest during n years, which will bring in Kin pounds, and will become A (1 + in). Discount. If a sum A be paid n years before it is due only A (1 - in) is paid. GEOMETRICAL FORMULAE. 137 Present value. A sum A due in n years is represented at the present time by a sum A', such that if it were placed at the rate of interest i during the time n, it would become equal to A ; therefore, A A' = 1 + m Compound interest. A sum A placed at compound interest for n years becomes Annuities. A sum a due annually for n years has a present value A given by the equation OEOUIETRICAI, Length. SQUARE. Diagonal s \/2 1'414 s (s length of side of square). CIRCUMFERENCE 2^r (r radius). ABC OP = Hg. Area. CIRCLE =. w s = ~ ( r = radius, d = diameter). ELLIPSE irab (a =. semi-major axis, 6 rr semi-minor axis). CYLINDER (lateral area) si (s = circumference, I length of generatrix, or 2"T/, r =: radius) . CONE (lateral area) -^ (s circumference, I length of generatrix, or nr l/h? -\- r 2 . r rr radius of base, h height of cone) . FRUSTRUM OF CONE (lateral area) = /"^W sands' circumference of base and top, / = generatrix. SPHERE 4 great circles =: 4;rr 2 . ZONE ON A SPHERE =. 2^rh (h =. width of the zone measured on the surface of the sphere). 138 PRACTICAL INFORMATION. Volume or cubic contents. -r> L PYEAMID AND CONE= -^- (B area of base, h height). CYLINDER or PRISM = BA. TRUNCATED PYRAMID WITH THE TOP PLANE PARALLEL TO THE BASE = h (B -|- B'-{- x/BB') (B and B' areas of base and top plane). FRUSTRUM OP CONE WITH TOP PLANE PARALLEL TO BASE =. lirh (r 2 -f- r" 2 -f rr") (r and r' radii of base and top plane) . SPHERE = wr3 4-19?- 3 . SEGMENT OF A SPHERE. (t ) * + 6 7r ^ 3 (B and B' areas of the plane surfaces, h width of the zone). ELLIPSOID f IT abc (a, b, c, semi-axes of ellipsoid). THE SURFACE OF REVOLUTION, generated by an area S in the plane of the axis of rotation, encloses a volume equal to the product of the area S, by the circumference traced out by its centre of gravity. If d be the distance of the centre of gravity from the axis of rotation, the volume of the solid generated V is EADII AND AREAS OF BEGULAR INSCRIBED POLYGONS. IN TERMS OF THE SIDE. o M H to 2 H p NAME OP POLYGON. ptj O B 9 8 a ? 3 5 b M 5 Equilateral triangle 3 4 60 90 288 5 576 706 433 1 Pentagon Hexagon Octagon Decagon Dodecagon 5 6 8 10 12 108 120 135 144 150 688 866 1-207 1-539 1-866 850 1 1-305 1-618 1.93 1-72 259 4-838 7-694 11-196 SINES AND TANGENTS. 139 TABLE OF SINES AND TANGENTS. DEGREES. SINES. TANGENTS. DEGREES. SINES. TANGENTS. 1 017 017 46 719 1-036 2 035 035 47 731 1-073 3 052 052 48 743 1-111 4 07 07 49 755 1-151 5 087 088 50 766 1-192 6 105 105 51 777 1-236 7 122 123 52 788 1-281 8 139 141 53 799 1-328 9 157 159 54 809 1-377 10 174 177 55 819 1-429 11 191 195 56 829 1-483 12 208 213 57 839 1-541 13 225 231 58 848 1-601 14 242 2.50 59 857 1-665 15 259 288 60 866 1-733 16 276 287 61 875 1-805 17 293 306 62 883 1-882 18 309 325 63 891 1964 19 326 345 64 899 2-052 20 342 364 65 905 2-146 21 359 384 66 914 2-248 22 375 404 67 921 2-358 23 391 425 68 927 2-477 24 407 445 69 934 2-607 25 423 467 70 94 2-75 26 439 488 71 946 2-907 27 454 510 72 951 3-081 28 47 532 73 956 3-274 29 485 555 74 961 3-481 30 5 578 75 966 3-736 31 515 601 76 97 4-016 32 53 625 77 974 4-337 33 545 650 78 978 4-711 34 559 675 79 982 5-152 35 574 701 80 985 5-681 36 588 727 81 988 6-326 37 602 754 82 990 7-130 38 616 782 83 992 8-164 39 629 810 84 994 9-541 40 643 839 85 996 11-468 41 656 &70 83 997 14-361 42 669 901 87 998 19-188 43 682 933 88 999 28-877 44 695 966 89 999 58-261 45 707 r 90 1- 00 140 PRACTICAL INFORMATION. TRIGONOMETRICAL FORMULAE, sin a 2 sin - a cos - a ; sin a 1 tan a, -- cot # - cos a ' ~~ tail a 1 cos 2 a, tan # = rr sin 2 a sin 2 a -f- cos 2 # 1 tan a, 2 a 1 cos a, =. -y -- _ Vl+tan 2 sin 2 a =. 2 sin a cos a cos 2 ~ cos 2 sin 2 a 2 tan 1 - tan 2 a cos a =. I 2 sin 2 - # cos =. I -f- 2 cos 2 - a 2 1 cos 2 a tan 2 a z= 1 + cos 2 -(A + B); a sin C ~ sin A ' Third case. Given two sides and the angle included between them (0, b, C). Knowing - (A B) we then get j _ a sin C_ sin C_ (a -|- 6) sin \ C r T5 _ ~ sin A~ sin B ~~ cos \ (A - B) Fourth case. Given the three sides (#, b, c). then Similarly for the other angles B and C. 144 PRACTICAL INFORMATION. COINS OF DIFFERENT COUNTEIES. Belgium, Greece, Italy, Switzerland. -These four nations since 1880 have formed a union for gold and silver coins, based on the franc '04 of 1, Ifr. = 100 centimes. Germany. The Reichs-mark of 100 pfennigs Ifr. -2345, or nearly Is. Gold coins, 20, 10, and 5 mark pieces: silver coins, 5, 2, 1, ^, and \ marks. Austria. Florin of 100 kreutzers = 2-4691fr., or nearly 2s. 8 florins = 20fr. ; about 16s. 1 ducat zz ll-85fr. ; about 9s. 5d. Spain. 1 peseta = Ifr. ; a little less than lOd. 1 real = \ peseta. Holland. Florin of 100 cents = 2'lOfr. ; about Is. lOd. Portugal* Milre'is = 5'6fr. ; nearly 4s. 6d. Russia. Rouble 100 kopecks = 4fr. ; about Is. 5^d. Sweden and Norway. Krona = 100 ore = l-3888fr. = lOd. India. Rupee = 2'3757fr. ; less than 2s. United States. Dollar of 100 cents = 5'1825fr. ; about 4s. Brazil. Milreis = 2-83fr. = 2s. 3d. PHYSICAL, FORMUI.JE. Formulae for falling bodies and the pendulum. t =. time in seconds. s =. space passed over in time t. v =. velocity at end of time t. h = height from which the body falls. g =. acceleration due to gravity. / = length of pendulum. MOMENT OF INERTIA. 145 Moment Of inertia. The moment of inertia of a body is the sum of the products of the masses of its every material point into the square of the distance of that point from the axis of rotation. Calling it I, 1 = 2 i>*. The radius of gyration is the distance from the axis of rotation at which the whole mass of the body, concentrated at a point, would have the same moment of inertia as the body. If M be the whole mass of the body, and R the radius of gyration, ME 2 = 2*r2. Whence R2 2/n; ' 2 . M In the case of homogeneous bodies, when the radius of gyration has been determined, the moment of inertia can be deduced from it. STRAIGHT ROD. Let I be the length of the rod. If the axis of rotation is perpendicular at one end, If the axis is perpendicular and in the middle, 2 - ROD BENT INTO THE ARC OF A CIRCLE, axis passing through the centre of the arc of radius ; and perpendicular to its plane, R2 = r2. Axis passing through the middle of the arc along a radius, 7-2 Disc. Axis passing through the centre, perpendicular to its plane, 2 ^ Axis passing through a diameter, CONE. Radius of base r } axis passing through the axis of figure, 146 PRACTICAL INFORMATION. SPHEEE of radius r, axis passing along a diameter, Formula of the bifilar suspension. Let I be the length of the suspending threads or wires, a their distance apart at their upper ends, b their distance apart at their lower ends, W the weight which they bear, o the angle of deflection. The moment of the couple exerted by the bifilar suspension when its position of equilibrium is changed, is, ab W M X g i n a - For very small angles the sine is equal to the arc, and the moment becomes proportional to the deflection. In practice the moment is varied, and thus the sensibility changed by altering a. VELOCITIES. Velocity Of sound in metres per second and feet per second : Metres Feet In air at O la water at 8 In cast iron per second, per second. 330-9 10857 337-2 1106-3 1435 4708-2 3480 11417-9 The increase in the velocity of sound in air is '626 metre (2 feet) per degree C. Velocity of light : Kilometres Miles per second, per second. Foucault (1862) 298,000 185,171 Cornu (1874) 300,000 186,414 Velocity of wind: Pressure in Metres per second. Feet per second. Kilogrammes per square inch. In pounds Pei fo S ot! ar< Fresh breeze 7 23 6 1-23 Strong wind 15 49-2 30 6-15 Storm . 24 787 78 16 Hurricane 45 147-6 275 56-4 VELOCITIES. 1 47 Mean velocity of engine straps : Metres Feet per sec. per sec. Lower limit for transmission of power by pulleys ft. in. and straps I'l 37 Velocity for small powers 1'5 4 11 Limit of speed for transmission of energy by ropes and cords 25 83 Velocity of large straps 61 20 Limit of velocity for large straps . . 9' 15 33 Velocity of translation of the armatures of some dynamo machines: The five-light Gramme machine, revolving at 1300 revolutions par minute, with a ring 26 cm. (10'4 inches) in diameter, has a velocity of 17*7 metres per second (58 feet per second). In the new 12-pole machines, the large size of the ring gives the high velocity of 43 metres per second (141 feet per second) for the outside of the ring. In the Fcrrantl machine, the speed of the middle part of the armature is 38 metres per second (124 feet per second), and of the outside part 54 metres per second (177 feet per second). In the Siemens machines, the small armatures only move over about 8 to 10 metres per second (26 to 32 feet per second) . The large alternating current machines (no iron in the armatures) have as high a speed as 32 metres per second (105 feet per second). Other conditions remaining the same, the higher the speed of trans- lation the lighter the machine, and the more its internal resistance can be diminished. Work produced toy men and horses. -A man turn- ing a handle can work 8 hours a day, and produce 6 kilogrammetres per second (43 '4 foot-pounds per second). His total daily work is therefore 172,800 kilogrammetres (1,249,879 foot-pounds). A draught -horse walk- ing and dragging a carriage or a boat at the rate of I'l metres per second (3 feet 7 inches per second) produces 59 '4 kgms. per second (429 '6 foot- pounds per second), so that in 8 hours it produces 1,712,000 kgms. (123,830,672 foot-pounds). A horse trotting or cantering, dragging a light carriage on rails at the rate of 4*37 metres per second (14 feet per second) can produce 61 kgms. per second (441 foot-pounds per second) for 4 hours, or a daily work of 881,280 kgms. (6,374,386 foot-pounds). 148 PRACTICAL INFORMATION. SPECIFIC GRAVITIES (Wurtz and Rankine). WEIGHT IN GRAMMES OF ONE CUBIC CENTIMETRE AT 0C. Metals. Indium . 22-38 Brass (wire). . 8-54 Platinum 21 to 22 Steel . 7-8 to 7-9 Gold . 19 to 19-6 Wrought iron . 7-8 Lead . . 11-4 Tin ... 7 '3 to 7'5 Silver . . 10-5 Zinc . . 7-19 Bismuth . 9-82 Cast iron . 7- Copper (hammered) . 8-9 Selenium (black) . . 4-8 (rolled) . . 8-8 (red) . .- . 4-5 (cast) . . 8-6 Aluminium (rolled) * . 2-67 Cadmium (rolled) . 8-69 Magnesium . . 1-74 Nickel (cast) . 8-57 Sodium 97 Brass (cast) . 7'8 to 8'4 Lithium 59 Insulators. Flint . 3 to 3.5 Silica . . ' . 1-7 Crown . 2-5 Pitch . . 1-65 Green glass . 2-64 Tar . . 1-02 Plate . , 2-8 Hooper's indiarubber . 1-18 Marble . 2-7 Guttapercha 97 to -98 Paraffin 87 Indiarubber 93 Quartz . 2'65 Ebonite . 1-15 Porcelain . 2-15to 2-3 Sulphur (octohedialj . 2-07 Ivory . 1'8 1 ,, (prismatic) . 1-97 Liquids. Mercury . 13-596 Olive oil . -915 Bromine (at 15^) . 2-99 Naphtha , ' . '848 Carbon bisulphide . 1-263 Alcohol (pure) . , . -791 Sea-water . . 1-026 Petroleum . . -878 Water at 4' . 1 JEther . -716 Various substances. Carre's carbon . . 1-62 Coke . . 1 to 1-66 Retort carbon . 1-91 Ice at 4 3 . 92 Diamond . 3-5 Loose snow. 1 SPECIFIC GRAVITIES. 149 TABLE OF THE DEGREES OF BAUME, CARTIER, AND GAY-LUSSAC. FOR LIQUIDS LIGHTER THAN WATER, WITH THEIR CORRESPONDING SPECIFIC GRAVITIES. The Gay-Lussac degrees correspond to the percentage by volume in of water and alcohol at 15 C. (Agenda du Chimiste}. mixture DEGREES. DEGREES. |' * SPECIFIC d SPECIFIC w d CO GRAVITY. -w t CO GiiAVl FY. | 5 p H? S3 p 3 4 M o H < PQ o H 4 Ci5 10 10 1 31 965 1 999 15 32 964 2 997 33 963 3 996 16 34 964 4 994 35 96 11 11 6 993 36 959 6 992 16 37 957 7 99 38 956 8 989 17 39 954 9 988 40 953 12 10 987 17 41 951 12 11 986 1 42 949 12 984 18 43 948 13 983 41 946 14 982 45 945 15 981 18 46 943 16 98 19 47 941 13 17 .979 18 94 13 18 978 49 938 19 977 19 938 20 976 51 934 21 975 52 932 22 974 21 20 53 93 14 23 973 54 928 24 972 55 926 14 25 971 22 21 56 924 26 97 57 922 27 969 58 92 28 968 23 22 59 918 15 29 S67 60 915 30 966 61 913 .grJCZ^-~. r~~:r=5^^ 150 PRACTICAL INFORMATION. DEGREES. DEGREES. 4 rf I SPECIFIC GRAVITY. pj si i SPECIFIC GRAVITY. S & 1 t= P 1 ^3 d < i .1 j D 24 23 62 911 82 86 63 909 34 32 83 857 25 64 903 35 84 854 24 65 904 33 85 851 66 902 36 34 86 848 26 67 899 87 845 25 68 896 37 35 88 842 27 69 893 38 33 89 838 23 70 891 835 28 71 888 33 37 91 832 27 72 . '886 92 829 29 73 884 40 38 93 826 28 74 881. 41 94 822 30 75 879 42 39 95 818 76 87o 43 40 96 814 31 29 77 874 44 41 97 81 78 871 45 42 98 805 32 30 79 868 46 43 99 3 80 '8^5 47 4i 100 795 33 31 81 863 48 791 NOTE. If the temperature be (15 + n) ('4n) degrees must be subtracted iu order to obtain the percentage of alcohol. ('4n) must be added if t --= 15 - n. Density of water at ordinary temperatures. (Eossetti] : Temperature 2 4 6 . 8 10 Densities. 999871 999747 Temperature. 15 . 20 . 25 . 30 . 100 3 Densities. 99916 99712 995765 D5865 SPECIFIC GRAVITIES. 151 TABLE OF THE DEGKEES OF BAUME AND BECK FOR LIQUIDS HEAVIER THAN WATER, WITH CORRESPONDING SPECIFIC GRAVITIES. DEGREES BAUME OR BECK. CORRESPONDING SPECIFIC GRAVITIES. DFGREES BAUME OR BECK. CORRESPONDING SPECIFIC GRAVITIES. BAUME. BECK. BAUME. BECK. 1 1 37 1-3447 1-2782 1 1-0039 1-0059 38 1-3574 1-2879 2 1-014 1-0119 39 1-3703 1-2977 3 1-0212 1-018 40 1-3834 1-3077 4 1-0285 1-0241 41 1-3968 1-3178 5 1-0358 1-0303 42 1-4105 1-3281 6 1-0134 1-0366 43 1-4244 1-3386 7 1-0509 1-0429 44 1-4386 1-3492 8 1-0587 1-0494 45 1-4531 1-33 9 1-OS65 1-0559 46 1-4378 1-371 10 1-0744 1-0625 47 1-4828 1-3821 11 1-0825 1-0692 48 1-4984 1-3934 12 1-0907 1-0759 49 1-5141 1-405 13 1-099 1-0828 50 1-5301 1-4167 14 1-1074 1-0897 51 1-5466 1-4286 15 1-116 1-0968 52 1-5633 1-4107 16 1-1247 1-1039 53 1-5804 1-453 17 1-1335 1-1111 54 1-5978 1-4655 18 1-1425 1-1184 55 1-6158 1-4783 19 1-1516 1-1258 56 1.6342 1-4912 20 T1G08 1-1333 57 1-6529 1-5044 21 1-1702 1-1409 58 1-672 1-5179 22 1-1798 1-1486 59 1-6916 1-5315 23 1-1896 1-1565 60 1-7116 1-5454 24 1.1994 1-1644 61 1-7322 1-5596 25 1-2095 1-1724 62 1-7532 1-5741 26 1-2198 1-1806 63 1-7748 1-5888 27 1-2301 1-1888 64 1-7969 1-6038 28 1-2407 1-1972 65 1-8195 1-619 29 1-2515 1-2057 66 1-8428 1-6346 30 1-2624 1-2143 67 1-839 1-6505 31 1-2736 1-2230 68 1-864 1-6667 32 1-2849 1-2319 69 1-885 1-6832 33 1-2965 1-2409 70 1-909 17 34 1-3082 1-25 71 1-935 35 1-3202 1-2593 72 1-96 36 1-3324 1-268 152 PRACTICAL INFORMATION. SPECIFIC GRAVITIES OF SOLUTIONS OF SULPHURIC ACID IN WATER AT 15 C. (J. Kolb). . 100 PARTS BY WEIGHT CO 100 PARTS BY WEIGHT -w W CONTAIN w w CONTAIN 1 p I H F 1 s m o 8 8 S t3 B 1 8 8 g p u 4 & g rH 3 w si T* 5W E ft ^h GM H O o 5 ^ i I 5 o ^o P E CO ft S i % CO 02 W 5 co QB W H 1 7 9 1-2 34 1-308 32-8 40-2 51-1 1 1-007 1-5 1-9 2-4 35 1-32 33-9 41-6 53-3 2 1-014 2-3 2-8 3-6 36 1-332 35-1 43 55-1 3 1-022 3-1 3-8 4-9 37 1-345 36-2 44-4 56-9 4 1-029 3-9 4-8 6-1 38 1-357 37-2 45-5 58-3 5 1-037 4-7 5-8 7-4 39 1-37 38-3 46-9 60 6 1-045 5-6 6-8 8-7 40 1-383 39-5 48-3 61-9 7 1-052 6-4 7-8 10 8 9 10 1-06 1-067 1-075 7-2 8 8-8 8-8 9-8 10-8 11-3 12-6 13-8 41 42 43 1-397 1-41 1-424 40-7 41-8 42-9 49-8 51-2 52-8 63-8 65-6 67-4 44 1-438 44-1 54 69-1 11 1-083 9-7 11-9 15-2 45 1-453 45-2 55-4 70-9 12 1-091 10-6 13 16-7 46 1-468 46-4 56-9 72-9 13 1-1 11-5 14-1 18-1 47 1-483 47-6 58-3 74-7 14 1-108 12-4 15-2 19-5 48 1-498 48-7 59-6 76-3 15 1-116 13-2 16-2 20-7 49 1-514 49-8 61 78-1 16 1-125 14-1 17-3 22-2 50 1-530 51 62-5 80 17 1-134 15-1 18-5 23-7 18 19 20 1-142 1-152 1-162 16 17 18 19-6 20-8 22-2 25-1 26-6 28-4 51 52 53 1-540 1-563 1-58 52-2 53-5 54-9 64 65-5 67, 82 83-9 85-8 54 1-597 56 68-6 87-8 21 1-171 19 23-3 29-8 55 1-615 57-1 70; 89-6 22 1-18 20 24-5 31-4 56 1-634 58-4 71-6 91-7 23 1-19 21-1 25-8 33 57 1-652 59-7 73-2 93-7 24 1-2 22-1 27-1 34-7 58 1-672 61 74-7 95-7 25 1-21 23-2 28-4 36-4 59 1-691 62-4 76-4 97-8 26 1-22 24-2 29-6 37-9 60 1-711 63-8 78-1 100 27 1-231 25-3 31 39-7 28 29 30 1-241 1-252 1-263 26-3 27-3 28-8 32-2 33-4 34-7 41-2 42-8 44-4 61 62 63 1-732 1-753 1-774 65-2 66-7 68-7 79-9 81-7 84-1 102-3 104-6 107-7 64 1-796 70-6 86-5 110-8 31 1-274 29-4 36 46-1 65 1-819 73-2 89-7 114-8 3! 1-285 30-5 37-4 47-9 66 1-842 81-6 100 128 33 1-297 31-7 38-8 49-7 DENSITIES OF SOLUTIONS. 153 DENSITIES OF SOLUTIONS OF NITEIC ACID AT 15 C., GIVING THE PERCENTAGE OF NITRIC ACID HNO 3 OR NITRIC ANHYDRIDE N 2 5 . H H g B 2 w B fc I DEGREES BAUME. COMPOSITION. WATER P CENT. NITRIC A( HNO 3 PER < IP BOILING PO^T. 1-522 49-3 HNO 3 ICO 85-8 86 1-486 4S-5 + 1/2 H 2 11-25 88-75 75-1 99 1-452 45 H 2 22-22 77'78 667 115 1-42 42-6 3/2 H 2 O 30 70 60-1 123 1-39 40-4 2 H 2 O 36-36 63-64 54-5 119 1-361 35-2 5/2 H 2 O 41-67 58-33 50-1 117 1-338 36-5 3 H 2 O 46-16 53-84 46-2 117 1.315 34-5 7/2 H 2 50 50 42-9 113 1-297 33-2 4 H 2 53-33 46-67 40'1 113 1-277 31'4 9/2 H 2 O 56-25 43-75 37-6 113 1-26 29-7 5 H 2 O 58-82 41-18 35-4 113 1-245 28-4 11/2 H 2 61-11 38-89 33-4 113 1-232 27-2 6 H 2 63-16 36'8i 31-6 113 1-219 25-8 13/2 H 2 O 65 35 30-1 113 1-207 24-7 7 H 2 66-67 33-33 28-6 108 1-197 23-8 15/2 H 2 68-18 31-82 27-3 108 1-188 22-9 8 H 2 69-56 30-44 26-1 108 1-18 22 17/2 H 2 O 70-83 29-17 25 108 1-173 21 9 H 2 72 28 24 108 1-166 20-4 19/2 H 2 73-08 23-92 23-1 108 1-16 19-9 10 H 2 74-07 25-93 22-2 108 1-155 19-3 21/2 H 2 O 75 25 21-4 about 104 DENSITIES OF SOLUTIONS OF ZINC SULPHATE AT 15 C. (Gerlach). ZnSO 4 PER 100 BY WEIGHT. i DENSITIES. ZnSO 4 + 7H 2 O PER 100 BY WEIGHT. DENSITIES. i 5 1-0288 35 1-231 10 1-0593 40 1-2703 15 1-0905 45 1-31 20 1-123S 50 1-3522 25 1-1574 55 1-3986 30 1-1933 60 1-4451 154 PRACTICAL INFORMATION. DENSITIES OF SOLUTIONS OF COMMON SALT AT +15 C. (GerlocJi). NaCl PEE, ICO BY WEIGHT. DENSITIIS. NaCl PER 100 BY WEIGHT. DENSITIES. 2 1-01450 16 1-11938 4 1-029 18 1-13523 6 1-04366 20 1-15107 8 1-05851 . 22 1-16755 10 1-07335 24 1-18101 12 1-08859 26 1-20098 14 1-10384 23-39,* 1-20433 * Saturation. SPECIFIC GRAVITY OF GASES AND VAPOURS (Berthelot). WEIGHT IN GRAMMES OF NAMES. DENSITY, AlE BEING 1. A CUBIC DECIMETRE AT C. AND 760 MM. PRESSURE. Ah- 1 1-2932 Oxygen . . 1-056 1-43 Hydrogen 03926 08958 Nitrogen 9714 1-256 Chlorine 2-47 3-18 Bromine 554 7-16 Iodine 8-716 11-3 Mercury 6-976 8-96 Ammonia 597 761 Oxide of carbon .... 968 1-254 Carbonic acid .... 1-529 1-9774 Vapour of water 6235 806 ,, of absolute alcohol 1-613 2-095 ,, of sulphuric ether 2586 3*395 ,, of essence of turpen- tine 5-013 6-512 BAROMETER. 155 DENSITIES OF SOLUTIONS OF COPPER SULPHATE AT 15 C. (Gerlach). PERCENTAGE BY || PERCENTAGE BY WEIGHT OF DENSITIES. WEIGHT OF DENSITIES. CuS0 4 + 5H 2 O. CuS0 4 + 5H 2 0. 2 1-0126 14 1-0923 4 1-0254 16 1-1033 6 1-0384 18 1-1208 8 1-0516 20 1-1354 10 1-0649 22 1-1501 12 1-0785 24 1-1659 BAROMETER. Correct formula for reduction to O of the height of the barometer. h, reduced height ; H, observed height ; t, temperature at the time of observation in degrees C. ; K, linear coefficient of expansion of the scale. For brass ....... K=r -000016782. crystal ...... K = -00007567. MEAN HEIGHT OF BAROMETER FOR DIFFERENT HEIGHTS ABOVE THE SEA LEVEL. HEIGHT. HEIGHT OF BAROMETER. HEIGHT. HEIGHT OF BAROMETER. metres. millimetres. metres. millimetres. 762 3147 660 21 760 1269 650 127 750 1393 640 234 740 1519 630 342 730 1647 620 453 720 1777 610 564 710 1909 600 678 700 2013 590 793 690 2180 580 803 680 2318 570 1027 670 24GO 5tiO 156 PRACTICAL INFORMATION. MEASUREMENT OF TEMPERATURE. FAHRENHEIT AND CENTIGRADE THERMOMETER SCALES. FAHREN. CENTIGRADE, i FAHREK. CENTIGRADE. ; FAHREN. ' CENTIGRADE. o o o 4 20 33 56 70 2rn 3 19-44 34 1-11 71 21-67 - 2 - - 18-89 35 1-67 72 22-22 1 18-33 36 2-22 73 22-78 - 17-78 37 2-78 74 23-33 1 17-22 38 3-33 75 23-89 2 16-67 39 3-89 76 24-41 3 16-11 40 4-44 77 25 4 - 15-56 41 5 78 25-56 5 - 15 42 5-56 79 26-11 6 - 14-44 45 6-11 80 26-67 7 - 13-89 41 6-67 81 27-22 8 13-33 45 7-22 82 27-78 9 12-78 43 7-78 83 28-33 10 12-22 47 8-33 84 23-89 11 - 11-67 48 8-89 85 29-44 12 11-11 43 9-44 88 30 13 - 10 56 | 50 10 87 30-56 14 10 51 10-56 88 31-11 15 - 9-41 52 11-11 89 31-67 16 - 8-89 53 11-67 90 32-22 17 - 8-33 54 12-22 91 32-78 18 7-78 55 12-78 92 33-33 19 7-22 53 13-33 93 33-89 20 6-67 57 13-89 94 3444 21 6-11 53 14-44 95 35 22 - 5-56 59 15 96 35-56 23 5 60 15-56 97 36-11 24 - 4-44 61 16-11 98 36-67 25 3-89 62 16-67 99 37-22 26 3-33 63 17-22 100 37-78 27 - 2-73 64 17-78 101 38-33 28 - 2-22 65 18-33 102 38-89 29 - 1-67 63 18-89 103 39-44 30 I'll 67 19'4t 10 1 40 31 0-53 68 20 105 40-53 32 69 20-53 103 41-11 MEASUREMENT OF TEMPERATURE. 157 DETERMINATION OF HIGH TEMPERATURES IN DEGREES C. BY THE COLOUR OF HOT PLATINUM (Pouillet). COLOUR OF CORRESPONDING | COLOUR OF CORRESPONDING PLATINUM. TEMPERATURE. PLATINUM. TEMPERATURE. Beg inning to be rc Dark red 525 700 Dark orange . Bright orange 1100 1200 Beginning to be ) cherry-red )" 00 White . Welding white 1300 140) Cherry- red . 00 Dazzling white . 1503 Bright cherry-red 100J CUBIC COEFFICIENTS OF EXPANSION OF SOME SOLIDS FOR 1 between AND 1CO C. SOLID. COEFFIC. SOLID. COEFFIC i 00000 o-oooo Steel 11503 i; Granite .... 08S25 Tempered steel 12250 !, Gypsum . . . 14010 Aluminium 222o9 ! White marble . . . 10720 Silver .... 19097 Black marble . . . 04260 Pibe wood 03520 Gold . . . 15136 Bricks . ... 05502 Platinum. . . . 08842 Bronze .... 18492 Lead 28484 Pine charcoal . 10300 Fluor spa- . . . 20700 Brass 18782 Glass tube . . . 08969 Copper .... 17182 rod . . . 09220 Tin 21730 Plain glass . . . ! C8613 Wrought iron . 11821 Plate glass (St. Gobaiu) . ! 08909 Iron wiie .... 14401 Flint glass . . . 08167 Cast iron .... 11100 Ziuc . . 29680 Ice from 27 to 1 51813 CUBIC COEFFICIENT OF EXPANSION OF MERCURY. Absolute between and 100 K = 0-003180180. Apparent in glass : = 0'0001544. 158 PRACTICAL INFORMATION. MELTING AND BOILING POINTS OF COMMON SUBSTANCES. THE BOILING POINTS DETERMINED AT THE PRESSURE OF 760 MM. OF MERCURY. SUBSTANCES. MELTING. BOILING. < - 90 78'3 Alloys (See Fusible alloys) . 600 Amber . . . . . Antimony ' Arsenic ....... 288 440 210 Benzine Bismuth Bromine .... . Bronze Butter Cadmium Cane sugar Carbon bisulphide 7 265 - 7-5 900 30 3JO 160 80-8 63 860 48 - 78 Cast iron Caustic potash (saturated solution) Chloride of sodium (saturated solution) Copper . Distilled water 1050 to 1200 1050 o 175 108 10D Essence of turpentine .... Fine gold Gold 900 ths - 10 1250 1180 156-8 Iodine" Lead Linseed oil Mercury Nitrate of silvtr Olive oil . Palm oil Paraffin Petroleum Phosphorus Platinum Sea water Selenium Silver 107 . 335 - 20 - 39-5 198 2-5 29 437 4*1 2030 - 2-5 217 1000 49 176 387'5 350 370 106 290 103-7 665 70 Stearine Steel Sulphur Sulphuric rether .... 61 1300 to 1400 114-5 - 32 400 35 5 Sulphurous acid Tallow - 79-2 33 - 10 White wax ...... 76 2 1500 to 1600 Yellow wax 687 Zinc 412 1040 MEASUREMENT OF TEMPERATURE. 159 Boiling points of liquids at pressure 76O mm. of mercury (Regnault}. Absolute alcohol (?) jEther - 90 34-97 Chloroform Essence of turpentine Alcohol Ammonia . Benzine . . 78-26 - 38-5 80'36 Mercury . Nitrogen monoxide . Sulphuric acid Carbon bisulphide Carbonic acid . Chlorine . 46-20 - 78-2 - 33-6 Sulphurous acid Water . 60-16 . 159-15 . 357-25 - 87-9 - 61-8 - 10-08 . 100 HEAT DISENGAGED BY THE OXYDATION OF 1 GRAMME (Everett), IN CALORIES (GRAMME DEGREE). SUBSTANCES. COMPOUND FORMED. HEAT DISENGAGED. Alcohol Carbon Carbon monoxide C0 2 CO? 6,900 8,000 2 420 Copper Hydrogen .... Iron . CuO H 2 Fe^Oi 602 34,000 1 576 Marsh gas Oleflantgas Phosphorus Sulphur . . . . . ....... Tin Zinc . . C0 2 + H 2 O P 2 5 S0 2 Sn0 2 ZnO 13,100 11,900 5,747 2,300 1,233 1,301 HEAT DISENGAGED BY THE COMBINATION OF 1 GRAMME WITH CHLORINE (Everett). SUBSTANCES. COMPOUND FORMED. HEAT DISENGAGED. Copper Hydrogen Iron Potassium Tin CuCl 2 HC1 Fe 2 C' 6 KC1 SnCl4 961 23,033 1,745 2,655 1 079 Zinc . . . . . ZnCl2 1,529 160 PRACTICAL INFORMATION. Heat disengaged (+} or absorbed (-) by che- mical actions (Favre and Silbermanri). (The figures relate to the equivalent in grammes in relation to that of hydrogen taken as unity, and not to unity of weight.) They are expressed in calories (g.-d.). Oxydation of amalgamated zinc + 42,800 Combination of zinc oxide with sulphuric acid . + 10,450 Decomposition of water 34,450 Decomposition of copper sulphate .... - 29,600 Decomposition of nitric acid : a. Nitrogen dioxide and oxygen ... 6,880 b. Niti ous acid and oxygen .... - 13,650 Heat disengaged by combustion of common gas* The complete combustion of one cubic metre of gas (=35317 cubic feet) produces 8000 calories (kg.-d.). In practice it is reckoned in town burners at 5000 calories per cubic metre (35 '31 7 cubic feet) on account of the incomplete combustion. In the case of burners which burn 100 litres (=r 3 '5 cubic feet) per carcel the heat developed is 500 calories (kg.-d.) per hour per carcel. Powerful Siemens burners (40 litres (=rl'4 cubic feet) per carcel) disengage 200 calories (kg.-d.) per hour per carcel. Heat developed by the electric light in calories (kg.-d.) per hour per carcel, neglecting the combustion of the carbons. Small incandescent lamps . iQ Small arc lights (candles) 20 Powerful arc lights 5 As one cheval-heure (nearly one horse - power) corresponds to 270,000 kgm. or 637 calories (kg.-d.) the above figures assume that the light produced per cheval or per horse-power of electrical energy is : Small incandescent lights 16 carcels. Small arc lights . 32 Powerful arc lights 128 ,, which corresponds tolerably to the mean figures given by experiment. Heat Of evaporation. In calories (g.-d.) per gramme at a pressure of 760 mm. of mercury : Water 537 Methyl alcohol ... 264 Common elcohol ; . . 208 Acetic acid .... 102 Sulphuric aether ... 1 Essence of turpentine . . 69 RESISTANCES. 161 Heat Of fusion. In calories (g.-d.) per gramme : Water . Zinc 79-25 28-13 Tin . 14-25 Sulphur 9'37 Phosphorus Mercury Specific heat. Solids and liquids : In calories (g.-d.) per gramme. Silver .... "057 Platinum Copper .... '0952 Lead Tin .... '0362 Sulphur Iron .... '1138 Zinc Mercury . . . '0319 Ice Nickel .... '1092 Water . Gold .... '0321 Alcohol. Specific heat of gases at constant pressure. Air Oxygen . Hydrogen 2374 2175 3-4090 Ammonia Carbonic acid Sulphurous acid 5'03 324 0314 1776 0956 504 L 5475 5084 2169 1544 RESISTANCES. LIST OF COMMON BODIES IN ORDER OF DECREASING CONDUCTIVITY OR INCREASING EESISTANCE (Culley). CONDUCTORS. SEMI-CONDUCTORS. INSULATORS OR DIELECTRICS. Silver. Wood - charcoal and Wool. Copper. coke. Silk. Gold. Acids. Glass.t Zinc. Saline solutions. Sealing wax. Platinum. Sea water. Sulphur. Iron. Earefied air.* Eesin. Tin. Melting ice. Guttapercha. Lead. Pure water. Indiarubber. Mercury. Stone. Gum lac. Ice. Paraffin. Dry wood. Ebonite. Porcelain. Dry air. Dry paper. * The place in this list of dry air depends on the degree of rarefaction. + Certain kinds of glass when quite dry insulate better than guttapercha. 162 PRACTICAL INFORMATION. Resistance of metals and alloys. The table below enables the calculation to be made of the resistance at C. of a con- ductor of given material when its length and its sectional area (and its diameter, if the conductor be circular) or its length and its "weight be known. It is only necessary to remember that the resistance of a con- ductor is proportional to its length, inversely proportional to its section, and inversely proportional to its weight. One of the three coefficients a a' or a" is used, taking care to express lengths, sectional areas, diameters, and weights in suitable units. RESISTANCE OF COMMON METALS AND ALLOYS AT C. (Matthiessen), * s 1 fll f I? 2 g to a & S fl Q, fl ^ f3 rf 3 a S^ . c3 ' y ^ c3 c3 "~* ^^ a t> t, 0) g Jj 03^ sg>ls "o g io all METAL. S'alJ ill! g^ 1 ^ ||| |1| sj 1*1 55 fs a a ^ | o.^P 8 'S3 * gl ~ I M 1 (^ 2 () (a') (a") Microhms. Ohms. Ohuis. Ohms. Annaled silver . 1-521 01937 1544 377 Hard silver 1-652 02103 168 Annealed copper 1-616 02057 144 388 Hard copper 1-652 02104 1489 Annealed gold . 2-081 02650 408 365 Hard gold .... 2-118 02697 415 Annealed aluminium 2-945 03751 0757 Compressed ?inc 5-689 07244 40 J7 335 Annealed platinum . 9-158 1166 1-96 _ iron . 9-825 1251 7654 63 nickel. 12-60 1604 1-071 Compressed tin . 13-36 1701 9738 365 lead v 1985 2526 2-257 387 antimony 35-90 4571 2-411 389 ,, bismuth 132-7 1-689 13-03 354 Liquid mercury . 99-74 1-2247 1308 072 2 silver, 1 platinum . 24-66 314 2-959 031 German silver . 21-17 2695 1-85 044 2 gold, 1 silver . 10-99 1399 1-668 065 CONDUCTIVITY. 1G3 EELATIVE CONDUCTIVITY OP COPPER ALLOYED WITH FOREIGN SUBSTANCES. PURE COPPER = 100 (MattMessen). SUBSTANCES FORMING THE ALLOY WITH PURE COPPER. CONDUCTIVITY COMPARED WITH PORE COPPER. TEMPERATURE IN DEGREES C. 0*5 / of carbon 77-87 18-3 0'18 ,, of sulphur . . . . 92-03 19-4 0'13 of phosphorus 70-34 20 0-95 .... 24-16 22-1 2-5 .... 7'52 17-5 Copper with traces of arsenic . 60-08 197 2*8 of arsenic 13-66 19-3 5-4 6-42 16-8 Copp r with traces of zinc 88-41 19- 1-6 of zinc 79-37 16-8 3-2 ...... 59-23 10-3 0'48 of iron 35-92 11'2 1-66 ...... 28-01 13-1 1-33 of tin 50-44 16-8 2-52 ...... 33-93 17-1 4-9 ...... 20-24 14-4 1 22 of silver 90-34 207 2-45 82-52 197 3'5 of gold 67-94 18-1 lO'O of aluminium 12-68 14 CONDUCTIVITY OF DIFFERENT SAMPLES OF COPPER (MaMhiessen). SUBSTANCES. CONDUCTIVITY. TEMPERATURE. Pure copper Spanish copper (Bio Tiuto) Russian copper Australian copper American copper Polished copper wire Hard copper wire 100 14-24 59-34 88-86 92-57 72-27 71-03 14-8 127 14' 15- 157 17-3 164 PRACTICAL INFORMATION. Influence of temperature on the resistance of metals (Matthiessen). The resistance of metals increases with the temperature according to the following empirical formula : Br=r(l-f *-f *0). B resistance at temperature t. r resistance at C. t =: temperature in degrees C. a and b are numerical coefficients. The following are some of the values of a and b : a b. Very pure metals + -OD3824 + '00000126 Mercury -0007485 - -000000398 German silver -0004433 + -000000152 Platinum silver alloy .... -00031 Gold and silver alloy .... -0008999 - 000000062 CONDUCTIVITY OF METALS. Coefficients for temperature t in degrees C. METALS. COEFFICIENTS. Silver c = 100 38278 t + 0009848 t 2 Copper .... c = 100 38701 1 + 0009009 t Gold c = 100 36745 t + 0008443 t Zinc c = 100 37047 t + 0008274 t* Cadmium .... c = 100 36871 t + 0007575 t Tin c = 100 36029 t + 0006136 *8 Lead .... c 100 38756 1 + 0009146 t Arsenic .... c = 100 38996 t 4 0008879 t Antimony .... c = 100 39826 t + 0010364 1 2 Bismuth .... c = 100 35216 t + 0005728 1 Mean .... c = 100 37647 t + 0008340 t Influence of temperature on the resistance and conductivity Of pure copper. Increase of tempera- ture diminishes the conductivity and increases the resistance of copper. Between and 100 this variation is about nAftro P er degree centigrade. The annexed table gives the coefficients by which the resistance of pure copper wire must be multiplied in order to obtain its resistance at t degrees between and 30, and the corresponding figures for the con- ductivity table. RESISTANCE OF CARBONS. 165 RESISTANCE AND CONDUCTIVITY OF PURE COPPER AT DIFFER- ENT TEMPERATURES. a g C g g g if s ^ 1 ' 2 1 i i K S w H 3 OK a i- 1- 16 1-06168 9419 1 1-00381 99824 17 1-06563 '93841 2 1-03756 9925 18 1-06959 93494 3 1-01135 -98878 19 1-07356 93148 4 1-01515 -98508 20 1-07742 92814 5 1-01896 98139 21 1-08164 92452 6 1-0228 97771 22 1-08553 92121 7 1-02663 97405 23 1-08954 91782 8 1-03048 97042 24 1-09356 91445 9 1-03435 '96679 25 1-09763 9111 10 1-03822 "96319 26 1-10161 90776 11 1-04199 -9597 27 1-10567 90i43 12 1-04599 95603 28 1-11972 90113 13 1-0499 -95247 29 1'11382 89784 14 1-05406 -94893 30 1-11782 89457 15 1-05774 -94541 Electric light carbons (M. Jouberfs experiments). Carre '* Carbons. Specific resistance : 3927 microhms at 20 C. RESISTANCE OF CYLINDRICAL CARBONS PER METRE. DIAMETER, IN MILLIMETRES. RESISTANCE IN OHMS. DIAMETER IN MILLIMETRES. RESISTANCE IN OHMS. 1 50 8 781 2 12-5 10 5 3 555 12 348 4 3125 15 222 5 2- 18 154 6 1'39 20 125 The resistance diminishes as the temperature increases. Between O 3 and 100 C. the coefficient of reduction is -^ per degree centigrade. 166 PRACTICAL INFORMATION. Retort carbon. Specific resistance 66750 microhms, about. Graphite. Very variable, between 2400 and 42000 microhms. Gauditfs carbon (Mignon and Rouart). Specific resistance 8513 microhms. Between and 100 C., the resistance diminishes -o^th. Coating of carbons with metal under ordinary conditions reduces their resistance to g of its original value. Metalloids. Crystallised selenium. Specific resistance at 100 C. , 60,000 ohms. Bed phosphorus. 132 ohms at 20. Tellurium. '213 ohms at 20. Specific resistance of some liquids at 14 and 24 in ohms per cubic centimetre (S lamer). 14 457 247 21-5 88 4-67 1-45 Distilled water (Pouillet), unknown temperature Solution of copper sulphate (8 per cent.) (28 per cent.) Saturated solution of zinc sulphate. Solution of sulphuric acid (density = II) (density = 17) Nitric acid (density = 1'36) Distilled water with 20000 of sulphuric acid . 24 37-1 18-8 17-8 73 3'07 1-22 1550 CONDUCTIVITY OF SOLUTIONS. PUKE COPPER = 100,003,000 (Matthiessen.) SOLUTIONS. CENTIGRADE TEMPERATURE CONDUCTIVITY. 1. Copper sulphate concentrated 9 5'42 , , , , with an equal volume of water H 3-47 ,, ,, with 3 volumes of water M 2-08 2. Common salt concentrated .... 13 31-52 ,, ,, with an equal volume of water 23-08 ,, with 2 volumes of water . tt 17-48 ,, with 3 volumes of water . 13-58 3. Zinc sulphate concentrated .... 14 577 ,, with 1 volume of water . M 7-1 ,, with 3 volumes of water . " 5-43 RESISTANCE OF SOLUTIONS. 167 SPECIFIC RESISTANCE OF SOLUTIONS OF SULPHURIC ACID. (Matthiessen) . SPECIFIC GRAVITY. PERCENTAGE BY WEIGHT OP SULPHURIC ACID. CENTIGRADE TEMPERATURE. RESISTANCE. 1-003 5 16-1 16-01 1-018 2-2 15-2 5-47 1-053 7-9 13-7 1-884 1-080 12 12-8 1-368 1-147 20-8 13-6 96 1-190 26-4 13 871 1-215 29-6 12-3 83 1225 30-9 13-6 862 1-252 34-3 13-5 874 1-277 37-3 920 1-348 45-4 179 973 1-393 505 14-5 1-086 1-493 60-6 13-8 1549 1-638 73-7 143 2-786 1-726 81-2 163 4-337 1-827 92-7 14-3 5-32 SPECIFIC RESISTANCE OF NITRIC ACID (D = T36). (TEMPERATURE IN DEGREES C.) 2 . 4 . 1-94 1-83 8 12 1-65 1-5 16 20 1-39 1-3 24 . 28 . 1-22 1-18 SPECIFIC RESISTANCE OF SOLUTIONS OF COPPER SULPHATE AT 10^ C. (Ewing and MacGregor) . DENSITY. SPECIFIC RESISTANCE. DENSITY. SPECIFIC RESISTANCE 1-0167 1644 11386 35 10216 1348 1-1432 34-1 1-0318 987 1-1679 31-7 1-0622 59 11823 30-6 1-0858 47-3 1-2051 (saturated) 29-3 11174 38-1 168 PRACTICAL INFORMATION. SPECIFIC RESISTANCE OF SOLUTIONS OF ZINC SULPHATE AT 10 C. (Ewing and MacGregor). DENSITY. SPECIFIC RESISTANCE. DENSITY. SPECIFIC RESISTANCE. 1-014 182-9 1-2709 28-5 1-0187 1405 1-2891 28-3 (minimum) 10278 111-1 1-2895 28-5 1-054 638 1-2987 28-7 1-076 50-8 13288 29-2 1-1019 42-1 1353 31' 1-1582 337 1-4053 32-1 1-1845 32-1 1-4174 33-4 1-2186 303 1-422 (saturated) 337 1-2562 29-2 The above table shows that the most saturated solution is not always the best conductor ; the same phenomenon is observed with a solution of common salt. Mixtures of zinc sulphate and copper sulphate. The resistance of this mixture is always less than the mean of the resistances of the two solutions, often it is less than the resistance of the least resisting solution {Ewing and MacGregor}. APPROXIMATE SPECIFIC RESISTANCES OF WATER AND ICE (Ayrton and Perry). CENTIGRADE TEMPERATURE. SPECIFIC RESISTANCE IN MEGOHMS. CENTIGRADE TEMPERATURE. SPECIFIC RESISTANCE IK MEGOHMS. 32-4 2240 - -2 284 6'2 1023 + '75 118-8 - 5-02 948-6 + 2-2 24-8 - 3-5 642-8 + 4 9-1 - 3-0 569-3 + 7-75 54 - 246 484-4 + 1102 34 - 1-5 387-6 RESISTANCE OF GUTTAPERCHA. 169 Specific resistance of glass (G. Fousscreau, 1882). Common glass, soda and lime, d 2539. Specific resistance in Temperature. millions of megohms. + 61-2 -705 + 2

. I CYLINDER of length I : ~ T ' (logs = Naperian log). Two CONCENTRIC CYLINDERS of length I : r' radius of external cylinder ; r radius of internal cylinder. I CIRCULAR DISC of radius r and negligable thickness : Two PARALLEL CIRCULAR DISCS of radius r and area S, thickness of dielectric b : (This last formula is applicable to two parallel discs of any shape when their dimensions are large as compared with their distance from each other b.) MAGNETS. The power Of magnets is estimated by the weight they will carry. The most powerful magnet known is the laminated magnet 180 PRACTICAL INFORMATION. belonging to M. Jamin, which weighs 50 kilogrammes and carries 500 ; another of the same form, weighing 6 kilogrammes, carries 80, or 13'5 times its own weight. Some small magnets carry as much as 25 times their own weight. A horse-shoe magnet carries three or four times the weight which a straight bar of the same mass can carry. Bernouilli's rule. If w be the weight of a magnet, p the weight which it can carry, then F=< a is a constant depending on the quality of the steel and the method of magnetisation. For the best qualities of Wetteren of Haarlem a varies between 19*5 and 23. The steels of Allevard have also a very high constant. Mr. Le Neve Foster has found that all steels of very high constant contain tungsten, and that the constant increases with the quantity of tungsten present. Coefficient of induced magnetism. The magnetic moment of a long bar placed in a uniform magnetic field is, for a loeak Jield, proportional to its length /, its sectional area s, the intensity of the field H, and a numerical constant k, which is called the coefficient of induced magnetism, k is negative for diamagnetic bodies. The follow- ing are the mean values given by Barlow and Pliicker for some substances. MAGNETIC SUBSTANCES. Soft iron (wrought) Cast iron . Soft steel . Hard steei . Nickel Cobalt DIAMAGNETIC SUBSTANCES. i i 32-8 Water . - 10*65 x 10 - 23 Sulphuric acid (d. - 216 1-839) . . - 6'8 x 10-6 174 Mercury . . - 33-5 x 10- 6 15-3 Phosphorus . - 18-3 x 10 6 32-8 Bismuth . . - 25-0 x 10 - 6 These coefficients are only approximate, and change for every sub- stance with the absolute value of H. For example, according to Weber, in a very weak magnetic field the value of k is five times greater for nickel than for iron. Supersaturation of magnets. A magnetised bar often takes up a magnetic supersaturation, which it gradually loses at a pro- gressively decreasing rate until its magnetisation is reduced to its permanent value. In all experiments depending on the constancy of magnets they ought to be magnetised at least six months beforehand. METHODS OF MAGNETISATION. 181 Professor Hughes finds that by smartly hammering the magnetised bar it can be brought to its lowest limit of magnetisation. He suggests the use of this method whenever a trustworthy permanent magnet of small power is required ; and, also, as a test of the durability of perma- nent magnets for compasses and other purposes, those that fall below a certain intensity being rejected, and those that are retained being re- magnetised. Influence of temperature on magnetism. Magnetisation diminishes with increase of temperature, and conversely. The diminution becomes permanent if the temperature rises too high. A magnet heated to cherry-red loses its magnetism, and at this tempera- ture soft iron ceases to be attracted by a magnet. For nickel the temperature at which this effect takes place, called the magnetic limit, is about 350. Temper. Compressed steel. The coercitive force of steel is greater the more it is tempered. M. Ckmandot (1882) gives coercitive force to untempered steel by compressing it in a hydraulic press. This mechanical temper allows of the steel being worked by the file, chisel, or in the lathe, either before or after magnetisation, which is a valuable property in the construction of a great number of instruments. Experimental determination of the moment of inertia of a magnetised bar (Gauss). The bar or needle is made to oscillate : let t be the time of one oscillation ; two equal weights q are suspended at equal distances from the centre ; let the first distance be 1} the second distance # 2 ! let t\ and t- 2 be the respective times of one oscillation, then To bring an oscillating magnet to rest. By means of a small magnet so held as to repel the nearest end of the oscillating magnet. At the moment when the oscillating magnet is passing zero as it swings towards the observer the small magnet is sharply brought near it. The oscillating magnet stops, and at the moment when it begins to swing in the opposite direction the magnet in the hand is withdrawn. A magnetised steel lever or turnscrew does very well. METHODS OF MAGNETISATION. Single touch* Stroke the bar to be magnetised from end to end with one pole of a natural or artificial magnet, repeating the strokes in 182 PRACTICAL INFORMATION. the same direction. The pole at the end of the bar at which the strokes begin is of the same name as the pole used to stroke it with. Separate touch. Two magnetised bars of the same name are placed at the middle of the bar to be magnetised with poles of con- trary name downwards, these bars should be inclined at about 30 ; they are separated, stroking the magnet in opposite directions, replaced in the middle and again separated, and so on. This method is quicker than the preceding. Double touch. Two magnets fixed in an inclined position in a wooden frame are passed from end to end of the bar to be magnetised, always in the same direction. A more regular magnetisation is thus obtained. The effects produced by the two last methods are better and quicker if the bar to be magnetised is laid on two magnets with their opposite poles facing each other, these poles to be of the same name as the pole of the magnetising magnet on the same side (Cottlomb"). These methods are now replaced by others depending on the action of currents, the simplest being to rub the bar to be magnetised over the poles of a powerful electro -magnet. Eli SIS' method. A coil through which a current is passing is passed backwards and forwards over the bar to be magnetised. For a horse -shoe magnet two coils are used, which are moved together up and down the two branches. With strong currents a bar may be magnetised to saturation by one pass. The rapidity of the passes has no influence on the magnetisation; their number has greater influence as the current is weaker. To magnetise a needle. Place the needle on a horse-shoe magnet, putting the end which is to be a north pole on the south pole of the magnet, and vice versa ; rub the needle against the magnet two or three times in the direction of its length. Armatures of magnetised oars. To preserve the magnetism of the bars they should be provided at their ends with soft iron armatures, or they may be placed with their opposite poles in contact. The opposite poles tend to preserve their reciprocal magnetism, poles of the same name to destroy it. The armatures ought always to be slid off, and not pulled off. The earth's magnetism tends to preserve the magnetism of a freely suspended needle. ELECTRO-MAGXETS. 183 TERRESTRIAL MAGNETISM. Elements of the earth's magnetism, Jan. 1st, 1879. Declination at Paris (west) 16 56 Mean annual diminution 9' Mean inclination at Paris 65 32' 6" Horizontal component of the earth's magnetism at Paris (in dynes) '19324 Total force (in dynes) '46485 Elements of the earth's magnetism at the observa- tory at the Pere Saint-Maur, Jan. 30th, 1883 (Mascarf). Inclination 65 17' Declination (west) . . 16 33' Horizontal component (in dynes) .... '1932 Total intensity (in dynes) '46485 ELECTRO-MAGNETS. Laws Of electro-magnets. When a magnet is far from the point of magnetic saturation, the following laws are applicable. The magnetic strength is proportional to the strength of the magnetising cur- rent and the number of turns of wire in the coil. It is independent of the size and nature of the conductor and the diameter of the coil. When account is taken of magnetic saturation, Muller gives the fol- lowing rule. The magnetic strength m of an electro -magnet is pro- portional to the arc of which the tangent is the strength C of the magnetising current. m A tan 1 C. Maximum attraction (Joule). The maximum attraction is 200 pounds per square inch, or 14,515 grammes per square centimetre, which corresponds to an intensity of magnetisation 7 1500 : / being the maximum attraction, and S the area of the attracting surface. The formula shows that the attraction of an electro-magnet depends only on the diameter of its core, the length is only of use in separating the poles, and thus preventing them from interfering with each other. Joule has constructed small electro-magnets which carry as much as 3,500 times their own weight. 184 PRACTICAL INFORMATION. Action of a bar of iron in a solenoid. A bar of iron introduced into a solenoid makes the internal magnetic field about 33 times more intense by concentrating the lines of force near the poles, and allows the current to produce powerful effects in a limited space. Looked at in this way the action is analogous to that of a lens which concentrates a ray of light on to the point where the maximum luminous action is required (Fleeming Jenkiti). Formulae for electro-magnets before magnetic saturation. For relatively feeble currents and soft iron cores of which the length is much greater than the diameter, such as the electro- magnets of telegraphic instruments, M = knG^Jd\ M magnetic intensity. n number of turns of wire. C strength of the current. d diameter of the core. 1c a constant. We may here remark that the maximum value for M occurs when n has a certain value such that the resistance of the coil of the electro- magnet is equal to the resistance of the rest of the circuit. This is in ac- cordance with the doctrine of the conservation of energy, as it shows, in other words, that the power of the electro-magnet is a maximum when the electric energy expended in its coils is a maximum. This condition enables us to calculate for each particular case the value of C and the resistance E of the wire to be coiled on the electro-magnet. From this consideration alone we should be led to indefinitely increase the dimensions of the core and of the wire, since for any given e. m. f . M increases with d and n if R be kept constant, so that C may remain the same. In practice, the indeterminate nature of the problem as thus ex- pressed, is overcome by introducing another factor, for example, the weight of copper wire to be coiled on the magnet, or, more simply, the space to be occupied by the wire on the reel. Let V be this space, de- termined by a cylindrical annular space of known dimensions. Let s be the sectional area of the wire, / its length, a its specific resistance. The condition that the resistance of the coils must be equal to R, gives ELECTRO-MAGNETS OF TELEGRAPH INSTRUMENTS. 185 and the space occupied by the wire (V being affected by a practical co- efficient, taking into account the thickness of the covering of the wire and the space between the turns) gives V = fr. From these two equations may be deducted 'VRT. V . " I ' Knowing the sectional area * of the wire, its diameter d is obtained by the formula d Practically these formulae enable the length and diameter of the wire required to fill the reel of an electro-magnet, of which the dimensions are known, so that the coil may have a given resistance, to be calculated. This is the most general case. We know of no simple practical formulae which enable the dimensions of the different parts of an electro-magnet to be calculated so that it may carry a given weight, or produce a magnetic field of given intensity. ELECTRO -MAGNETS OF TELEGRAPH INSTRUMENTS. The problem in this case is simplified, because the dimensions of the reel are given, and are determined by considerations which are indepen- dent of the absolute strength of the magnetic field to be produced. The indeterminate nature of the general problem thus disappears. Let A be the area of the section of the wire space on the reel on one side only of the axis made by a plane passing through the axis, and at right angles to the turns of wire. I the mean length of a turn of wire in millimetres. p radius of the wire in millimetres. thickness of the covering of the wire in millimetres. c conductivity of the wire (pure copper :zi 1). r resistance of the coil in ohms. t total number of turns. a a coefficient depending on the mode of winding. 186 PRACTICAL INFORMATION. If the layers are exactly superposed, A is supposed to be divided into squares, and a 4 ; if the turns of one layer lie in the interstices of the one underneath, A is divided into hexagons, and a 2 V3 3*46. If the layers are separated by some insulating material (paraffined paper or thin guttapercha cloth), e is increased by one quarter of the thickness of this material. Then A Al To express r in ohms a coefficient must be introduced, and the formula becomes __ It !_ ~~ 194456 P 2 X e To find the resistance of a coil of wire of given thickness wound on a reel A. Say the coil of the electro-magnet of a Morse receiver: the reel being 60 millimetres long, wire space 10 mm. deep, and the core 10 mm. in diameter, wound with wire No. 32 of fhejauge carcasse ; for which 2p = -16 2 (p -f e) = -20. . . thickness of the silk e -02 mm. Suppose it to be so wound that a = 4, A = 60 X 10 600 ; I 20 ir. Then for the number of turns t, and for the resistance r, It 1 COO X 15000 1 1 x - = 759X ~ If c =. 1 r = 759 ohms, if c = -9, about the usual practical value for commercial wire, 759 EEELS OF ELECTRO-MAGNETS. 187 When the dimensions of the reel, the number of turns of wire t, the resistance r of the coil, and the diameter 2p of the bare wire are known, the conductivity c of the wire, and the thickness e of the covering can be calculated. To calculate the diameter 2p of a wire of conductivity c, with a cover- ing of thickness e, the resistance of the coil being r ohms. Let The value of b is calculated, then, =v- But e being very small -,-- may be neglected ; then, p = b - - or 2p = 24 e . Thickness of tvire with which a galvanometer or electro -mag net coil must be wound so as to obtain the maximum magnetic effect with a given external resistance. It can be shown by calculation that if 2p be the diameter of the bare wire, 2 (p -f- e) the diameter of the wire with its covering, r the resistance of the coil, and E the external resistance, that the best effect is produced when 2p : (p + ) : : r : E, or-'- 55. *. E p + e Construction of the reels of electro-magnets. It is better to make them of box or ebonite than of copper or brass, but if of metal they should be split ; it is also as well to cut a groove aboTit 2 mm. wide and 2 mm. deep, in the core, to hasten demagnetisation. During the winding, the turns of wire must be well insulated from each other, and metallic filings, which would penetrate the coating, must be carefully excluded. If a disc be fixed in the middle of a reel and the two halves of the wire be wound one on each side of it, starting from the disc, the two ends of the wire will both come out at the surface of the coil, and thus the inconvenience is avoided which is so often felt when the end of the wire leading from the innermost layer of the coil breaks off (CWfey). 188 PRODUCTION AND APPLICATIONS OF ELECTRICITY. The apparatus used for the production of electrical energy may be divided into three classes : 1st. Batteries which convert chemical energy into electrical energy ; 2nd. Thermopiles, which convert heat energy into electrical energy ; 3rd. Dynamo and magneto machines, which convert mechanical energy into electrical energy. The applications of this energy may always be reduced to the pro- duction of chemical, heating, or mechanical effects. The production of electrical energy is, strictly speaking, only the conversion of one form of energy into another form of energy, one mode of motion into another mode of motion. This reciprocity of cause and effect may be expressed by saying that producers or generators of elec- tricity are reversible and interchangeable, that is to say, that any one of them can be the seat of analogous but reciprocal actions to those for which it is originally constructed, and that they may be substituted one for the other for the production of the same effects. Thus, a magneto - electric machine when it is put in motion produces a current at the expense of mechanical work, or sets itself in motion and produces mechanical work if a current be supplied to it from some other source of electrical energy. This is expressed by saying that a magneto -electric machine is reversible. The magneto machine may also be set in motioi by the current furnished by a battery or thermopile, the three sources of electricity may be substituted one for the other ; that is to say, they are interchangeable. The applications of electricity may be divided into three large groups characterised by the nature of the actions produced. Chemical actions* All forms of apparatus which produce electrical energy at the expense of chemical action are called batteries. Accumulators are reversible batteries. The chemical actions produced by currents are embraced under the general title of electrolysis. The applications of electrolysis are electro- metallurgy, including electrotyping, electro -gilding, silvering, nickel plating, etc., and a form of colouring in metal, a new process which has been used at Nuremberg for the decoration of metallic toys. Electrolysis has also been applied to the purification of alcohol, and the more rapid EFFECTS OF CURRENTS. 189 amalgamation of gold in the quartz -crushing method of obtaining that metal. Heatillg effects. Apparatus which convert heat into electrical energy are called thermopiles. The heating effects of currents have received the following applica- tions. Melting of metals (but little used as yet), firing of fuses (for mines, torpedoes, blasting, etc.), safety catches for electric light, and electric power leads, and arc and incandescent electric lights. Mechanical actions* Two different types of machines exist ; the first, called static machines, produce electrical energy in the form of charges, either by friction, or by influence, or electrostatic induction. They have no practical application as yet, though the Voss induction machine is reversible ; that is to say, that if the two conductors of such a machine be kept charged by means of another it will rotate (Silvanus Thompson) . The second type is based on the magnetic action of currents, and electro-magnetic induction. Magneto and dynamo -electric machines convert mechanical into electrical energy, whilst electrical energy produces mechanical energy, work, or motion in bells, railway signals, clocks, telegraph instruments, telephones, the regulating mechanism of arc lamps, and the motors which are used in the transmission of power to a distance, etc. Other effects of currents. The mutual actions of light and electricity form the as yet almost purely scientific branch, electro -op tics, but which, however, in the case of the change of resistance of certain bodies under the influence of light, has given rise to Various beginnings of practical applications, such as Graham Bell's photophone, the radio- phone, the teleradiophone, and the teleradiophone multiple auto-reversible of M. Mercadier, etc. The phys iological action of currents has lately been much studied, and its effects are of daily use in the physiological laboratory. Some of the physiological effects are now recognised as infallible means of diagnosis in certain diseases, and others have been used with much success, though without any very great certainty, as means of cure. In the case of lead palsy, or painter's dropped wrist, the action of interrupted currents enables cures to be effected in cases which would formerly have been hopeless. These two branches of the subject are foreign to the nature of this work, and must be studied in special treatises. In the following pages the order of the subdivisions just laid down 190 APPLICATIONS OF ELECTRICITY. will be followed as strictly as possible, the reversible and interchangeable nature of the phenomena, however, make some small departures from this order inevitable. BATTERIES. These will be divided into three distinct groups : One -fluid batteries with no depolariser. One-fluid batteries with solid or liquid depolariser. Two -fluid batteries. ONE -FLUID BATTERIES WITH NO DEPOLARISER. Volta'S battery (1800). Plate of zinc, plate of copper, sulphuric acid diluted with sixteen times its volume of water. The current is pro- duced by the oxydation of the zinc and its conversion into zinc sulphate. It polarises rapidly when the circuit is closed ; the hydrogen sticks to the copper plate, the sulphate of zinc is decomposed and produces a deposit of zinc on the copper. The first form was the Volta's pile, so called because it consisted of a pile of plates arranged thus : copper, flannel, zinc, copper, flannel, zinc, and so on. Modified by Cruikshank (1801) under the form of the trough battery, then the separate trough battery of Volta, who had already employed the same principle in his " crown of cups ; " the windlass battery, due to Crahay (1841). The spiral battery was in- vented in 1821 by Offershaus, with the view of diminishing the internal resistance of the elements ; Wollaston (1815) increased the surface of the copper, leaving the zinc unchanged. Munch (1841) constructed a trough battery with no partitions between the elements, but short circuits occur between the elements ; Faraday (1835) prevented this by separating the elements by sheets of well-varnished paper. Pulvermacher (1857) con- structed galvanic chains formed of zinc and copper wires coiled on cylinders of porous wood, which absorb the exciting fluid (vinegar and water) when the chain is dipped into it. Amalgamation of the zincs prevents the formation of local couples due to impurities in the zinc. This fact was discovered by Kemp (1828), and applied to batteries by Sturgeon (1830). Modifications of the exciting fluid, In order to prevent polarisation, many exciting fluids have been proposed ; sulphate of copper, chromic acid, oxygenated water, sal-ammoniac, etc. Modifications of the copper plate in order to diminish the polarisation, Poggendorff(lMV). 1st. Heated the copper in air until the colours which appear at first had passed away. BATTERIES. 191 2nd. Dipped the copper in nitric acid and then washed it with water. 3rd. Covered the plate with a powdery deposit of copper by electrolysis. Page (1852) pierced the plate full of holes and covered it with an electro -deposit of rough copper. Walker (1852) electro-deposited copper on the plate, allowing the so- lution to become almost exhausted, or formed the plate of copper wire gauze. Carbon battery plates. Eetort carbon was used in one- fluid batteries by de Leuchtenberg (1845) and Stohrer (1849), a solution of alum being employed. Carbon agglomerates are becoming more used than retort carbon, which, though cheap in itself, is expensive to work. Sttiee (1840). Copper plate replaced by platinised platinum, or better, platinised silver. The e. m. f . '47 volt, about. Used for electrotyping. Walker (1859). Platinised carbon. Cheaper than Smee's, e. m. f. = '66 volt. Maiclie (1879). Fragments of platinised carbon only partly im- mersed in the fluid. Scraps of zinc in a bath of mercury. Water acidu- lated with sulphuric acid saturated with common salt or sal-ammoniac. E = T25 volts with common salt. Quantity small, high internal resis- tance. Iron positive plates. Sturgeon (1840) used cast iron with water acidulated with one-eighth its volume of sulphuric acid : Munnich (1849) used amalgamated iron ; Callan (1855) a flattened cast-iron vessel and slightly diluted pure hydrochloric acid. ONE-FLUID BATTERIES WITH SOLID BEPOLARISER. Warren de la Rue (1868). Unamalgamated zinc, sal-ammo- niac, silver surrounded by chloride of silver. E = 1 '03 volts. The invention of this battery is also claimed for Marie-Davy. Skrivanow (1883). A pocket battery formed of a plate of zinc and chloride of silver wrapped in parchment paper immersed in a solution of 75 parts caustic potash and 100 parts of water. An element weighing 100 grammes has an e. m. f. of 1-45 to 1'5 volts. It can give out 1 ampere for one hour. The potash solution must be renewed after this work, and the chloride of silver must be replaced after the potash has been renewed two or three times. 192 APPLICATIONS OF ELECTRICITY. Oaiflfe. Zinc (not amalgamated) ; silver, surrounded by chloride of silver; 5 per cent, solution of chloride of zinc. E T02 volts. Used as a standard cell with condensers and electrometers. ]Hari6-Davy Amalgamated zinc, acidulated water, carbon, and paste of sulphate of mercury. E = 1'52 volts. LeclclllcIlC (1868). Amalgamated zinc, sal-ammoniac, carbon surrounded by fragments of carbon ("carbon shingle"), mixed with black oxide of manganese (needle form). E == 1 '48 volts when the battery is not polarised. POROUS POT ELEMENTS. SMALL. MEDIUM. LARGE (Disc ELE- MENT.) Diameter of porous pot in centi- metres Height 6 11 15 8 15 Internal resistance in ohms (min.) Annual chemical work in grammes of copper Annual chemical work in cou- lombs 9 to 10 40 C0,000 5 to 6 60 to 70 100,000 4 100 to 125 150,000 Agglomerate Leclaiiche batteries. The depolariser is formed by one or more agglomerate plates, kept in position against the carbon by indiarubber bands. This form is handier, more economical, and of less internal resistance. E = 1 -48 volts. No. 1, with one plate . No 2, with two plates . Disc element with three plates r = 1'8 ohms, r = 1'4 , Agglomerate. A paste of 40 parts black oxide of manganese, 52 of carbon, 5 of gum lac, and 3 of bisulphate of potassium, compressed by a pressure of 300 atmospheres at a temperature of 100 3 C. Lalande and Chaperon's oxide of copper battery (1882). Zinc; 30 or 40 per cent, solution of caustic potash ; binoxide of copper in contact with a plate of iron or copper. E. m. f . '8 to '9 volt, according to the external work. Practically inactive on open circuit. The current varies with the dimensions of the element. The small hermetically sealed form can give 40,000 coulombs at the rate of BATTERIES. 193 '1 to '2 ampere. The spiral form 200,000 coulombs and '5 ampere. The small trough form 500,000 coulombs and To amperes. The large trough form 1,000,000 coulombs and 6 to 8 amperes. To prevent the caustic potash from absorbing carbonic acid, the trough elements have the fluid covered by a layer of heavy petroleum. ONE -FLUID BATTEBIES WITH LIQUID DEPOLARISES. The type of these batteries is Poggendorff's bichromate of potassium battery. The shape and dimensions of the battery and the composition of the fluid have been varied by different makers, in order to produce particular effects. PoggeudorfPs formula (1842). 100 grammes of bichromate of potash dissolved in one litre of boiling water, with 50 grammes of sulphuric acid added. Delaurier's formula. Water, 200 grammes ; bichromate of potash, 18'4 grammes ; sulphuric acid, 42'8 grammes. This formula is that given by the chemical equivalents : K02CrO 3 + 7S0 3 -f- 3Zn = 3ZnS0 3 + KOS0 3 -f Cr 2 3 3S0 3 . The final products are solution of zinc sulphate and a chrome alum. CllUtaux's formula (1868). The fluid (which is kept circu- lating through the cells of Chutaux's battery) is composed of Water 1~00 grammes. Bichromate of potash 100 Bisulphate of mercury 100 ,, Sulphuric acid at 66 50 Dronier's Salt. A mixture of one-third bichromate of potash and two-thirds bisulphate of potash ; when dissolved in water, this mixture forms the exciting fluid. Special modifications of Poggcndorff's battery. For short experiments, M. Grenet devised the bottle battery. The zinc is dipped into the fluid during the experiment, and then withdrawn. Trouve, Gaiffe, and Ducretet suspend the plates from a windlass, so that they may be withdrawn from the fluid, or more or less immersed at will. 194 APPLICATIONS OF ELECTRICITY. Troiive*'s cell (1875). One zinc and two carbons, active surface 15 centimetres inside. During the "spurt " at the beginning, E - 2 volts ; r = '0016 ohms. After the " spurt " . . . . E = 1'9 volts ; r - '07 to '08 ohms. On short circuit, one element gave 24 amperes for 20 minutes without polarising (d'ArsonvaT). A fully charged element can give 180,000 cou- lombs (=: 50 ampere hours) before the solution becomes exhausted. Tissandier's cell (1882), giving a very large current, 100 amperes through an external resistance of '01 ohm. SOLUTION. Water 103 parts by weight. Bichromate of potash 16 ,, ,, Sulphuric acid 66 37 The bichromate to be reduced to fine powder, taking care not to inhale the dust, which produces ulceration of the lining membranes of the nose. Part of the bichromate is dissolved in water at about 40 C. in an earthen vessel ; the acid is then added, and the mixture is violently stirred until the whole of the bichromate is dissolved. It must be allowed to cool down to 35 C. before being used. Below 15 C. the liquid works badly. This battery gives more than one kgm. of useful electrical energy per kilogramme of weight for two to three hours, and effective mechanical work of more than a horse-power for the same length of time for a weight of about 200 kilogrammes (24 elements in series, and a Siemens dynamo as motor). TWO -FLUID BATTERIES. Becquerel (1829). Zinc, nitrate of zinc; bladder; copper, and nitrate of copper. ]>:iili<'ll (1836). Zinc, acidulated water; bladder or porous pot; copper, saturated solution of sulphate of copper. E 1 *079 volts. Action goes on even on open circuit, the solution is maintained by adding sul- phate of copper. The solution round the zinc may be pure water, salt and water, or a solution of sulphate of zinc. There are many modifi- cations of the Daniell cell. Trough battery. Flattened elements arranged in a trough with par- titions. The Post-Office pattern is a teak trough, marine glued inside to make it water-tight, with alternate diaphragms of slate and porous earthenware. BATTERIES. 195 Eisenlohr (1849) replaced the dilute sulphuric acid by a solution of tartar (sodium bitartrate) . MinottVs cell. The porous pot is replaced by a layer of sand or saw- dust, the copper and copper sulphate below and the zinc above. Gravity battery. The two liquids are kept separate by their difference of density, there is no porous diaphragm. Called Meidmger^s (1859) in Germany and Gotland's (1861) in France. It is known under both names. Sir W. Thomson's tray battery. Large -surfaced horizontal elements, the zinc in the form of a grating enveloped in parchment paper so as to form a tray to contain the sulphate of zinc solution ; very low internal resistance. E. Reynier (1880). Porous cell made of parchment paper so folded as to have no seams. Amalgamated zinc; solution, 300 parts of caustic soda to 1,000 parts of water ; copper, solution of sulphate of copper containing sulphate of soda or sulphuric acid. The conductivity of the solutions is increased by the addition of small quantities of different alkaline salts. E. m. f. 1'5 volts. Kesistance of a 3-litre cell with lined parchment-paper porous cell, 075 ohm. E. Reynier (1881). External cell of copper of flat form, forming the positive plate. The bottom is provided with a wooden flooring. Jacketed zinc. Only the sulphate of copper solution requires to be re- newed. The sulphate of zinc passes through the jacketing by itself by Orove (1839). Zinc (amalgamated), dilute sulphuric acid; porous pot; nitric acid, platinum. E 1-96 volts. The surface of the platinum may be increased by bending it into an S shape (Poggendorff, 1849). Callan (1847) replaced the platinum by platinised lead, and the nitric acid by a mixture of 4 parts concentrated sulphuric acid, 2 of nitric acid, and 2 of a saturated solution of nitrate of potash. BlinsCIl (1840) replaced the platinum by artificial carbon in the form of a hollow cylinder. E =. 1'9 volts. Archereau (1842). Put the block of carbon in the middle and the zinc outside. cell (tfArsonval). Amalgamated zinc in dilute sul- phuric acid (one-twentieth by volume). In the porous pot a plate of carbon, in common commercial nitric acid, sp. gr. 36 to 40 Baume. An element 20 cm. high has an internal resistance of "08 to '11 ohm. 196 APPLICATIONS OF ELECTRICITY. The e. m. f. = 1'8 volts. When the nitric acid is about 30' Baume the battery runs down rapidly. The Bunsen element consumes 1 '3 grammes of zinc per ampere per hour (Faraday's law gives 1'295). Nitric acid of density 36 Baume contains 45 per cent, of anhydrous nitric acid ; it will work until it has fallen to 28 Baume. Under these conditions only 130 grammes of acid are utilised per kilogramme expended. The weight of acid expended is at least ten times that of the zinc consumed. D' Arson vals depolarising liquid (to be used instead of nitric acid, and in the same way, 1879). Nitric acid 1 part. Hydrochloric acid 1 Water 2 is used in circulating batteries, zinc in the porous cell, the positive poie being formed by a crown of carbon rods 1 cm. in diameter. The current is constant, the internal resistance reduced to a minimum, and the depolarising surface very large. An element 20 cm. high can give as much as 40 amperes on short circuit. Carbons for Bunsen cells. Carre's carbons are better than retort carbon ; they have a very high conducti vity, and their close- ness of texture prevents the acids from escaping by capillary attraction, and so attacking the metallic connections. This fault can be completely overcome by steeping the upper part of the carbon for several minutes in melted paraffin. When cold electroplate it with copper, and then dip it into melted type metal. Perfect and indestructible contact can thus be insured (d?Anontal). D'Arsonval's zinc carbon element differs from the Bunsen cell by the composition of the fluids. Fluid round the zinc, or exciting fluid. Water 20 volumes. Sulphuric acid (purified by oil ; see page 297) . 1 Common hydrochloric acid 1 , Fluid round the carbon or depolariser. Common nitric acid 1 volume. Common hydrochloric acid 1 , Water acidulated with ^jth of sulphuric acid . 2 This cell does not polarise on short circuit ; its e. m. f. is as much as 2-2 volts. BATTERIES. 197 Couples in which the negative electrode is jacketed lm*o**ee) (E. Jteynier). In most two-fluid combinations the negative electrode is immersed in a solution of some salt of the metal of which it is composed. If the negative electrode be jacketed, that is to say, provided with a tight covering not attacked by the liquids .in the battery, but yet permeable by them, a constant couple may be formed by simply dipping a positive electrode in the ordinary state into the depolarising liquid along- side of the jacketed negative electrode. The small quantity of liquid confined in the jacket against the negative electrode is soon charged with a salt of its metal ; the couple then acts like a two-fluid cell, the excess of salt being eliminated through the jacket as fast as it is formed by a process of osmosis, the rate of which is auto- matically regulated by the current This plan reduces the maintenance of constant batteries to the keeping in good order of one fluid only ; it has been applied with success to the combination zinc, sulphate of zinc ; sulphate of copper, copper. The cell being composed of a copper vessel and a jacketed zinc. (If the sulphate of copper be replaced by " gilder's verdigris " the battery becomes the most economical known.) E. 111. f. of some jacketed zinc cells (E. Btynier): New Polarised volts. volte. Common zinc jacketed, bare copper, dilute sulphuric acid -848 -411 Common zinc jacketed, bare iron, dilute sulphuric acid* -401 *4 9 Amalgamated zinc jacketed, bare iron, dilute sulphuric acid -496 '496 Amalgamated zinc jacketed, bare iron, 20 per cent, solution of bisulpbate of soda . . '301 -509 Jf. Reynier has tried to apply jacketing to bichromate cells ; but he has not been able to construct any flexible jacket which will resist the destructive action of the bichromate mixture. Modifications of Crove's and Bnnsen's cells. Efforts have been made, but as yet without success, to find a substitute for zinc in these cells. M. Rott*sc proposed lead or iron attacked by nitric acid. X. Maicht (1864) a cylinder of sheet iron attacked by water containing one-hundredth of nitric acid, etc. Attempts have also been * ObMrratioK. The couple zinc, acidulated water, iron, is perfectlj constant. 198 APPLICATIONS OP ELECTRICITY. made to replace the platinum by passive iron (Hawkins, 1840 ; Schonbein, 1842). Concentrated nitric acid or aqua regia is necessary for this purpose. Attempts have also been made to replace the depolariser (nitric acid) by other bodies : chromate of potassium, Bunsen (1843) ; chlorate of potash, Leeson (1843) ; chromic acid, chloric acid, perchloride of iron, picric acid, etc. Maries-Davy's cell. A Bunsen cell in which the nitric acid is replaced by a paste of sulphate of mercury protoxide (Hg 2 O,SO 3 ) packed round the carbon. E rz 1-2 volts. Answers for intermittent work, requires very porous cells, weak solutions of high resistance. * Dlirlieniin (1865). Zinc in a solution of common salt, the nitric acid replaced by a solution of perchloride of iron. The solution is refreshed by passing a stream of chlorine through it. E zr 1 '54. Delaurier (1870). Nitric acid replaced by : Chromic acid (4 equivalents) .... 25*14 parts. Sulphate of protoxide of iron (1 equivalent) . 25' ,, English, sulphuric acid 30'62 Water 60' The hydrogen is absorbed, and a mixture of sulphate of protoxide of iron, and sulphate of sesquioxide of chrome is formed. Bichromate Of potash. Depolarising liquid of 100 parts of water, 25 of sulphuric acid, and 12 of bichromate ; prrous pot, amalga- mated zinc, water acidulated with one-twelfth its weight of sulphuric acid. E = 2'03 volts for the first few seconds. In Fuller's battery the central zinc stands in a small pool of mercury to keep up the amalgama- tion. Water only is in practice put into the porous pot with the zinc. E = 2 volts. In the element invented by Claris Baudet (1879), there is a supply of sulphuric acid and bichromate arranged in the outer pot with the carbon, so as to keep up the strength of the depolarising liquid. E = 2 volts : r = '22 to -3 ohm for the 20 cm. form. In JUggins* cell the zinc, which is perfectly amalgamated, is immersed in a solution of sulphuric acid (^th by volume), the carbon plate in a chromic solution containing 45 parts water, 15 sulphuric acid, and 5 of bichromate of potash (by weight). E = 2'2 volts. The 15 cm. high element has an internal resistance of '4 to '5 ohm. BATTERIES. 199 D'Arsonval's bichromate cell. Porous pot full of broken-up retort carbon, plain water with the zinc ; the depolarising liquid is : Water saturated in the cold with bichromate of potash . 1 volume. Common hydrochloric acid 1 This liquid should flow continuously through the cell ; this element makes no smell, and is always ready when wanted. Niaudet's chloride of lime battery (1879). Plate of zinc in 24 per cent, solution of common salt ; plate of carbon in porous pot, with fragments of carbon and chloride of lime (bleaching powder), the depolarising agent is the hydrochlorous acid. Initial e. m. f . 1 '65 volts after being left alone for several months. E =r 1 -5 volts, r of the common form =z 5 ohms. Action only takes place when the circuit is closed, but smells disagreeably, so that the cells have to be hermetically sealed. Circulation, agitation, and blowing air through the cells are three excellent ways of disengaging hydrogen from the carbon plates, and bringing oxygen in contact with them. Agitation has been employed by Chutauz, Camacho, etc. ; blowing air through by Grenet and Byrne. Thermo-chemical batteries. The current is produced by the oxydation of carbon at a high temperature under the action of nitrate of potassium or sodium. The fundamental experiment is due to Becquerel (1855), repeated by Jablochko/ (1877), and taken up again by Dr. Brard (1882), who has produced an electrogenic torch which produces a current as it burns. This new generator of electricity has not yet come into use, we therefore only notice it. Electromotive forces of one-fluid batteries with 11O depolarise!' (reduced to volts from observations by Poggendorff and E. Becquerel} : Open After circuit, polarisation. Copper, dilute sulphuric acid, common zinc . '81 Silver, 1-03 Copper, ,, ,, amalgamated zinc '94 Silver, ,, ,* . 1'24 '52 Platinum, > I' 44 ' 65 200 APPLICATIONS OF ELECTRICITY. ELECTEOMOTIVE FORCE OF GROVE'S CELL (Poggendorff) . FLUID HOUND THE ZINC. FLUID ROUND THE PLATINUM. ELECTROMOTIVE FORCE IN VOLTS. Sulphuric acid : Density . . = T136 . = 1-136 . = 1-06 . = 1-136 . = 1-06 Solution of sulphate of zinc ,, of common salt . Fuming nitric acid . Nitric acid, d . = 1 '33 . = 1'33 . = 1-19 . = ri9 . = 1-33 . - 1-33 1-955 1-809 1-730 1-681 1-631 1-673 1-905 ELECTROMOTIVE FORCES OF AMALGAMS OF POTASSIUM AND ZINC. (The amalgams were enclosed in porous cells) (Wlieatstone) . AMALGAM. SOLUTION. POSITIVE POLE. ELECTROMOTIVE FOKCE. ( Sulphate of zinc. Zinc. 1-043 Sulphate of copper. Copper. 1-122 POTASSIUM*; Chloride of platinum. Platinum. 2-482 Sulphuric acid. Peroxide of lead. 3-525 I Sulphuric acid. Peroxide of manganese. 2-921 C Sulphate of copper. Copper. 1-079 Nitrate of copper. Copper. 1-043 ZINC . 4 Chloride of platinum. Platinum. 1-438 Sulphuric acid. Peroxide of lead. 2-446 I Sulphuric acid. Peroxide of manganese. 1-942 Electromotive forces of cells containing only one electrolyte (E. lteynier).The electromotive force of such cells is very variable ; it decreases when the circuit is closed, and in- creases when the battery is at rest ; for the same voltaic combination, it appears to be higher when the surface of the positive plate is very large compared to that of the negative plate. Thus the apparent e. m. f. varies with the design of the cell, the circumstances of the experiment, and the method of measurement employed. The two values of the e. m. f . which must be known are the highest and the lowest. M. Eeynier has measured these two extreme values by means of two different types of cell, specially constructed for this purpose, which he calls pile a maxima and pile a minima. The positive plate of the first type has 300 times more surface than the negative, whilst in the second type the negative plate ELECTROMOTIVE FORCE OF BATTERIES. 201 exposes far more surface than the positive. The e. m. f . is measured after the cell has been for some long time on short circuit. The following are the figures which he has obtained for some voltaic combinations. DESCRIPTION OF CELL. ELECTRO MOTIVE FORCE IN VOLTS. LIQUID. NEGATIVE PLATE. POSITIVE PLATE. MAXIMUM. MINIMUM. ( Common /inc. Platinum. 5 Amalgamated zinc. Platinum. 561 Common zinc. Silver. < '098 Amalgamated zinc. Silver. 108 Water acidulated Common zinc. Carbon. 1-22 04 with sulphuric acid. Water, 1030 vols.- Monohydrated sulphuric acid, 2 vols. ! Amalgamated zinc. Common zinc. ! Amalgamated zinc. Common zinc. Amalgamated zinc. Common zinc. Carbon. Lead. Lead. Copper. Copper. Iron. 1-26 55 684 94 1-072 429 226 144 152 194 272 309 Amalgamated zinc. Iron. 476 323 Amalgamated zinc. Common zinc. 09 - Iron. Copper. 5 Common zinc. Platinum. 034 Common zinc. Carbon. 1-08 < -04 Common zinc. Silver. 043 Solution of sodium chloride. Common zinc. Amalgamated zinc. Copper. Copper. 78 82 025 Water, 1000 gr/ Sodium chloride, 250 gr. Common ziuc. Amalgamated zinc. Common zinc. Amalgamated zinc. Iron. Iron. Lead. Lead. 378 469 503 52 046 044 Iron. Copper. 26 - Lead. Copper. 26 Zinc Chloride. Water, 1,000 gr. ( Zinc chloride,-} 110 gr. ( Common zinc. Amalgamated zinc. Copper. Copper. 85 86 Zinc sulphate. Water, 1,000 gr. ( Ziuc sulphate, < 500 gr. I Common zinc. Amalgamated zinc. Copper. Copper. 998 1-04 - Caustic soda. Water, 1,000 gr. ( Caustic soda, 250-5 gr. I Common zinc. Amalgamated zinc. Copper. Copper. 1-06 1-09 202 APPLICATIONS OP ELECTRICITY. Electromotive forces of some two-fluid cells (E. Eeynier). Volts. Standard Daniell. Unamalgamated zinc, sulphate of zinc d = T09. Copper, sulphate of copper d = 1'16 . . 1'068 The same, a very small quantity of sulphuric acid added to the sulphate of copper '993 The same, with a very small quantity of sulphuric acid added to both liquids -929 The same, with a small quantity of tartaric acid added to the sulphate of copper 1'015 Unamalgamated zinc, caustic potash, 30 per cent, so- lution. Copper, sulphate of copper d = 1*16 . . . 1*555 Unamalgamated zinc, solution of soda and potash (potash 175, soda 250, water 1000) . Copper, sulphate of copper d = 1-16 1-661 Unamalgamated zinc, solution of soda (Eeynier's formula). Copper,solution of sulphate of copper(Eeynier's formula) 1'473 Amalgamated zinc, solution of soda (Reynier's formula). Copper, solution of sulphate of copper (Reynier's formula) 1'5 Iron, commercial sulphate of iron d = 1*20. Copper, sul- phate of copper d = 1*16 "711 Theoretical electromotive forces. Calculated from the electro -chemical equivalents. Smee'scell '886 volt. Darnell's cell T156 Grove's cell T991 Direct observation always gives lower values than these, because of the secondary actions which are always going on in the cells. Theoretical conditions of a perfect battery. 1. High e. m. f. 2. Small and constant internal resistance. 3. Constant e. m. f., no matter how large the current. 4. Consumption of cheap substances. 5. Chemical action always proportional to the output of energy, and consequently no consumption when the circuit is open. 6. Convenient and practical form enabling the state of the battery to be easily observed, and the cells to be easily refreshed when necessary. No battery fulfils all these conditions. In every case a form of ele- ment must be chosen, having qualities suited to the purpose for which it is wanted. DEFECTS OP BATTERIES. 203 CONSTANTS AND WORK OF SOME KNOWN FORMS OF BATTERY * (E. Reynier). CELLS. E. r. WORK PER SECOND. KGM. CALORIES (g.-d.). Bunsen round, '2 metre high Rhumkorff, '2 metre high W Thomson . . 1-9 1-9 1-06 1-5 1-77 24 06 12 075 2 384 1-536 238 765 399 888 3-555 551 1-77 924 Reynier, rectangular form, 3 litres capacity, porous cell of two thicknesses of parchment paper Tommasi, zinc, sulphuric acid, and water (^TT), carbon, nitric mix- ture ..... Defects Of batteries. When a battery does not give the expected results, one of the following defects is to be looked for : (1) Ex- hausted solutions ; for example, in a Daniell battery, the sulphate of copper worked out, leaving the solution colourless, or nearly so ; (2) bad contacts between the electrodes and the wires, oxydised or badly screwed- up binding screws, etc. ; (3) empty or partly empty cells ; (4) filaments of metallic deposit causing short circuiting between the battery plates ; (5) creeping or deposits of salts forming short circuits either between the plates or from cell to cell. Shaking the cells increases their e. m. f . tempo- rarily by disengaging the gases adhering to the plates. Floating filaments and broken plates give rise to false contacts, which cause the current given by a battery to vary suddenly when it is shaken (Fleeming Jenkiri). Choice of a battery for different purposes. The following list may serve as a guide in most ordinary cases. Electro -chemical deposition. Daniell, Smee, Grove, Bunsen, bichro- mate, Slater. Gilding. Daniell, Smee. Silvering. Daniell, Smee, Grove, Bunsen, Slater. Electric light. Grove, Bunsen, bichromate (Grenet, Cloris Baudet), Tommasi, Carre, Reynier, Accumulators. * The constants were measured on new cells, and the work deduced from them by calculation ; as soon as the circuit is closed, the elements vary from these figures in a manner unfavourable to the battery. This is the case even with batteries which are supposed to be constant. 204 APPLICATIONS OF ELECTRICITY. Induction coils. One-fluid bichromate, Grove, Buiisen ; for small pocket coils, sulphate of mercury. Lecture -room and laboratory experiments. Bichromate, bottle or wind- lass form. Grove or Bunsen (in a well -arranged stink chamber), well cared for gravity Daniell. Medical batteries. Smee, Trouve, Onimus, Seure, Leclanche, bichloride of mercury, chloride of silver. Large telegraph lines. Daniell, Callaud, Meidinger, Fuller, Leclanche. Bells and domestic purposes. Leclanche, sulphate of mercury, sulphate of lead. Torpedoes. Leclanche (Silvertown firing battery), special form of bichromate. Electrical measurements. Leclanche, bichromate, Daniell's standard. Standards. See Measuring Instruments (page 62). Practically, only the standard Daniell and Clark's standard cell are used. CARE AND MAINTENANCE OF BATTERIES. In the first place, in setting up batteries, all parts should be as nearly as possible chemically clean. The chemicals and the water should be pure. For laboratory work these conditions should be strictly fulfilled, the water used being distilled, and for practical work they should be approached as nearly as possible . Groves' and Bunsen' s cells should be emptied after use, all parts well washed, and kept separately in large pans of clean water, zincs in one, platinums or carbons in another, and porous cells in another. All cells of the Daniell type require careful watching from time to time. A little of the fluid surrounding the zinc should be drawn off with *, syringe, and fresh water added. If there be any considerable deposit of copper on the zinc, it must be carefully scraped off, and the solution round the zinc poured away, and fresh added. In practice, water alone is always used for the zinc fluid. The zinc of batteries of the Daniell type should never be amalgamated, as, if copper be deposited on the zinc, it spreads in a film of amalgam over the whole surface. Gravity cells require some skill in their management. If the blue colour due to the sulphate of copper spreads too high up, a syringe or pipette must be plunged well into the blue solution, and some of it drawn off. Water must then be carefully added on the top, taking care not to agitate the fluid. A funnel with a tube turned up at the end is useful. The tube should be immersed until the turned up end is just below the surface of the fluid, and the water then gently poured into the funnel. A screen of perforated zinc may be suspended a little below the BATTERY TESTING. 205 zinc plate to reduce any sulphate of copper which rises too high. From time to time some of the clear fluid near the zinc should be drawn off, and replaced with water, because if the sulphate of zinc solution becomes too strong, the salt is electrolysed, and zinc is deposited on the copper. All forms of Daniell are liable to creeping of the salts. All deposits of crystals should be cleared away, and all parts of the battery above the fluid should be smeared from time to time with paraffin, wax, vaseline, or hard tallow, which checks the creeping. A good working rule to prevent exhaustion of the copper solution in all forms of Daniell's cell is to take care that there is always some sulphate of copper undissolved. In gravity cells fresh crystals may be added without disturbing the fluid much, by dropping them down a glass tube of large bore plunged nearly to the bottom of the cell. Leclanche cells re- quire but little attention. Sometimes they creep ; the remedy is the same as for the Daniell. They should be examined from time to time, and fresh water added if the quantity of fluid has diminished from evaporation. Care should be taken that there is always some undissolved sal-ammoniac at the bottom of the cell. If the cell be full and there be plenty of sal- ammoniac, and yet it will not work well, it may be that the solution is too rich in zinc chloride. Empty the cell, and put fresh sal-ammoniac and water. If it then fails, the manganese is worked out, and a new cell must be substituted. Fuller's batteries require some of the zinc solution to be removed and replaced by water from time to time, and occasionally the bichromate solution must be renewed. Take care in emptying the cells not to lose the mercury. All cells require the zincs to be renewed from time to time. In Daniell's cells the copper deposit is peeled off the copper plates from time to time and preserved, as it commands a good price in the market. Battery testing. This is generally roughly done with the linesman's detector, a form of upright galvanometer, wound with one coil of low resistance, called the quantity coil, and one of high resistance, called the tension coil. A linesman soon knows by experience that so many cells of a given type should give so many degrees " quantity " and so many "tension;" i.e. he has always at hand a rough index of the internal resistance and electromotive force of the batteries under his charge, and in the event of weakness knows in which direction to work in order to set matters right. The telegraph engineer can, if he wishes, easily calibrate the detectors of his linesmen, so that he can translate their reports into electrical units. The method used in the Post-office service is of considerable accuracy, 206 APPLICATIONS OF ELECTRICITY. and yet easy to carry out. Two resistance boxes are used, one of 10, 25, 50, 100, 200, and 400 ohms; the other of 1*07 (A), 3'21 (B), 4-28 (C), 8-56 (D), 17'12 (E), and 34-24 (F) ohms; i.e. in the proportion of 1 : 3 : 4 : 8 : 16 : 32. Also a tangent galvanometer of resistance 1'07 ohms. Electromotive force test. First the standard cell (e. m. f. T07 volts) is joined direct to the galvanometer, and the deflection brought to about 25, or a very little under, by means of the directing magnet. The battery to be tested is then put in circuit with the galvanometer and the resistance box of T07, 3 '21 etc., ohms; if the battery to be tested is a NUMBER OF CELLS TO BE TESTED. COILS TO BE PLACED IN CIRCUIT IN BI. DANIELLS. BICHROMATES. LECLANCHES. 5 _ 3 A 10 5 6 B 8 C 15 _ 10 A + C 20 10 12 B + C 25 16 A + D 30 15 18 and 20. B + D 35 A + C + D 40 20 24 B + C + D 45 30 A + E 50 25 32 B + E 55 A + C . + E 60 30 36 B + C +E 40 D + E 65 A + D + E 70 35 B +D + E 75 48 and 50. A + C + D + E 80 40 B + C + D + E 85 A + F 90 45 60 B + F 95 A + C + F 100 50 B + C + F 105 A + D + F 110 55 B + D + F '115 A + C + D + F 120 60 B + C + D + F 125 A + E + F 130 65 _ B + E + F 135 A + C + E + F 140 70 B + C + E + F 145 A + D + E + F 150 75 B + D + E + F 155 A+C+D+E+F 160 80 B+C+D+E+F BATTERY TESTING. 207 Daniell, then as many times T07 ohms are inserted as there are cells in the battery (taking into account the 1 '07 ohms in the galvanometer for one cell), if the battery is in good order the deflection remains the same, if not the e. m. f. can be calculated. For other types of cell, tables are issued showing the most convenient resistances to employ in order to make the calculation easy, and the deflections which ought to be obtained if the cells are in good order. Test for internal resistance. After the deflection for electromotive force has been noted, the second resistance box is put as a shunt to the battery; let E2 be the resistance employed. This reduces the deflection. Let c be the current passing through the galvanometer, then if E be the electromotive force and x the internal resistance of the battery, - E B 2 ^ EB> where Bi is the resistance employed in taking the e. m. f . The current C passing through the galvanometer previous to the insertion of the shunt is c = E therefore But since x and Ba are very small compared with BI -j- Gr, we may consider in which case 208 APPLICATIONS OF ELECTRICITY. If the first deflection (on the degrees scale) be called D and the reduced deflection be called d, then tan d _ c ta^D ~ ~CT' therefore tan d _ R. 2 tan D ~~ x -f- B 2 ' or tan d X x + tan d X BS = tan D X R* therefore tan d X x = R 2 (tan D tan d) ; that is /tan D x = H 2 (- - Vtan rf ACCUMULATORS OR SECONDARY BATTERIES. Though many forms of battery are theoretically reversible, only salts of lead as yet have been found to answer in practice. M. Gaston Plante was the first to use lead for a reversible regenerative or secondary battery in 1860. Since these cells have come into practical use they have been called Accumulators, a name which is very unfortunate, being based on an erroneous theory of their action, which, as far r s we know, has never been held by any electrician. It has now passed into the language, and must therefore be accepted. M. Gaston Planters secondary cell or accumu- lator (I860). Two plates of lead, separated by flannel or other absorbent non-conductor, and rolled up in a spiral immersed in a 10 per cent, (by volume) solution of sulphuric acid. formation. A preliminary operation, the object of which is to form as thick a coating of peroxide as possible on the positive plate and to convert as great a depth as possible of the negative plate into spongy or crystalline lead. This is effected by changing the direction of the charging current after discharge, and keeping the cells charged for longer and longer time. In order to shorten the forming process, M. Plante has lately suggested heating the forming bath, or, more ACCUMULATORS. 209 simply, immersing the plates for from 24 to 48 hours in nitric acid diluted with half its volume of water. The acid attacks the lead, and makes it more or less porous, thus assisting the action afterwards set up by the charging current. Electromotive force. During the first few moments after the stoppage of the charging current, the e. m. f. = 2 '53 volts. In two minutes it falls to 2-1 volts, and for two-thirds of the discharge it remains steady at 2 '02 volts. M. Plante explains the excess of e. m. f. at first by the formation of liquid or gaseous compounds rich in oxygen and hydrogen round the electrodes, which tend to decompose or escape very quickly. Their action is added to the normal action, which remains sensibly con- stant for two -thirds of the discharge. Internal resistance. A couple exposing 50 square decimetres of total surface, the plates being five millimetres apart, has an internal resistance of from '04 to '06 ohm, according to the extent of the formation of the plates. Total quantity of electricity stored. A well-formed couple containing 15,000 grammes of lead will deposit 18 grammes of copper in a sulphate of copper voltmeter by its whole discharge. This corresponds to 54,540 coulombs, or 36,360 coulombs per kilogramme of lead. The cell gives out during its discharge from 89 to 90 per cent, of the quantity of electricity which has passed through it during its charge, if the discharge be made immediately after the charge. In recent experiments, M. Plante has succeeded in depositing as much as 19 grammes of copper per kilogramme of lead. Useful discharge. About two-thirds of the discharge may be utilised without the e. m. f. falling below 2 volts, i.e. about 24,240 coulombs. The total energy given out is 4,850 kilogrammetres, or 3,230 kgm. per kg. of lead. Many modifications of M. Plante's accumulator have been devised to increase the active surface without increasing the weight. (The corru- gated plates of MM. de Kabath, de Pezzer, de Meritens, etc.) Faure's accumulator (1881). Flat or spiral plates of lead covered with minium (red lead) kept in place by parchment paper and felt. The experiments made in January, 1882, by the commission of the Paris Electrical Exhibition, gave the following results : Thirty-five elements, each weighing 43 '7 kg., electrodes coated with minium 10 kgs. per square metre. Liquid : water acidulated with one- tenth of its weight of sulphuric acid. The accumulators arranged in series were charged for twenty-four hours forty-five minutes, by a current varying between 11 and 6 '36 amperes, and a mean difference of potential 210 APPLICATIONS OF ELECTRICITY. of 91 volts, and received 694,500 coulombs. The charging was effected by a shunt Siemens' dynamo. The work supplied is thus divided : Effective work in charging .... 6,382,109 kgms. Excitation of field magnets .... 1,383,600 Heating of the ring 269,800 Heating of passive resistances . . . 1,034,500 Total work given out 9,570,000 The discharge occupied ten hours thirty-nine minutes, with a mean current of 16 '2 amperes, and 61'5 volts difference of potential at the terminals of 12 Maxim lamps in parallel arc. 619,600 coulombs were recovered, the loss was 74,900 coulombs, or about 10 per cent. The external or useful electrical work was 3,809,000 kgm., or 40 per cent, of the total work, and 60 per cent, of the stored work. The patterns made in England vary from 28 to 45 elements to the ton. The first require 32 amperes for twelve hours to charge them, the second 20 amperes for twelve hours. Same current given by the discharge, but it may be doubled by halving the time of discharge. For special efforts, then, this current may be largely exceeded for a few moments. Faure-Sellon-Volfcmar accumulators (1882) without felt, etc. ; lead plates pierced with holes, or cast-lead gratings ; minium, reduced lead, or some lead salt is compressed into the openings. The reduced plates last indefinitely ; the oxydised plates are eaten away after about a year's service. A cell containing forty-three plates and weighing 140 kgs., can give 120 amperes for six hours. Another form containing fifty-three plates, and weighing 170 kgs., will melt a copper wire 5 mm. in diameter, and 30 cm. long, which implies a current between 400 and 500 amperes. The good results obtained from the cells manufactured by the Power Storage Company (Limited) are probably as much due to the selection of materials (which is as yet a trade secret), and the care bestowed on their manufacture, as to the fundamental design of the plates. Copper accumulators (J?. Eeynier). Positive: peroxydised lead ; negative : copper-plated lead ; liquid acid solution of copper sulphate: E = I 1 68 volts. Mr. Sutton, of Australia, laid before the Boyal Society a form of copper accumulator : copper ; copper sulphate solution ; amalgamated lead. It is found that amalgamation makes the peroxydising process more rapid. Professor McLeod, of Cooper's Hill, ACCUMULATORS. 211 has observed that the first action of the current is to remove the mercury from the lead in the form of sulphate, the lead surface then begins to peroxydise rapidly, being probably left in a more or less spongy condition. The advantage claimed for copper accumulators is that the colour of the solution is a gauge of the quantity of charge in the cell, being colourless when the cell is fully charged, and deep blue when it is nearly discharged. Zinc accumulators (E. Reynier). Positive : peroxydised lead; negative: zinc -coated lead; liquid acid solution of zinc sulphate: E = 2'3 volts. Zinc plates may be used ; the difficulty of construction is the necessity for keeping the zinc well amalgamated. Storing power and output of accumulators. In order to get good efficiency from accumulators their output ought not to exceed half an ampere per kilogramme of total weight ; when, however, a rapid output is required, 5 or 6 amperes per kilogramme may be taken at the expense, however, of efficiency. From this point of view the small Plante cells with thin lead plates are the most powerful. The storing power, on the other hand, increases with the dimensions of the cell, and varies in practice between 2,000 and 4,000 kgm. of available electrical energy per kilogramme, or from 70 to 150 kgs. of accumulators per hour horse -power. Theory shows that this weight might be much reduced, but we know of no authentic experiments giving higher results than those quoted here. To avoid heating the accumulators, and so wasting work, the charging current ought not to exceed half an ampere per kg. of accumulators for large sizes, and 2 to 3 amperes per kg. for small. The duration of charging in seconds is given by the ratio of the storing capacity of one element in coulombs to the charging current in amperes. Under the same conditions the duration of the discharge is proportional to the weight of the element. CALCULATION OF ELECTRO-CHEMICAL DEPOSITS. When 1 coulomb of electricity passes through a decomposition cell it liberates 0105 milligrammes of hydrogen*. * Kohlrausch found by experiment '010521. Mascart 'OlOilS. 212 APPLICATIONS OF ELECTRICITY. r-l N -^ r-l (N CO t>. r-l iiOi-i 10 w - 8 H 1! CHEMICAL EQUIVALENTS. 213 If e be the chemical equivalent* of an element (hydrogen 1), the weight z of this element set free by one coulomb of electricity will be : z '0105 emg., z is the electro-chemical equivalent of the element. y A current of strength C (in amperes) will deposit a weight P per second : P' = zC = -0105 eC mg. A current of strength C (in amperes) will deposit a weight P' per hour : P' = 3600 zC = 37'8 eC mg. One ampere hour (3600 coulombs) will liberate : 37 '8 milligrammes of hydrogen. 37 '8 e milligrammes of any given element. These formulae enable the deposit which would be produced by a given current in a given time to be calculated, or conversely the strength of current necessary to produce a given deposit in a given time. Calculation of the electromotive force of polarisation of an electrolyte. The electromotive force of polarisation of an electrolyte is a measure of the electro -chemical work done by the current in its decomposition. The principle of the conservation of energy enables this e. m. f. to be calculated by equating the work done by the current in overcoming this polarisation e. m. f., and the mechanical equivalent of quantity of heat which the liberated element would disengage in recombining, so as to reform the original electrolyte. Let E be the polarisation e. m. f. (in volts) of an electrolyte, Q the number of coulombs which has passed through it, the electro -chemical work of decomposition is : QB If z be the electro -chemical equivalent of the liberated element (see page 212), the total weight liberated by Q coulombs will be equal to Q^. Combining weight or atomic weight * e the chemical equivalent = Valency Atomic weight Thus potassium a monad equivalent = j Atomic weight Zinc, a diad, equivalent = 214 APPLICATIONS OF ELECTRICITY. Let H be the quantity of heat disengaged by 1 gramme of this element in combining so as to form the original electrolyte, then the heat disengaged by the weight Qz of this element will be Q:H. As the mechanical equivalent of heat is '421 kgm. per calorie (g. -d.) the heat dis- engaged by Q^ grammes will be : 424 Q:H. (0) Equating (a) and ()8) we get finally : E=:4-16zH. Electrolysis Of water. Applying the above formula to this case, as the heat disengaged by the oxydation of 1 gramme of hydrogen is 34450 calories (g.-d), and the electro -chemical equivalent of hydrogen is 0000105, we get : E = 4-16 X -0000105 X 31450 = 1'5 volts. The polarisation e. m. f. in the electrolysis of water is thus To volts. This fact explains why one Daniell's cell is unable to decompose water, at least two in series being required. Calculation of the e. m. f. of batteries. The formula E ~ 4'16 zH enables the e. m. f. to be easily calculated for any voltaic combination when the nature of the chemical actions occurring in it and the heat disengaged by those actions are known. The Daniell's cell. Two distinct actions go on : 1st, solution of the zinc in sulphuric acid ; 2nd, deposition of copper by the decomposition of copper sulphate. 1st. The heat disengaged by the solution of 1 gramme of zinc in sul- phuric acid, HI, is, according to Julius Thomson, 1670 calories ; the electro -chemical equivalent of zinc, z =. '0003412 ; thus : E! = 4-16 X '0003412 X 1670 = 2'36 volts. 2nd. The heat absorbed by the deposition of the copper H 2 is 881 calories per gramme, the electro-chemical equivalent of copper 22 1-21 volts. The e. m. f . of the Daniell cell is equal to the difference between the two, i.e. 2-36 - 1-21 = 1-15 volts. This theoretical value is not far from the practical value, 1 -079 volts. Electrolysis \vithoiit polarisation. When electrolysis is carried on with a soluble anode, if the bath be a solution of a pure ELECTRO-METALLURGY. 215 salt of the metal, there is no polarisation, and the work done by the current is reduced to mere transport of matter from one plate to the other, which only requires a very small expenditure of electrical energy.* The expenditure of energy in the decomposition cell is thus practically reduced to the heating effect due to the passage of the current, and may be calculated by Ohm's law. If W be this work, T?r^2 W rr kgm. per second, y'ol R being the resistance of the bath in ohms, and C the strength of the cur- rent in amperes. In practice the baths are never perfectly pure, and a certain amount of polarisation is produced in them which has to be taken into account. EUECTRO-METAI^URGY. Under this title are included all operations in which a metallic deposit is formed by means of electrolysis. The term ' ' electrotype ' ' is applied exclusively to those deposits which are so thick that they can be detached from the surface on which they have been deposited without losing their shape. Electrotypes are almost always of copper. Adherent deposits of this metal are used for cop- pering. ELECTROTYPING. Copper electrotyping. For whatever purpose copper is to be deposited, the bath is always the same. It is thus prepared : Bath. A certain quantity of water is taken, to which from 8 to 10 per cent, of sulphuric acid is added slowly and by degrees, stirring well the whole time. As much sulphate of copper is then dissolved in this acidulated water as it will take up at the normal temperature, stirring well. The saturated bath ought to have a density of T21. It is always used cold, and must be kept saturated, either by the addition of fresh crystals or the use of soluble anodes. It must be used in vessels of porcelain, glass, hard faience, or guttapercha. For large baths wooden vats are used, lined with a thin coating of guttapercha, marine glue, or varnished lead-foil. The vats should never be lined with iron, zinc, or tin. * M. Lossier has calculated the energy absorbed by this transport by con. eidering it as an induction effect produced by the movement in the fluid of polarised molecules. 216 APPLICATIONS OF ELECTRICITY. Moulds. Plaster of Paris is the substance which has been longest in use ; but, as it is porous, it has to be made waterproof, which is a complication in its use. Moulds are now generally made of stearine, wax, marine glue, gelatine, guttapercha, and fusible alloy. "When the moulds are hollow, a skeleton of platinum wires is arranged in the interior. This is connected to the anode, and serves to direct the current, and so to render the deposit uniform in thickness. These wires are wound with a spiral of indiarubber to prevent their touching the walls of the mould. M. Gaston Plante uses lead instead of platinum for these wires, and has thus effected a great saving in cost. When several things are being covered with metal at the same time, it is well to connect each one separately to the negative pole by an iron or leaden wire of appropriate thickness. This wire melts if there be any short-circuiting at its corresponding mould, and thus cuts it out of the circuit. The surf ace of the moulds is made conducting by pure plumbago, gilt or silvered plumbago, or bronze powder (a form of finely- divided copper, prepared by dropping granulated zinc into a solution of sulphate of copper). The mould is rubbed over with a clock-maker's brush or polishing brush. Wax requires very soft pencils. Moulds are also metalised by a wet process. A solution of nitrate of silver is brushed several times over the moulds, and reduced by the vapour of a concen- trated solution of phosphorus in bisulphide of carbon. The wet method is best for very delicate objects, such as lace, flowers, leaves, moss, lichens, insects, etc. An agate cameo can be reproduced, without metalising, by simply winding a copper wire round it, and suspending it in the bath. General management of baths and currents. When the solution is too weak, and the current is too strong, the deposit is black ; when the solution is too strong, and the current is too weak, the deposit is crystalline. The metal is deposited in a sound, flexible state when the conditions are the mean between these two extremes : such a deposit was named by Smee reguline. The stratification of the liquid, and the circulation produced in the bath by the solution of the anode and the deposit on the cathode, produce long vertical lines, like notes of excla- mation. The objects must be shaken about as much as possible, so as to keep the bath thoroughly homogeneous. Large baths are the best. A long distance between the anodes and cathodes produces a more regular deposit. It is especially necessary for small things ; but it either decreases the rapidity of the deposition or requires a more powerful source of elec- tricity. The same bath may be used for several objects at once, each one connected to a separate source of electricity, if one anode only be used, which is joined to the positive poles of all the sources. The surface of ELECTROTYPING. 217 the anode generally ought to be the same as that of the cathodes : too small an anode weakens the solution ; too large an anode strengthens it. Experience shows which effect it is desirable to produce in any particular Copper cliches or electrotypes (Stcesser). Wax moulds. Deposition requires twenty-four hours; mean thickness of deposit three - tenths of a millimetre, corresponding to a deposit of 25 grammes per square centimetre, or one gramme per hour per square centimetre. The strength of the current may be increased, so that the same thickness of deposit may be obtained in twelve hours, or less, without injuring the quality of the metal. Making the process last for twenty-four hours is, however, convenient, as the moulds may be prepared during the day and put in the bath at night. Density of the current (Sprague}.Th& best bath for all objects not attacked by acid is : 3 volumes. 1 Saturated solution of copper sulphate . Solution of sulphuric acid (one-tenth by volume). The density of the current, that is, the current strength per unit of electrode area, may vary between certain limits which depend on the rate of work and the nature of the desired deposit. In this work we have taken as the unit of density, one ampere per square decimetre. One ampere deposits 1'19 grammes of copper per hour. The following are the results of Mr. Sprague's experiments : NUMBER OF EXPERIMENT WEIGHT OF DEPOSIT PEK HOUR PER SQUARE DECIMETRE, IN GRAMMES. STRENGTH OF CURRENT PER SQUARE DECIMETRE, IN AMPERES. NATURE OF DEPOSIT. 1 1 085 Excellent. 2 3 4 3' 342 2'6 Good tenacious copper. Magnificent. 4 12- 10-2 Very good. 5 50' 427 Powdery at the edges. 6 124- 106 Bad all round the edges. ADHERENT DEPOSITS. These are now deposited on all metals and of all metals. We will only describe the most important : coppering, brassing, gilding, silvering, and nickeling. All these deposits require a preliminary process of seating 218 APPLICATIONS OF ELECTRICITY. and cleaning to make the surface fit to receive the deposit, and to ensure as perfect adherence as possible between the two metals or alloys. Some hints on this process will be found in the Fifth Part. Coppering" is always performed by means of a bath of a double salt, either hot or cold ; the composition of the bath varies with the nature of the metal to be coated. Below we give the formulae recommended by an esteemed practical authority, M. Roseleur; but these formulae differ immensely with different operators. The copper acetate is dissolved in 5 litres of water, the ammonia and other substances in other 20 litres. They are mixed, and the fluid ought to be discoloured ; if not, cyanide must be added until discoloration is produced, and then slightly in excess. The oldest baths work the best. Agitate the objects as much as possible. When the bath is too old, it may be refreshed by adding copper acetate and potassium cyanide in equal weights. COPPERING BATHS (Roseleur}. The weights expressed in grammes are the quantities for 25 litres of wafer. IRON AND STEEL. TIN, CAST IRON, SMALL Cold. Hot, AND ZINC. OBJECT. Sodium bisulphate Potassium cyanide 500 500 200 700 300 500 100 700 Sodium carbonate 1000 500 Copper acetate 475 00 350 450 Ammonia . . 350 300 LVO 150 Brassing 1 . Hot (50 to 60 C.) for iron and zinc wire in bundles, and sham gold ; cold for other objects. for iron (cast and wrought}, and steel. Dissolve in 8 litres of soft water : Sodium bisulphate Potassium cyanide (70 per cent.) Sodium carbonate 200 grammes. 500 1003 Again, in 2 litres of water : Copper acetate Neutral zinc chloride . 125 grammes. 100 Add the second fluid to the first. Avoid ammonia. GILDING. 219 For zinc, Dissolve in 20 litres of water : Sodium bisulphate 70D grammes. Potassium cyanide (70 per cent.) . . . 1000 Again, in 5 litres of water : Copper acetate 350 grammes. Zinc chloride 350 Ammonia 400 ,, Add the second fluid to the first, and filter. Use a brass anode ; add more zinc to produce a greenish deposit, more copper for a redder one. Too weak a current produces a red deposit, too strong a current a white or blueish-white deposit. Bemedy by altering the battery-power, or using a copper or zinc anode. The density of the bath may be allowed to vary from 5 to 12 Baume without injury. Gilding (Roseleur). Hot for small things, cold for large ones. JBath of the double cyanide of gold and potassium. Cold. Distilled water 10 litres. Pure potassium cyanide 200 grammes. Virgin gold 100 The gold transformed into chloride is dissolved in 2 litres of water, the cyanide in 8 litres ; the two fluids are mixed, a change of colour takes place, and the mixture is boiled for half an hour. The richness of the bath is kept up by adding as required equal weights of pure potassium, cyanide and chloride of gold, a few grammes at a time. If the bath be too rich in gold, the deposit is blackish or dark red. If there is too much cyanide, the gilding goes on slowly, and the deposit is grey. The anode should be entirely immersed in the bath, suspended by platinum wire, and should be taken out when the bath is not working. Hot gilding. It is better to first copper objects made of zinc, tin, lead, antimony, and alloys of these metals. The following are the formulae for other metals, the quantities being for 10 litres of distilled water : Silver, copper, Cast and and alloys wrought iron, rich in copper. steel. grammes. grammes. Crystallised sodium phosphate 600 500 Sodium bisulphate . . . .100 125 Pure potassium cyanide 10 5 Virgin gold transformed into chloride . 10 10 220 APPLICATIONS OF ELECTRICITY. Dissolve the sodium phosphate in 8 litres of hot water, allow it to cool ; dissolve the chloride of gold in 1 litre of water, mix the second fluid slowly with the first ; dissolve the cyanide and bisulphate in one litre of water, and add the third solution to the other two. The temperature of the bath may vary from 50^ to 80 0. A few minutes will produce thick enough gilding. A platinum anode is used ; if it only just dips into the bath pale gilding is produced, if immersed very deeply the gilding is red. The bath may be refreshed by successive ad- ditions of chloride of gold and cyanide of potassium ; but after long service it gives red or green gilding, according to whether it has been most used for gilding copper or silver. It is better to renew the bath than to refresh it. Green, white, red, and pink gilding, These different colours are obtained by mixed baths and currents of different strengths. Green is obtained by adding a very dilute solution of silver nitrate to the gold bath, red with a copper bath, and pink with a mixture of gold, silver, and copper baths. Rate of deposition (Delval).- About 30 centigrammes per hour per square decimetre may be deposited from a bath containing 1 gr. of gold per litre, but this mean rate may be very much varied without harm. Silvering. A good bath for amateurs contains 10 gr. of silver per litre, and is thus prepared: dissolve 150 gr. of silver nitrate (which contains 100 gr. of pure silver) in 10 litres of water, add 250 gr. of pure potassium cyanide, stir till all is dissolved, and filter. Silvering is generally done cold, except for very small objects. Iron, steel, zinc, lead, and tin (previously coppered) are best silvered hot. The articles after cleaning are passed through a solution of nitrate of binoxide of mercury, and are constantly agitated in the bath. When the current is too strong the articles become grey, turn black, and disengage gas. Use a platinum or silver anode in cold baths. Old baths are better than new. Baths may be aged artificially by adding 1 or 2 milligrammes of liquid ammonia. Silver baths are refreshed by adding equal parts of the silver salt and potassium cyanide. If the anode turns black the bath is poor in cyanide, if it turns white there is excess of cyanide ; the deposition is then rapid, but does not adhere. When all is going on well and regularly the anode turns grey when the current is passing, and becomes white again when it is interrupted. The density of the bath may vary without injury between 5 and 15 Baume. Silver plating of forks and spoons (Roselcur}. 1st. Boil them for a few moments in a solution of 1 kg. caustic potash in 10 litres of water, and wash in cold water. SILVERING. 221 2nd. Pickle in water with one-tenth (by weight) of sulphuric acid. 3rd. Immerse for a few seconds in the following mixture : Yellow nitric acid at 36 10 kg. Common salt 200 gr. Calcined tallow 200 Wash quickly in plenty of water. 4th. Pass quickly through the following mixture : Yellow nitric acid at 36 10 litres. Sulphuric acid at 60 10 Common salt 400 gr. Wash quickly in perfectly clean water. 5th. Pass them through the following mixture until they are quite white (an immersion of a few seconds will do). Water 10 litres. titrate of binoxide of mercury 100 gr. Just enough sulphuric acid to dissolve the binoxide. Wash in cold water. 6th. Place them in the bath, use a weak current; when sufficient silver has been deposited stop the current ; allow them to remain for a few minutes longer in the bath, remove them, wash first in water, then in very dilute sulphuric acid; scratch -brush and burnish if necessary. The weight of silver deposited is 72, 84, or 100 grammes per dozen. The process lasts four hours, but a better quality of deposit is obtained by working more slowly. DEPOSIT PER HOUR PER SQUARE METRE. IN GRAMMES. NATURE OF THE DEPOSIT. STRENGTH OF CURRENT IN AMPERES PER SQUARE METRE. 140 200 220 Pin-holes. Good deposit. Deposit. 35 50 55 M. Delval gives, as a mean rate for a bath containing 30 gr. of silver per litre, 2 gr. per hour per square decimetre. This agrees with the above figures. Nickeling (A. Gaiffe). Nickel is principally deposited on copper, bronze, German silver, wrought and cast iron, and steel. 222 APPLICATIONS OF ELECTRICITY. Cleaning from grease and pickling. (See Fifth Part.) Battery. The handiest for amateurs is the bichromate bottle battery. The current is regulated by immersing the zinc more or less. Bath. Saturate hot distilled water with the double sulphate of nickel and ammonium free from oxides of alkaline, and alkaline earthy metals. The solution is : Double sulphate of nickel and ammonium . . 1 part by weight. Distilled water 10 Filter when cold. Cell, and putting in the bath. The best cells are of glass, porcelain, or earthenware ; or of wood lined with waterproof varnish. Use a plate of nickel as a soluble anode, and suspend the articles by nickeled hooks. The objects are immersed for a moment in a bath of the same solution which has been used for pickling, washed quickly in common water, and then in distilled water, and quickly placed in the bath. Hate of deposit. M. Delval gives, as a mean rate for a bath containing 10 gr. of nickel per litre, T8 gr. per hour per square centi- metre. This rate must not be much varied in order to get a good deposit in a bath of this strength. Management of the current and time of the process. If the current be too strong the nickel is deposited in a black or grey powder ; one or two hours is long enough for a coating of mean thickness, five or six for a very thick coating. Polishing. Eub rapidly backwards and forwards on a strip of list fastened to a nail at one end and held by the other in the left hand ; apply polishing powder and water to the list ; hollow parts must be polished with pledgets of cloth fixed to handles. The polished objects are washed with water to remove the polishing powder and cloth fluff. In order to obtain a good polish the objects should be well polished before nickeling. THERMO-ELECTRICITY. It was discovered by Seebeck in 1821, that if the junction of two dissimilar metals be heated an e. m. f. is set up at the juncture. This e. m. f. is called thermo-electromotive force. The general group of electric phenomena produced by heating or cooling of junctions of dissimilar metals, and the passage of currents through such junctures, are known as thermo-electric phenomena. The thermo-electromotive force is constant when the temperature is constant and between certain limits, and for any pair of metals is proportional to the excess of temperature at the junction THERMO-ELECTRICITY. 223 over the temperature of the rest of the circuit. The total thermo- electromotive force developed in any circuit is the algebraic sum of all the e. m. fs. developed at the different junctures. The thermo-electric power of two metals is the magnitude of the e. m. f . produced when there is 1 C. difference, of temperature between the junctures. The following table gives the thermo-electric powers in microvolts per degree C. of different metals, lead being taken as the standard. Bismuth being the most thermo-positive, and antimony the most thermo- negative metal, the current produced by a bismuth- antimony couple passes from bismuth to antimony across the juncture, and from antimony to bismuth through the external circuit. TABLE OF THERMO-ELECTRIC POWER OF DIFFERENT METALS WITH RESPECT TO LEAD, AT A MEAN TEMPERATURE OF 20 C. (Matthiessen) . (The electromotive forces are expressed in microvolts per degree centigrade.) Commercial bismuth wire . Pure bismuth wire Crystallised bismutb in di- rection of axis . Crystallised bismutb normal to the axis .... Cobalt +22 German silver Mercury LEAD .... Tin .... Commercial copper Platinum Gold .... Impurities have considerable influence on the thermo-electric power of metals ; some alloys and some sulphides, such as galena (zinc sulphide) , have a very high thermo-electric power. Thermo-electric inversion. Neutral point. The thermo-electric power of metals is a function of the mean temperature of the junctions as well as of the difference of temperature between the junctions. The following figure enables the variations of this thermo- electric power to be studied. The abscissae represent the mean tempera- tures in degrees C., and the ordinates the e. m. f. in microvolts. The distance between the two lines of two given metals at a given mean temperature shows the thermo-electric power of the two metals at that mean temperature. The lines are plotted, taking lead as a standard. + 97 + 89- + 65 + 45 Pure antimony wire . Pure silver .... Pure zinc .... Electro-deposited copper . Commercial antimony wire Arsenic ..... - 2'8 - 37 - 3-8 - 6- - 13 '56 + 22 + 1175 + -418 1 1 *9 - 1-2 Pianoforte wire . Crystallised ant.mouy, hi direction of axis Crystallised antimony nor- mal to axis. Red phosphorus . Tellurium Selenium - 17-5 - 22-6 - 26-4 - 297 -502 -807 224 APPLICATIONS OF ELECTRICITY. The point where the lines of metals cut each other is the neutral point. At the corresponding temperature the thermo-electric powers of the two metals are equal. Beyond the neutral point the thermo- electromotive force changes its sign ; thus the neutral point is also the point of reversal. Tait has shown that between and 300 C. these lines are sensibly straight. The calcu- lation of thermo -electromotive forces is thus reduced to the calculation of the areas of triangles or trapeziums. Let m be the distance in microvolts which separates the line of two metals at the mean temperature, t\-t- 2 the difference of temperature in centigrade degrees, the e. m. f . would 50 100 150 200 ZM* 300 350 *00* Degrees Centigrade. Fig. 44. Diagram of Thermo-electric Powers. 500 550 800 then be m (t\-t- Therefore, if the mean temperature is that of the neutral point or point of inversion, there will be no current produced, because m is nothing. This enables the neutral point of different metals to be determined. Thus we see that it is not sufficient to maintain a great difference of temperatures between the junctures to get a large e. m. f. It is also necessary to make a judicious choice of the metals and the mean temperatures, so as to keep as far as possible from the neutral point. Formula for calculating thermo-electric power- This formula, due to Tait, is a result of the graphic representation above. It is based on the supposition that the lines referring to the THERMO-ELECTRICITY. 225 different metals are straight lines. This hypothesis has been verified experimentally between and 400. Let hi and k. 2 be the tangents of the inclinations of the lines of the two metals considered in relation to lead, t\ and t 2 the neutral point of each in relation to lead, t m the mean temperature of the two junctions, the mean ordinate m or thermo-electric power is given by the formula : The total e. m. f . E* is then : TABLE FOR CALCULATING THERMO-ELECTRIC POWERS. NEUTRAL POINT METALS. WITH RESPECT TO LEAD IN CENTIGRADE TANGENT OF THE ANGLE WITH LEAD fc. DEGREES. Cadmium - 69 - -0364 Zinc - 32 - -0289 Silver - 115 - '0146 Copper - 68 - '0124 Brass -1- 27 - '0056 Lead Aluminium - 113 + '0026 Tin + 45 + '0037 German silver - 314 + -0251 Palladium - 181 + -0311 Iron + 357 + '042 Bismuth-copper couple (Gauyairi) has been u?cd as a standard in measurements of e. m. f. One of the junctions is at 0% the other at 100 : pile. One of the metals is German silver, the other an alloy of antimony and zinc. Each element in regular work gives an e. m. f . of volts and an internal resistance of -^ ohm. The battery of 20 elements in series has therefore an e. m. f. of 1*25 volts and an internal resistance of '5 ohm. C' I mil O lid's pile. Iron and an alloy of bismuth and antimony cast 011 the iron. A battery of 6,000 elements in series heated by coke P 226 APPLICATIONS OF ELECTRICITY. produced a e. m. f. of 109 volts, and had an internal resistance of 15-5 ohms. Thermo-electric batteries have as yet only been applied to the measurement of small differences of temperature and as standards of e. m. f. As yet the best of them transform less than one per cent, of the heat energy given out by the source of heat. HEATING ACTION OF CURRENTS. When a current passes through a conductor, it heats it. The quantity of heat produced by the passage of a current is given by the formula : ' H, quantity of heat produced in calories (g.-d.). B, resistance of conductor in ohms. C, strength of current in amperes. t, time during which the current has passed in seconds. J, mechanical equivalent of heat. P2~R, H = -^ calories (g.-d.). Minimum diameter for wires depends on the conduc- tivity of the wire, its shape, the facilities it has for cooling, and the use to which it is applied. Conductors of platinum wire, used to light spirit lamps or gas, small incandescent lamps, etc., ought to become red-hot, but not to melt. The safety catches of cables for electric light leads ought to melt and automatically interrupt the circuit as soon as the strength of the current on the branch becomes double or triple that which it ought to be normally. The wires of dynamos and covered conductors ought never to reach the temperature at which the insulation would be damaged. In machines wound with wire not more than 2 millimetres in diameter, it is safe to allow a current to pass of 5 to 6 amperes per square milli- metre, and only 3 amperes per square millimetre for wire of 5 millimetres in diameter. For lead-covered copper conductors, where the cooling is slow, not more than 2 amperes per square millimetre should be passed for a conductivity of 80 to 90 per cent., and currents less than 20 amperes. L.OSS Of energy in Conductors. The heat produced is calculated by the last formula. In all cases of transmission of energy to HEATING EFFECTS OF CURRENTS. 00' a distance, it is advantageous to diminish this loss by reducing the resis- tance of the conductors as much as possible. In the following table the value of the energy wasted in the wire in the form of heat is given for currents from 1 to 100 amperes, and a resistance of 1 ohm, in calories (g.-d.), kilogramme tres per second, and horse -power. STRENGTH OF CURRENT IN AMPERES. CALORIES (G.-D.) PER SECOND. K ILOGRAMMETRES PER SECOND. HORSE-POWER. 1 24 '102 '013 2 96 '408 054 5 6-01 2-548 034 10 24-03 ! . 10-2 134 20 96-12 40-8 536 30 216-2 917 1-223 40 384-48 163-1 2-144 50 601 255 3'4 60 865 367 4-892 70 1177 499 6-653 80 1538 652 8-576 90 19 18 826 11-C07 ICO 2403 1019 13-59 From this table, when the current is known, and the loss of current by heating of the conductor, which can be allowed, is known, the resis- tance, and hence the diameter, of the conductor can be calculated. Heating of a conductor traversed by a current (Or. Forbes}. Let C be the strength of the current which heats the con- ductor at a certain temperature, and D the diameter of this conductor. To heat another conductor placed under the same conditions to the same temperature C and D, it must be varied so as to satisfy the equation : a being a constant which depends on the temperature of the wire. Heating of coils of the same dimensions wound with wire of different diameters (&. Forbes). The length of wire wound on coils of the same dimensions is inversely proportional to the square of the diameter of the wire, and the resistance is inversely proportional to the 4th power of the diameter. In order that the two wires, under these circumstances, may be heated to the sam 228 APPLICATIONS OF ELECTRICITY. temperature, the strength of the current C and the diameter of the wire D must satisfy the equation : a being a constant which depends on the temperature of the wire, Heating of two similar coils by the passage of a current (G. Forbes). Let C be the strength of the current passed through a given coil at a given temperature, C' the strength of the current which passes through a second similar coil, of which the linear dimen- sions are n times those of the first, and diameter of the wire n times that of the first wire, for the same temperature we have the following equation : C' rz n f C. This law, deduced by equating the heat produced by the current and the heat lost by the coil, has been confirmed by experiment. ELECTEIC LIGHT. Electrical energy used for electric lighting being now almost exclu- sively furnished by magneto and dynamo -electric machines, it is im- possible to go into this important application of the heating power of currents until after having spoken of the mechanical generators of elec- tricity. (See page 260.) MECHANICAL, GENERATORS OF EJLECTRI- CITY. We will not here discuss instruments based upon electrostatic actions. All mechanical generators of electricity based upon electro-magnetic action are composed of two parts, the field magnet and the armature. The field magnet produces the magnetic or galvanic field necessary for the production of the current which is produced in the armature, which is called an induced current. Every displacement of the armature relative to the field magnet produces an induced current. In all magneto and dynamo-machines this relative displacement is produced by a mechanical movement. The electrical energy developed is equivalent to the work expended in this movement. Induction coils, for example, are instru- ments in which the relative displacement of the field and the armature is produced without mechanical movement. They act as transformers, and MECHANICAL GENERATORS. 229 are not mechanical generators of electricity, although the same principle underlies the action both of the coil and of the machines. Work expended. The work expended in driving a mecha- nical generator of electricity is measured either by a transmission dynamometer or by diagrams taken from the prime mover, taking into account the loss of work due to the friction in the prime mover itself. The work expended in driving a mechanical generator of electricity determines the choice of the prime mover which is to drive it. The power of electric generators varies from a few hundred kilogrammetres up to 400 horse -power. Total electrical energy produced. Let E be the e. m. f. developed by a generator, and C the strength of the current in its normal conditions of working. The total electrical energy Wt produced is : CE "Wt kgm. per second ; y "oi or CE r. CE v W t -r- - horse-power =. chevaux-vapeur. 74:0 lob The difference between the total electrical energy produced and the work expended represents losses due to friction, passive resistances, and complex secondary reactions, which are produced between the field magnets and the armature of the generators. Available electrical energy. Let E a be the difference of potential at the terminals of the machines, i.e. between the ends of the external circuit, and C the strength of the current in the external circuit. The available energy W a is : W a = -r kgm. per second. 98'1 CE a CE a , VV a rr:- horse -power =. --chevaux-vapeur. 74o 9*81 Heating of the machine. The difference between Wt and W a , expressed in kilogrammetres or horse-power, represents the work transformed into heat in the machine, or its heating. This being lost work, it is advantageous to diminish it as much as possible, which may be done by reducing the internal resistance of the machine in relation to the resistance of the external circuit. 230 APPLICATIONS OF ELECTRICITY. When the internal resistance R; of the machine is known, its heating is calculated by the formula : Heating =.--^ kgm. per second =: horse-power ; y'ol 746 C2R or, Heating calories (kg.-d.) per second. Relation between the external and internal resistance. Calling H e the external resistance, and Rj the internal resistance, then tt - El R ' Ba- - or T , when the machines are under bad working conditions ; ~R e = 10 to 40 Ri, when the machines are under good working conditions. Classification. The principal characteristics of electrical generators which may be used as bases for classification are (a) the nature of the currents produced, () the nature of the field magnet, (c) the form of armature. As well as these principal characteristics, other secondary ones exist, such as the nature of the moving part, the power of the machine, the presence or absence of iron in the armature, etc. We will only consider here the first class of characteristics. a. THE NATURE OF THE CURRENTS PRODUCED. Induced currents are always alternating by their very nature ;* some machines re-reverse them, others make them sensibly continuous ; hence three classes of machines may be formed, according ta the character of the currents which they give. (1) Alternating machines. The currents produced are collected in the same condition as the coils produce them, and are thus reversed as often as 30,000 times per minute. (2) He-reversed machines. A commutator re-reverses the currents de- veloped in the armature each time that they are about to change sign. The current then becomes zero at each commutation. The type is the Siemens H armature machine. (3) Continuous current machines. The armatures which are split up into * Except in those machines which are very wrongly called uni-polar, which have not yet come into practical use ; they may be considered as practically continuous. MODES OF EXCITATION. 231 sections are joined to a commutator, which produces a great number of partial commutations. The strength of the current is, as it were, sinuous, and becomes more and more closely a straight line or steady current as the splitting up of the armature is greater. They may be considered as practically continuous. If a telephone, however, be placed between the terminals of the machine, it will show by its vibrations that the current is not altogether steady. b. NATURE OF THE FIELD MAGNETS. This character allows the machines to be divided into two classes : (1) Magneto-electric machines. The field magnet is a permanent magnet. (2) Dynamo-electric machines. The field magnet is an electro -magnet. c. FORM OF THE ARMATURE. The following forms may be dis- tinguished : (1) Ring : Elias Pacinotti, Gramme, Schuckert, Brush, etc. (2) Drum : Siemens, Edison, etc. (3) Pole : Lontin, Niaudet, "Wallace -Farmer, etc. (4) Disc : The " Arago " machine, Ferranti-Thomson. The armature, according to its shape, is called coil, ring, drum, etc. Modes of excitation of dynamo-electric ma- chines. To excite a machine is to supply it with the electrical energy necessary to maintain the magnetism of the field magnets. These are the methods employed up to the present time : Separate excitation. The field magnets are supplied by a distinct current furnished by a separate machine, which is called the exciting machine. The exciting machine may excite many dynamos at the same time, which produces a certain homogeneity in their magnetic fields, and consequently in their production and in their power. Excitation in circuit. The current produced by the machine itself passes through the field magnets, and keeps up their magnetism. Such machines are called series dynamos. Shunt excitation. The field magnets are arranged as a shunt between the brushes. The current produced by the armature is divided between the external circuit and the field magnet circuit (indicated by Wheatstone). Such machines are called shunt dynamos. Double circuit excitation (indicated for the first time by Brush). The field magnets are wound with two wires, one receiving the current from a separate machine, or arranged as a shunt between the brushes ; the other wire being in the main circuit. Applied by M. Marcel Deprez to his system of distribution. This method enables the production of electrical energy to be made more or less proportional to the consumption 232 APPLICATIONS OF ELECTRICITY. in the external circuit. A great number of such arrangements may be invented. Nature Of the machines. In normal conditions the working of the machine develops an e. m. f. of E, and gives out a current of strength C. As a remnant of the old misleading nomenclature, machines are still sometimes divided into two classes. Tension machines, those in which E is very large ; and quantity machines, those in which C is very large. But now machines are constructed which run through the whole scale of e. m. fs. from a fraction of a volt up to more than 3,000 volts, and the whole series of current strengths from a few milliamperes up to 1,000 amperes and more. Field, magnets. The field magnets ought to be as powerful and as massive as possible, in order to keep the magnetic field constant in spite of the rotation of the armature, and so as not to reach the point of magnetic saturation too soon. The field magnets ought to be made of as soft iron as possible, because its point of saturation is higher, and the poles ought to be as close to the armature as the design of the machine allows. Points and edges should be avoided. Care must be taken that the cast-iron bed plate of the machine does not disturb the distribution of the magnetic field by setting up a sort of magnetic short circuit between the poles. Armatures. Internal iron in the armature is of advantage so far as it concentrates the magnetic field, but difficulties of construction are found if it is to be kept fixed so as not to lose the work du to its changes of magnetisation when it turns with the armature, as for example in the gramme ring. A revolving armature ought to be of as soft iron as possible, and split up into plates, wires, etc. , separated by varnish, asbestos, paper, or thin leaves of mica so as to hinder the development of Foucault currents. Also, to avoid heating, abrupt changes of polarity of the armature should be avoided. The winding should be arranged so as to reduce to a minimum those parts of the wire which do not come under the direct and useful action of the magnetic field. Wire of the highest conductivity possible should be chosen. (At least 96 per cent, of con- ductivity.) When an armature has poles the wire ought to be wound as near these poles as possible, because it is at this point where the variations are most sensible. The armature ought to be easily ventilated, and the coils perfectly insulated with substances which are not easily melted, such as asbestos, mica, etc. CONSTRUCTION OF MACHINES. 233 Conditions to be aimed at in the construction Of a powerful machine. The current developed in a conductor which is passing through a magnetic field is greater the more lines of force the conductor cuts through per unit of time. Consequently, to build a powerful machine it is necessary, first, to give the conductor a high velocity of translation; secondly, to move it in an intense magnetic field ; thirdly, to have as many turns as possible on the armature ; fourthly, to diminish its electrical resistance as much as possible. The first condition is limited by mechanical considerations. In practice, 20 to 25 metres per second is rarely exceeded for the middle part of the armature. The second condition explains the use of dynamo -electric machines, which give an intense magnetic field, and which for the same speed require fewer turns of wire on the coil than magneto -electric machines in order to develop the same e. m. f . It is thus possible to increase the thickness of the wire and diminish its length, and thus decrease the internal resistance of the machine. The advantage obtained more than com- pensates for the additional expenditure of energy in exciting the field magnets. The third condition shows that the number of turns of wire must be greater as the e. m. f. has to be greater, which forces us to diminish the diameter of the wire, so that it may occupy the same space. It is thus not because the machines have a high resistance, as is sometimes said, that they have a high e. m. f., but because it is impossible to put a large number of turns of wire into a given space without using fine wire, and thus introducing a high resistance. If high resistance were a necessary and sufficient condition for high e. m. f., coils might be made of German silver or platinum wire ; but, in practice, copper wire of the highest con- ductivity is always selected. The fourth condition to be fulfilled further justifies this choice, because Ohm's law shows that the strength of a current diminishes when the total resistance of a circuit increases. Influence' of the thickness of the wire. Other things being equal, the e. m. f. of the machine does not increase in proportion to the 'dimi- nution of the section of the wire, as some authors have considered. If a given machine, for example, develops 200 volts with a wire two millimetres in diameter, it would not necessarily develop 800 volts with a wire one millimetre in diameter, because the thickness of the insulating coating is greater in relation to the diameter of the wire as the wire is thinner. The second machine would thus not contain four times as many turns as the first, either on the armature or on the field magnets. The e. m. f . would dimmish then for two reasons : because the magnetic field would be less intense, and the number of turns of wire on the armature less than the theoretical proportionality requires. Lack of wire in the field magnets diminishes the e. m. f. of a given machine as 234 APPLICATIONS OF ELECTRICITY. the strength of the current given out increases. This fact is a result of the reciprocal reactions of the magnetic and galvanic fields. A magnetic field costs the less to produce, as the electro -magnets are of larger dimensions (Edison).- This is a consequence of the general laws of electro-magnets. Influence of speed on the work absorbed. With a constant magnetic field the work absorbed is sensibly proportional to the square of the speed of rotation, and the e. m. f . proportional to the speed, when the external circuit remains constant. In the case of series or shunt dynamo machines, the phenomena is much more complicated, because of the progressive increase of strength of the field with the increase of the current. Characteristic (Marcel Deprez).The curve given by the relation between the e. m. f. of a given dynamo revolving at a given speed and the strength of the current which it produces when the re- sistance of the circuit is varied. To.construct the curve, the field magnets are separately excited for each current strength, C corresponding to an e. m. f . E. The current strengths are made abscissas, and the e. m. fs. ordinates. Cabanellas has justly observed that the curve traced by this method is wrong in all cases in which the magnetic field is modified by the electric field. The curve thus obtained varies with the dimensions of the machine and the relation of its different parts. Generally it is more or less parabolic in form, and is very rarely approximately a straight line. Critical speed. The speed at which on a given circuit a dynamo begins to give out a sensible current : a very slight decrease of speed practically reduces the current strength to zero, whilst a very slight increase in speed produces a very large increase of current strength. This critical speed has been made the basis of some systems of regulating dynamos and of governing motors. Lead Of the brushes (A. Breguet).In magneto -electric machines, or separately -excited dynamos acting as generators of elec- tricity, the angular lead of the brushes should increase with the speed of rotation. For series machines the brushes require but a small lead so long as the field magnets are not saturated ; and after saturation, espe- cially with weak field magnets, the lead may be as much as 70 3 . In dynamo -electric machines acting as motors, the lead should be against the direction of the movement of rotation. The angle of the lead ought to be greater as the magnetic field is weaker and the current stronger. These facts are consequences of the reciprocal action of the SIZE OF WIRE FOR MACHINES. 235 magnetic and galvanic fields of the field magnets and the armature. The lead necessary for any given set of circumstances and the change of lead necessary on their variation vary very much with different types of dynamos, some requiring much more change than others. It is, however, well always to have some simple means of changing the lead whilst the machine is running, and to shift the lead whenever much sparking is observed at the brushes until the sparking is reduced to a minimum. Action of the iron ring: in Gramme machines (A. Breguef). (1) The retardation of magnetisation and demagnetisation makes it necessary to give the brushes a lead in the direction of the rotation of not more than 10 for the highest speeds. (2) The presence of the ring increases the intensity of the field and reduces its distortion, and consequently the lead of the brushes. The soft iron armature of the Gramme machine reinforces the magnetic field in the part in which the wires of the movable circuit move, and protects the internal parts of the coils from the normal action of the lines of force of the field by acting as a magnetic screen. Size of wire for dynamo-electric machines. In the Gramme machines built by Sautter and Lemonnier the following proportions are used : TkTTiT A TT Q f rYPES JJJiil A1LO. M. AG. CT. CQ. DQ. Armature. Diameter of wire in millimetres 1-2 1-8 2-8 3-65 4-3 Strength, of current given out Strength of current passing through the 13-5 24-5 48 65' 70 wire 675 12-25 24 32-5 35 Section in square millimetres . Current strength per square millimetre 1-13 6 254 4-8 6-16 3-9 10-46 3-1 14-52 2-4 Field Magnets. Diameter of wire .... 1-8 3'4 3-4 3-4 3-8 Section in square millimetres Strength of current .... 2'54 675 9-03 12-25 9-08 48 9-08 65 11-34 17-5 Strength of current per square milli mtre 2'6 1'3 5-3 7-2 1-6 In the case of the armature the law is very clear, so many fewer 236 APPLICATIONS OF ELECTRICITY. amperes per square millimetre of section must be passed as the wire be- comes larger, because with large wire the cooling is slower. For field magnets the figures va.ry much with the method of connection. Maintenance of the brushes and commutators. The brushes should press moderately on the commutators, and their lead be so arranged as to give the least sparking ; that is to say, contact of the brush with the armature should be opposite the neutral point. The brushes should be pushed forward slightly as they wear. If some of the wires get fused together by sparks, they must be care- fully separated. If the wires become detached and turned up, they must be bent into their proper shape with a pair of flat- jawed pincers. They should be cleaned with alcohol from time to time. The commutators may be lubricated with a piece of rag very slightly moistened with oil ; but care must be taken that not too much oil be applied. Sometimes they are rubbed with mercury, but this is a very bad practice. The brushes should be smoothed from time to time by rubbing them with emery-paper. Never break the circuit by throwing off the brushes when the machine is running. The machine ought always to pull on the brushes ; that is the simple practical way of determining which way the machine ought to turn. Best working conditions for machines. There is not space to give here a description of all the different magneto and dynamo -electric machines which are now used in practice ; we can only point out the best conditions of working of those most in use, or, at least, of those of which we have been able to collect the elements, but throwing the whole responsibility of the figures themselves on to the in- ventors or experimenters. The reader will rather find here useful infor- mation on the mean conditions of working, than on the relative value of different machines. Machines having been, up to the present time, for the most part specially constructed for electric lighting, a good deal of information on dynamos will be found in that part of the present work which deals with that subject. CONTINUOUS CURBENT MACHINES. A Gramme machine (Breguet's construction). Series dynamo : Resistance of the ring cold ... '47 ohm. ,, field magnets coll . . '37 Total resistance cold . . . . , 1'14 hot 1-2 CONTINUOUS CURRENT MACHINES. 237 Normal speed Strength of current Electromotive force Difference of potential at terminals Field magnets saturated at . 900 revs, per minute. . 25 to 30 amperes. . 80 volts. . 55 volts. 18 amperes. Heinrich's machine. U-shaped Gramme-ring dynamo. Experiments made on the type for 3 lamps in circuit (arc ; carbons 13 mm. in diameter) gave the following results (Kempe, Preece, and StroK) : Total resistance of machine .... 1'83 ohms. Resistance of ring ...... '85 ,, Electromotive force 130 to 150 volts. Strength of current 33 to 38 amperes. Revolutions per minute 850 Mean diameter of ring . . . . . 20 centimetres. Against carbon resistances the same machine gave the following results : NUMBER OF REVOLUTIONS. EXTERNAL RESISTANCE. STRENGTH OP CURRENT. ELECTROMOTIVE FOKCE. WORK IN HORSE-POWER (CALCULATED). 7CO 2'1 36'4 143-3 7 800 2-6 337 149-3 6-5 900 4'3 26-3 160 5-5 900 7-3 )57 143-3 3 1000 7'3 177 161-6 4 Oiilcher machine. Six-lamp machine, feeding six arc lamps in parallel arc at speed of 640 revolutions ; field magnets in the circuit : Resistance of field magnets ring . Total resistance . Difference of potential at terminals at brushes Total strength of current . Hot after Cold running some hours. (16 C.) (31 C.) 126 ohm. *129 ohm. 133 '136 259 '265 60 volts. 70-22 80 amperes. 238 APPLICATIONS OF ELECTRICITY. Work absorbed by generator . ,, external circuit . friction Total work absorbed . Hot after running some hours. (31 C.) 2'86 horse-power. 7'13 *5 10-49 The machine converts 68 -2 per cent, of the work put into it into elec- trical energy available in the external circuit, and produces 75 carcels per horse-power at an angle of about 35 (Gulcher). SCHUCKEKT MACHINE (F. Upperiborn). NAME OF TYPE. STRENGTH OF CDRBENT IN AMPERES. VOLTS AT TERMINALS. NUMBER OF TURNS PER MINUTE. WORK ABSORBED IN HORSE- POWER. MONOPHOTE. ELi . . . 7 50 1,300 1 ELi . . . 20 50 1,100 2 EL 2 36 50 1,000 EL 3 . . . 50 50 950 5'5 POLYPHOTE AND TRANSMISSION OF POWER. TLi 2 lamps 8 100 1,200 2 TLj 3 8 150 1,150 3 TL 2 a 4 . 8 200 1,100 4 TL 5 6 8 300 1.000 5'5 TL 4 9 , 8 450 950 8 TL e 14 8 750 930 12 INCANDESCENT (coiapound-dynamos) JIJ 5 lamps . 3-6 110 1.500 1 JLj 12 JL 3 18 JLaa 25 8*6 13 18 110 110 110 1,300 1,200 1,100 2 3 4-3 JL< 35 25-2 110 1,000 6 JL' 4 50 36 110 900 8-5 JL 5 72 52 110 750 12 JL 6 40 288 110 600 60 SIEMENS MACHINES. 239 Schuckert electroplating machines. -The nickel- plating machines (shunt dynamos) give 4 volts at the terminals, and from 90 to 1,400 amperes, absorbing from 1 to 12 horse-power. The copper- plating machines give 2 volts at the terminals, and from 200 to 2,800 amperes absorbing the same power. The 200 -ampere machine deposits 225 gr. of nickel per hour on a surface of 2-') sq. metres. The 200 ampere copper-plating machine deposits 816 gr. of copper per hour on a surface of 83 sq. decimetres, by arranging four baths in series. SIEMENS MACHINES (1883). NUMBER OF o> .2 h +3 ^ C H WATTS. .3 L ||| , i& f "8 M p< & -"in 2 H 8g 2'o.g .s ^ TYPE OF l?f 1 | 1! || fill ii MACHINE. fll ft !! sl II |1 3 X |1| f"S p 1 I 1 I 1 1* |.a i|f M (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) S JDS 12 12 248 796 1,164 68 19-5 41 9-5 SD7 25x2 308 370 3,316 3,994 83 51-25 64 13-75 SD7 40 328 233 2,653 3,214 82 64 41 10-75 SD2 30x2 536 319 3,980 4,835 82 119 33'4 925 SD2 60 526 326 3,980 4,832 82 118-5 33-5 9-5 SD1 60x2 803 532 7,959 9,294 85 264 30-1 10-25 SD1 DSDCO 50x3 150x2 615 2,080 1,200 2,562 9,949 1 11,764 19,890 24,532 84-5 91-7 274 389 37-7 51 13 1075 Bl . 400 1,654 2,665 26,532 30,851 86 368 72 13-75 W3. 60 193 456 3,979 4,868 81-7 103 38-5 18-25 D5 . 97 143 7'75 W6. 90 335 595 5,969 7,240 82 141 425 205 D6 . 121 220 8-15 W2. 120 630 633 7,959 9,523 83-5 163 49 22 D6 . 107 194 9-25 Wl. 200 1,357 1,257 13,266 16,034 827 237 56 24 D7 . llu 94 -. . __ 1075 W5. 400 1,034 1,496 24,030 26,777 20 227 106 28-9 D7 . 117 HO 1115 WO. 500 1,357 2,375 33,165 37,460 88 384 86-5 32-5 D2 . 177 206 9-5 240 APPLICATIONS OF ELECTRICITY. Continuous current Siemens machines. Normal working conditions : NUMBER OP TlPE. REVOLUTIONS PER VOLTS. AMPERES. MIMUTE. DO 750 95 108 Di 450 84 70 D* 1200 50 22 D6 1100 67 20 D7A 1250 129 20 D?B 1000 62 37 D8A 800 336 8'8 DB 1UOO 224 20 DSC 6i 78 37 Edison, machine* Continuous current shunt machine, giving 110 volts at the terminals and current strength proportional to the number of A lamps arranged in parallel arc. They are built at Paris (1882) of the following types : " I I w W en . s | J S . 3 A EL Eg i | 1 s S AH w w j i E (* o i y 2 rt fe o o < 23 i ji H o UMBER VOLUTK i! |l 2 o 05 - II W a * w 1 * !l 1 E 3 *fl p= H g M H fc (3 i E 15 108-84 226-75 335-5 76'2 127 2200 36 90 3 Z 60 136-05 859-38 1233 152-4 254 1200 138 38 10 L 150 226-75 1673-41 2580 228-6 355 900 071 19 177 K 250 317-45 2428-49 3814 900 032 13 34-4 c 1200 6031-55 i 13151 28707 350 0038 25 123 Edison machine (1881). Type for 1,000 lamps of 16 candle- power, or A lamps. Armature. 108 bars of copper, 2,000 iron discs forming the core : diameter, 71 centimetres ; length, 1-5 metres; surf ace velocity, 11 -3 metres per second ; resistance of the armature, "0005 ohm. field Magnets. 12 bars of iron 2-4 metres long, and 12 coils in two EDISON-HOPKINSON MACHINE. 241 parallel circuits, of which the resistance is 21 ohms, arranged as a shunt between the brushes. The driving engine is 128 horse-power nominal. I :P ' OE Trr,, foot-pounds per second, I'oO Let W be the electrical work produced by the motor, CE' CE' , JHJF gm8 ' Per second= 746" h ' p - foot-pounds per second, Let W" be the electrical energy expended in heating the circuit (machines and line) : 02 (R+R'-f R") , C2 (R-fR'-fR" 9-81 kgms> per Sec nd ~ ~ 746 ~ h -P- _Q2(R-f R' ^ -- rrr - foot-pounds per second. "W' "F 1 ' Electrical efficiency = . W Jii Or the efficiency is independent of the resistance, and hence of the TRANSMISSION OF ENERGY. 253 distance to which the energy is transmitted when the line is perfectly insulated. Maximum work of the motor. The work produced being proportional to C B' follows the variations of these two factors. Other things being the same, it diminishes when K" increases, that is to say, it diminishes as the distance increases. The distance affects the work produced, but not the efficiency. The work produced is a maximum when The electrical efficiency being 50 per cent. As E' increases, the efficiency increases from -5 to 1, but the work produced diminishes ; in the limit when E' = E the efficiency becomes 1 or 100 per cent. , and the work produced = 0. As the work produced diminishes as the whole resistance of the circuit increases, in order to transmit the same quantity of work at the same theoretical efficacy, it is necessary to increase the e. m. f. both of the generator and motor, and to diminish the current as the distance increases. The three equations which give W, W, and W" enable the theoretical values of C, E, and E' to be calculated, when the work to be transmitted, the work to be expended, and the loss which can be allowed by heating of the circuit are known, the resistance of the line being determined by the distance and by practical considerations of the cost of erection. Theoretical limit of the work transmitted by a line Of given resistance. Theoretically an infinite quan- tity of work can be transmitted by a line of any length by using suffi- ciently high electromotive forces. In practice a limit is soon reached, on account of the danger of high electromotive forces and the loss by leakage, which increases very rapidly as the electromotive force goes up. If, for example, we have the conditions that the e. m. f. of the generator is not to exceed 3,000 volts, and the loss by heating of the line to be 20 per cent, of the work expended, it is easy to calculate the theoretical limit of the work transmitted, the current strength, and the work re- covered by taking, say, a final efficiency of 50 per cent. ; the results are given in the following table : Theoretical limit of transmission of power. (E = 3,000 volts, heating of the line, 20 per cent, of the work expended by the generator. Loss by leakage = 0.) 254 APPLICATIONS OF ELECTRICITY. Resistance of the line in ohms. Maximum strength of the current in amperes. Maximum work transformed into electrical energy by the generator in horse-power. Work recovered at the motor in horse-power for an efficiency of per cent, in horse-power. Loss of energy by re- sistance of the line in horse-power. 5 120 473-3 236-6 947 10 60 236-6 118-3 47-3 20 30 118-3 59-1 23-6 50 12 47-3 23-6 9-5 100 6 23-6 11-8 4-75 200 3 11-8 5-9 2-37 500 1-2 4-7 2-36 95 ],000 6 2-35 1-18 47 Practical case* In practice the work put in is always greater, and the work taken out less, than the values given by the formulae, on account of friction, secondary actions, leakage losses, etc. ; so the formulae will have eventually to be modified by affecting them by practical co- efficients, which are as yet for the most part unknown. It is by no means surprising that direct measurements differ widely from the results given by calculation. Efficiency. There is no word with such divers meanings as efficiency as applied unqualified to electrical work. Its exact mechanical meaning is: The ratio of the work taken out of a machine to the work put into it. But in electrical nomenclature, on account of the number and variety of effects which a current can produce, it has many meanings. To avoid confusion, the word efficiency ought always to be accompanied by some name or adjective which exactly defines its particular meaning in the place where it is used. Electrical efficiency of a generator. The ratio of the total electrical energy given out to the mechanical work put in ; that is to say, between the whole work converted into electrical energy and the whole work put in. Available electrical energy. Ratio of the electrical energy at the terminals available in the external circuit to the whole mechanical work put in. Mechanical efficiency of a motor. Eatio of the mechanical work taken out, measured at the break, to the electrical work at the terminals. Electrical efficiency of a system of transmission of power. Ratio of the electrical work transformed into mechanical work by the motor to the TRANSMISSION OF ENERGY. 255 mechanical work transformed into electrical work by the generator. When there is no loss by leakage, the electrical efficiency is . Mechanical or commercial efficiency of a system. Ratio of the mechanical work done by the motor, measured at the break, to the mechanical work put into the generator measured at the dynamometer. This kind of efficiency is what ought to be meant when efficiency is spoken of without any qualifying epithet. Increase of resistance of the armature due to self-induction. Applicable both to motors and dynamos (Ayrton and Perry) . If L be the coefficient of self-induction of the coil, C the current passing, and n the number of revolutions per minute, then the loss of energy per second is 1TMLC8 120 ' which corresponds to an increase in the resistance of the armature equal to -TTftL ohms. To find the coefficient of self -indttct ion of a coil. The simplest method is that adopted by Lord Eayleigh for correcting for self-induction in his determination of the ohm by the British Association method. Arrange the coil in a Wheatstone's bridge as if to measure its resis- tance, using a very delicate undamped galvanometer. Get a perfect balance, and call the resistance of the coil thus found P. Now close the battery key before closing the galvanometer key ; on the galvanometer key being pressed down the needle will be momentarily deflected ; observe the throw, call this o. Now insert an additional resistance 5P in the same circuit as the coil. Close the battery key before the galvanometer key (in the usual way), and observe the throw of the needle ; call this . Also observe the time I of one-half complete vibration of the needle. Then if L be the coefficient of self-induction, 4 tan -0 Parcel Deprez's experiments between Miesbach and Munich (1882). Two A gramme machines wound with fine wira 250 APPLICATIONS OF ELECTRICITY. connected by a double overhead telegraph line of iron wire 4 '5 mm. in diameter. Diameter of wire on machines '4 mm. Resistance of line 950'2 ohms. generator 453'1 motor 453*4 Strength of current at generator . . . '519 ampere. Difference of potential at terminals of motor . 850 volts. Available electrical work at motor . . . *426 h.p. Electrical work of generator (calculated) . . 1*01 Effective work taken out of motor . . . '245 Electrical efficiency (calculated) . . . 38" 9 per cent. Mechanical efficiency (calculated) . . . 22'1 Experiments at the Chemin de Fer du Nord (1883). A Marcel-Deprez machine, with double gramme ring as generator and a D gramme as motor. Diameter of wire, 1 mm. (The machines being arranged side by side made leakage on the line an advantage, instead of a disadvantage as it is when the machines are at opposite ends of a double line.) The line was made of telegraph wire 4 mm. in diameter, 17 kilometres long, and of 160 ohms resistance. Resistance of generator 56 ohms. motor 83 The following are the results of two series of tests made by Messrs. Tresca, Hopkinson, and Cornu : 1st series. 2nd series. Strength of current in amperes . . . 2 '559 2: 687 Generator. Power expended at the dynamometer . 6'21 10*4 Number of revolutions per minute . . 590 814 Difference of potential at terminals . . 1290 1865 Electrical energy produced . . . . 4'42 6'81 Motor. Number of revolutions per minute . . 365'8 595 Difference of potential at terminals . . 908 1485 Electrical energy, put injto the motor . 3*12 5'42 Mechanical work (measured at the break) '326 '317 Between Vizelle and Grenoble (1883). Generator, a Gramme ma- chine with two rings coupled in series (Marcel Deprez type, No. 10) on the same axis. Field magnets, two U-shaped electro -magnets. Motor, D Gramme machine altered for the experiment. Distance of transmission 14 kilometres, overhead line formed of two wires (lead and return) of silicium-bronze two millimetres in diameter. TRANSMISSION OF ENERGY. 257 Resistance of the line Resistance of generator : Field magnets Rings 2 x 18'3 . Resistance of motor : Field magnets Rings . 167 ohms. 20-1 567 ohms. 97 EXPEBI MENTS. D2. Nl. Revolutions per minute of generator . ,, ,, motor .... Motive power at axis of break in chevaux vapeur 995 618 16-28 12-61 1140 875 16-9 11-56 Work with transmission deducted 12-27 6-33 11-18 6'97 51-6 62-3 Mean current strength in amperes Electromotive force of generator E motor e . 3-48 2848 1737 60-9 2-35 3146 2231 70-8 E Loss by leakage on the line. Experiments made by means of nitrate of silver voltmeter on the silicium bronze line when recently put up in a temporary way, gave the following results : EXPERIMENTS. 1 2 Electromotive force of the generator (in volts) Difference of potential at terminals ,, Strength of current at Vizelle in amperes . 2808 2627 3-268 3128 2934 3-514 ,, Grenoble ,, 3-099 3-282 Loss per cent 5-1 6'6 Let GENEBAL USEFUL FOEMUI^B. E be the e. m. f . of the dynamo. e be the back e. m. f . of motor. E, be the resistance of dynamo. R' be the resistance of line. r the resistance of motor. W, mechanical work put in to the dynamo. tc, work taken out of motor. 258 APPLICATIONS OF ELECTRICITY. To test, put an ammeter in circuit and observe the current passing C, place a vo tmeter between the terminals of the motor, and observe the difference of potential, P ; we then have * zr P - Cr E = P -f C (R + K'). Now for motor, electrical work put in is CP, and whole convertible or available electrical work is Ce, or C (P - O). Maximum possible efficiency of motor under _ P Cr Qr e the conditions of the test .... p p' w Real efficiency ...... 7T ' CP Ratio of real efficiency to maximum possible __ _ w _ ' efficiency ....... ~~ C (P - Cr) Loss due to friction, self-induction, and the _ group of phenomena called magnetic friction * ' Wm A test should be made to ascertain the loss by mechanical friction ; call this L, Then the loss due to electrical and magnetic _. /T1 ~ . ._ . . actions ....... C(P--Cr) (L+u>). If this loss be high it shows that the electrical design of the motor is faulty ; if L be high it shows that the mechanical design is faulty. For any system of transmission of energy : e The maximum possible efficiency . . . :=- or E P4-C(R + R') -/* The real electrical efficiency . . . . The real mechanical efficiency . . . m TRANSMISSION OF ENERGY. 259 Percentage of maximum possible efficiency to w (P-}-c (R-f-R') } efficiency obtained ~ ^y /p Q r \ Loss by heating in dynamo . . . . ~ C 2 R. Loss by heating in line . . . . = C 2 R'. Loss by heating in motor . . . . =. C 2 /-. Thus, in any system, there is to be considered as to efficiency the efficiency of the dynamo and the efficiency of the motor ; and as to quantity of power which this system will transmit, the whole resistance of the circuit. Having a good type of dynamo and motor, in order to get high efficiency and plenty of power, E and e should be high, so that ^ may be near unity and E e may be large. The resistance of the whole system should be low ; but as a practical rule, to avoid expense in erection of the line, the resistance of the system may be allowed to increase as E and e increase. Again, as in order to increase E and e we must increase R and r, R' may increase very rapidly as E and e increase. As yet so little has been done on a large scale in electrical transmission of energy, and the systems having been for the most part experimental, and there- fore not been kept running long, that there is a great dearth of practical information on the subject. According to the purpose for which the motor has to be used, very different types will be selected. Where weight is of no moment, several horse-power can already be obtained with very high efficiency from the Gramme and the Biirgin dynamos used as motors. At Vienna, Siemens Brothers obtained from the Siemens (Hef tner - Altneck) continuous current dynamo, used as a motor on board their electric boat, supplied by the Power Storage Company's accumulators (the Sellon-Volkmar- Faure-Swan combination), as much as 6 horse -power with an efficiency (work to CP) of 75 per cent. For light motors one of the best results lately was from some of Ayrton and Perry's motors : ~ , b.p. Efficiency Weight given out. (work to CP). of motor. 2,100 revs, per minute . . .35 38% 37 Ib. 1,3> 75 47% 75 1,600 ,, ,, 2-1 51% 127 2,000 . 2-6 not observed. 127 This series goes also to show that horse -power per unit of weight and efficiency increase as the weight increases in motors of the same type. The varying conditions of driving e. m. 1, speed, and lead of brushes 260 APPLICATIONS OF ELECTRICITY. all have the greatest possible influence, both on the horse-power and efficiency of motors. When any one of these variables is fixed, the other two will each have certain definite values in order to get the best effect. The values also, unfortunately, are not always the same for maximum h. p. and maximum efficiency, though probably the better the design of the motor, the more nearly the arrangements for maximum power will give maximum percentage of efficiency. As yet, the variation of the Ei secondary effects (self-induction and magnetic friction) make the arrange- ments for the highest power always differ widely from Jacobi's rule of Ll E~ 2* ELECTRIC LIGHTING. Electric light is the direct application of the" heat produced by currents. This heat is utilised and concentrated into the smallest possible space, so as to raise the temperature as high as possible, and so cause certain bodies to become luminous. According to the nature of the conductor passed through and made luminous by the current, three large classes of practical means of producing electricity may be formed. 1. Rarefied air, made luminous by the passage of a current. 2. The voltaic arc, formed by the passage of a current in air raised to a high temperature ; this air heats the carbons or other refractory bodies by direct contact and renders them incandescent. 3. Incandescence. Solid matter, generally carbon, raised directly to a high temperature by the passage of a current. We will only discuss here the voltaic arc and incandescence, light produced in vacuum tubes not having as yet been practically applied. VOLTAIC ARC. The voltaic arc is almost always produced between two pencils of artificial or agglomerated carbon, and the light is due, not to the arc pro- perly so called, but to the incandescence of the carbons raised to a high temperature by the passage of the current. The combustion of the carbons causes them to wear away, and it becomes necessary, in order that the light may be steady and to prevent its going out, to keep the carbons at a suitable distance from each other, either by hand or by the aid of properly -de vised lamps, which cause the carbons to approach each other automatically in different ways, which are more or less perfect, more or less simple, or more or less economical. ELECTRIC LIGHTING. 261 Classification principles of arc lamps. The arc lamp is said to be monophotal when its system of governing is such that only one source of light can be worked from each source of electricity, whether battery or machine. It is polyphotal when several can be placed on one circuit, either in series or in parallel arc or in several groups, according to the character and power of the machines which feed them. Generally, regulation is based on electro-magnetic actions, and is produced (1) By current strength. The mechanism tends to keep the strength of the current constant. (2) By a shunt circuit. The regulating electro-magnet, wound with fine wire, is arranged as a shunt between the terminals of the lamps, and tends to keep the difference of potential between these two points constant. (3) By differential action. The regulating machinery tends to keep a certain equilibrium between the two factors, strength of current and difference of potential at the terminals, and comes into action as soon as one or other of these two elements tends to become weaker or too strong. (4) Various lamps. There are a certain number of lamps based on different actions and difficult to classify. In some the carbons are re- adjusted at regular intervals of time, as one minute or half a minute (Brockie). Others keep a constant geometrical distance between the carbons, either by the wearing away itself (RapiejjF), or by arranging carbons side by side (electric candles), or by utilising the heat of the arc to produce the bringing together of the carbons at the desired moment (Solignac). As to mechanical arrangements, they vary infinitely, and the fruitfulness of inventors in this direction is inexhaustible. Gearing, cords, springs, weights, motors, water, mercury, compressed air, electro- magnets of all sorts, solenoids, double-wound magnets, ratchets, mecha- nical and magnetic breaks have been employed or proposed; and any classification based on these characteristics would be of no scientific or practical interest. Alternating: and continuous currents. When an arc lamp is fed by alternating currents, the wear of the two carbons is the same if they be horizontal ; if they be vertical, the upper carbon wears away a little faster than the lower one, in the ratio of about 108 to 100 for carbons of the same quality and same diameter. With continuous currents, the positive carbon, which is generally placed above, wears away twice as fast as the negative carbon, and is hollowed out into a crater. 262 APPLICATIONS OF ELECTRICITY. When it is desired to keep the light fixed in space, account must be taken of the different rates of wearing according to the nature of the current employed. Resistance of the voltaic arc. As yet there is the greatest uncertainty as to the true value of the resistance of the voltaic arc, because as yet the true value of the back e. m. f. developed in the arc by the passage of the current is unknown. We shall give no figures, as opinions are so contradictory ; further, such figures are absolutely use- less for purposes of calculation, because, if we know the strength of the current and the difference of potential at the terminals of a given arc lamp, we have all that is necessary for calculating its expenditure of electrical energy and the conditions which must be fulfilled by the machine which has to feed it. Electrical energy absorbed by an electric light. Let C be the strength of the current in amperes necessary for the good working of an electric lamp, arc, candle, incandescent, etc. , and E be the difference of potential in volts at the terminals of the lamp. The elec- trical energy W absorbed by it will be : W ir: ; kgms. per second, rz foot-pounds per second ; 9*81 I'oo Dividing W by the lighting power of the lamp L in candles or carcels, we get the price of unit of light in kilogrammetres or foot-pounds of elec- trical energy. Dividing the lighting power L by W, we get the number of units of light which one kilogrammetre or foot-pound of electrical energy can furnish. Either of these two numbers gives the absolute value of a given electric light in relation to the quantity of electrical energy which it consumes. Of course the number of units of light per kilogram- metre of effective work furnished by the electrical generator is always lower than the figures given by the above formula, because it necessarily includes the coefficient of the efficiency of the machine, the loss due to the resistance of the conductor, and other causes of loss independent of the light properly so called. CARBONS. When the carbons are too thin they give a very intense light, but burn away too quickly ; when the carbons are too thick very deep craters BARE AND PLATED CARBONS. 263 are formed so that the light is obscured and diminished. Coating with metal increases the life of the carbons. 1. Trimming of bare carbons. 2. Trimming of coppered carbons. 3. Trimming of nickel- plated carbons. Fig. 44. Experiments of M. E. Reynier on the Trimming of Bare and Plated Carbons. Bare and. plated carbons (E. Reynier). Experiments made in the shops of Sautier and Lemonnier with an A gramme machine and homogeneous Carre carbons from the same sample. Photometric measurements taken by projecting the light forward by means of an arrangement which Mons. Lemonnier considers sufficient for practical purposes. However, when the sections of carbons and the conditions of their surfaces are varied, this method may not be sufficient. Thus, the photometric values in the table must be considered as mere approxima- tions until less arbitrary measurements have been made. The metallic plating was not very adherent ; it often scaled off. By improving the plating processes, a good adherent metallic deposit can certainly be obtained. On the positive carbon, the ordinary method of trimming is good with copper, and excellent with nickel. On the negative carbon, the trimming which is a little too long for bare carbons appeared to be a little too short with plated carbons. Further, the metal sometimes remains round the carbon at the cut part, forming an injurious projection. This inconvenience might, no doubt, be avoided by plating the negative carbon with brass. 264 APPLICATIONS OF ELECTRICITY. LENGTH CONSUMED LENGTH IN ONE HOUR. OF TRIMMING. H STATE H DIMENSIONS. OF J g> 6 ? a THE SURFACE. I I | I I I d = 7 mm. fBare . I Blackened mm. 166 mm. 68 mm. 234 mm. 53 mm. 23 947 s = -384,6 cq. . C in rH t ( *OiO(M i-H-< iOCOr-1 l* tMlCl^) -*T-HCOCOlOCD 1 -* l CCI CO^T QO tX) OS Tfl CO tO 00 CO t-. GOt^ OJCOt-. OiiOrH J^CC 050(M ' ' *{> OOO "* 'GOT = jaddoo eand stuqo u ut jcad s s $ p i s i rH CO rH 4j( 05 TELEGRAPHIC INSTRUMENTS. 283 Higll-spced instruments enable the whole transmitting power of the line to be utilised, which is always much greater than the speed of transmission of the most skilful clerk. They work by multiplying the number of operators working on the same line. In the automatic instruments a certain number of operators perforate bands of paper which afterwards pass through the transmitter, and produce very rapid emissions of current, which are registered at the receiving end on a continuous band of paper like that of the Morse instruments. In duplex instruments two operators transmit the despatches simultaneously in opposite directions on one and the same wire. In the diplex the two operators transmit simultaneously in the same direction. In the quadruplex two operators at each end of the line transmit simultaneously four despatches ; two in one direction, and two in the other. Lastly, in the multiplex instruments based on the division of time by means of synchronism established between the sending and receiving stations, the line is placed for equal and equally divided fractions of time successively in communication with several groups of operators, who take advantage of the interval of time between two successive communications to prepare the next signal. These numerous high- speed instruments are not only very different in their principle, but may also be distinguished from one another by the nature of the signals they transmit. Thus the duplex, diplex, and quadruplex instruments gene- rally work sounders. The Wheatstone transmits Morse signals (exclu- sively) , which are recorded ; whilst the synchronous instruments transmit sometimes Morse signals, as in Meyer'' s instruments ; sometimes ordinary characters, as in Baudot's instrument, which is a marvel of mechanical ingenuity. Space preventing us from giving a description of all these instruments, we will only point out their general arrangements, and the working of their principal parts. Electro-magnets. Specification of French telegraph service. Soft iron cores and armature perfectly annealed, must retain no appreciable traces of magnetisation after a prolonged transmission of Morse signals with a battery of 100 Callaud elements ; must not be touched with the tool after being annealed. Wire of the coils. Copper of conductivity above 90 per cent, covered with white or cream-coloured silk. The fine wire to be in one piece, one of the ends soldered to the reel if it be of brass ; outside layer No. 16 wire of '44 millimetre. The finished coil to be covered with asphalte varnish, allowance 2 per cent. The difference between two coils must be less than 4 ohms, but the number of turns must be the same. 284: APPLICATIONS OF ELECTRICITY. Hughes' 1 instrument. Minimum carrying power of the magnet 5 kilos, coils of the electro -magnet of number 32 ('17 millimetre bare), minimum number of turns 11,000, maximum total thickness 11 millimetres, maximum resistance 600 ohms. Hollow soft iron core T5 millimetres thick, 6 millimetres external diameter, 6 centimetres long, and filled up to 3 millimetres of thickness to receive the screw fixing the pole piece. Testing speed ninety to 140 revolutions of the chariot per minute without slowing. Morse receivers. Clock-work movement to go for forty minutes, speed of unrolling ribbon T7 metres to 1/4 metres per minute, seven thousand turns of No. 29 wire ('21 millimetre bare) ; resistance less than 250 ohms, thickness of the coils not to exceed one centimetre. Relay speakers. Coil mounted on a brass reel ; in the centre, 2,000 turns of No. 36 wire '12 millimetre bare, then 5,000 turns of No. 34 wire *14 millimetre bare, in all 7,000 turns, minimum resistance 500 ohms. Reverse current coils. Each coil 4,500 turns of No. 32 wire (1*7 milli- metres bare), resistance 2,500 ohms. Bells with lightning guard, each coil 2,000 turns of No. 32 wire ; resistance 50 ohms, allowance 5 ohms. Maximum distance between the edges of a lightning guard half a millimetre. Methods of diminishing the extra current on breaking Circuit. The use of these methods is especially neces- sary when powerful currents are used, (#) Arrange a coil of as fine wire as possible as a shunt, having a resistance forty times that of the electro-magnet. The wire to be coiled half from left to right, and half from right to left, so as to prevent the formation of extra currents in the shunt (JDujardiri). Place a small condenser of tinfoil between the terminals of a receiver ; the capacity of this condenser must vary with the resistance of the electro -magnet and the power of the battery, generally from one -eighth to a quarter of a microfarad (Culley). When it is possible to arrange two coils of an electro -magnet for quantity or in parallel circuit, the extra currents which are produced in each of the coils tend to neutralise each other. This arrangement applied to the Wheat- stone instrument has enabled the rapidity of transmission to be increased from 10 to 20 per cent. (Prcece). Strength of telegraphic currents. Distinction must be made between the working current and the mean current. The working current is that sent out at the sending end, and measured at that end, which in France varies between 12 and 20 milliamperes. The received current which works the receiver is diminished by the influence of leakage, and according to the state TELEGRAPHIC INSTRUMENTS. 285 of the line and the atmosphere, the length of the line and its insulation, etc., varies between '7 and '2 of the initial current. The mean current, which varies between 7 and 13 milliamperes, represents the continuous current, which during the twenty -four hours would produce the same expenditure of chemical action as the daily work of the working current. The quantity of electricity expended per twenty-four hours varies between 500 and 1,200 coulombs, and represents a daily deposit of from *2 to "4 gramme of copper. The current which actually passes through the receiver varies between 3 and 8 milliamperes. Mean strength of telegraphic currents used in India (Schwendler). Working currents during the dry season, eight months, in milliamperes 6'4 During the rainy season, four months, in milliamperes 13 Local circuit working a speaker, in milliamperes . . 72 Resistance of the speaker, in ohms 25 to 35 Siemens relay. Resistance in ohms 500 Strength necessary to work the instrument, in milli- amperes 2 Range of electro-magnet receivers (Schwendler}. Let c be the weakest which will work a telegraph instrument, C the strongest current which it will bear, its range is : r> Range-- It is always as well that the range should be as high as possible. The range of an electro -magnet receiver is a decreasing function of the speed. The following is a table of the experiments made by Schwendler on a Siemens polarised relay to determine its variations : NUMBER OP EXPERIMENT NUMBER OF CONTACTS PER MINUTE. WEAKEST CURRENT IN MILLIAMPERES C. STRONGEST CURRENT IN MILLIAMPERES C. RANGE C c 1 53 89 14-35 16-1 2 101 1-03 14-.35 14 3 138 114 14-35 12-6 4 313 1-81 14-35 7-9 5 419 1-81 8-36 4-6 286 APPLICATIONS OF ELECTRICITY. Four hundred and thirty contacts per minute correspond to a speed of 20 words of 5 letters per minute, the word Paris being taken as a type. The range of a relay working at this speed cannot exceed 4. The relay experimented on above will work with currents varying between 2 and 8 milliamperes without changing its adjustment. Sensitiveness of a telegraphic instrument. The wire ought to be so arranged as to produce the most intense possible magnetic field at that part where the work is to be done. The movable parts ought to be as small as possible, so as to diminish their moment of inertia, and because a small magnetic field costs less to produce than a large field of equal intensity. Those parts which are magnetised by the current ought to magnetise and demagnetise rapidly; that is to say, have but little magnetic inertia, have a small mass and as little coercive force as possible. All contact between the armature and the electro- magnet should be avoided because of residuary magnetism. Siemens relays (ScJw'cndlcrj.The resistance E of a relay may be deduced from the formula : L being the resistance of the longest line on which the relay is required to work. Range. A Siemens relay ought always to have a higher range than 25 ; many have a range of 35, and some instruments have as much as 55. A Siemens relay of 500 ohms resistance works well with a current C of 2 milliamperes. The same relay having a resistance of r' would work with a current c' : c*/7 44-8 c'=.~ zz ._ milliamperes. yV -/'' This approximate formula does not take the thickness of the insulator into account. Local sounders. In India they have a mean of from 25 to 35 ohms resistance, and work with four Minotti elements in series, and a current of 72 milliamperes. Portable sounders* Pdlarised relay 500 ohms resistance, 250 for each coil. TELEGRAPHIC INSTRUMENTS. 287 Dial telegraph. Each turn of the handle represents 13 emissions of current and 13 interruptions. A well -constructed instrument gives two turns and a half of the needle per second ; in practice one turn per second is counted. Each letter requires as a mean one -half turn and a wait of half a second. The speed is 60 letters per minute, or 10 words, each word comprising 5 letters, and one return to the -f-> which indicates the end of the word. instrument. Spacing and length of the signs. One dash is equal to three dots ; the space between the signs of the same letter equal to one dot ; the space between two letters equal to three dots ; the space between two words equal to five dots ; mean word, five letters. Speed of transmission. A good clerk, 18 to 20 words per minute; mean, 12 to 18. Speed of the receiver. Depends upon the number of dots per minute which the armature can make, and varies from 800 to 2,000. The letter of mean length is r ( --- ) . The length of a dot which can be easily read is three-quarters of a millimetre. If the strip unrolls at the rate of 1*2 metres per minute, as many as 32 words per minute may be trans- mitted; beyond that speed, the rate of unwinding of the slip must be increased. Mean work. 25 simple despatches of 20 words plus the address (say 30 words) per hour, or 750 words or 3,750 letters per hour, the maximum of a letter being 4 dashes. The number of dashes produced is almost 15,000 to the hour, or 5 per second. ; MORSE ALPHABET. j k - 1 . m - n 5 - o - 6, oe P t u ii, ue v w - x 288 APPLICATIONS OF ELECTRICITY. Full stop . Colon .... Semicolou . Comma Note of interrogation . Note of admiration Hyphen Apostrophe . Parenthesis . Inverted commas Bar of division Call signal Understand message Repeat message Correction, or rub out . End of message Wait C' eared out, and all right Begin another line . The Hughes' instrument. The printing axle turns seven times quicker than the chariot and the type axle. The keys, which are pressed down successively, must be separated by an interval of four keys at least, as the number of keys is 28. The velocity of the type-wheel varies from 40 to 150 revolutions per minute; the mean is 110 to 124 revolutions. 1'54 letters are transmitted per revolution, or 185 letters per minute if the chariot perform 120 revolutions. Two letters per revolution of the chariot are generally counted, each word being com- posed of five letters and a blank. Thirty-one words per minute is the rate at 120 revolutions. The contact piece on the chariot covering three divisions of the contact box, the contacts last for '053 second. The mean rate of working is 45 to 50 despatches per hour ; 60 are often sent on short lines. Wheatstone's automatic transmitter. One operator can perforate 25 despatches in an hour. On a short line the instrument TELEPHONY. 289 can transmit 130 words per minute. Between Paris and Marseilles, 863 kilometres, the mean rate of sending is 85 despatches to the hour with five clerks at each end. A series of ten despatches passes through the transmitters in five minutes. The emissions of current vary between 10 and 90 per second. Speed of transmission of telegraphic instru- ments. These figures show the rates for despatches of a mean 20 words on a line of 600 to 700 kilometres in length per hour : Morse 25 ,, duplexed .... 45 Hughes 60 duplexed . . . .110 Meyer per key-board ... 25 with four key-boards . 100 Baudot per key -board . . 40 ,, with, four key -boards . 160 with six key-boards . 240 Wheatstone ,, duplexed . Keflecting galvanometer ,, diplexed Gray (reading by sound) per office Syphon recorder .... duplexed . . 35 Foot, 1000 words per minute between Boston and New York (460 metres). TELEPHONY. Telephony is the transmission of articulate sounds to a distance, telephonic system always includes : (1) A transmitter, which converts articulate sounds characterised undulatory vibrations into undulatory currents ; (2) The receiver, which transforms the undulatory currents from the transmitter into undulatory vibrations, similar to, but not identical with, the vibrations which have affected the transmitter ; (3) A line formed of one wire or two wires joining the instruments. Transmitters are divided into two classes : 1. Magnetic transmitters, requiring no battery. The sonorous waves produce undulatory currents, which afterwards act on the receiver. 2. Battery transmitters, carbon transmitters, microphones, etc. The sonorous waves modify the current furnished by a constant independent source (battery or accumulator). MAGNETIC TRANSMITTERS. All magnetic transmitters are reversible. They produce undulatory currents under the action of articulate sounds, and reciprocally reproduce the corresponding articulate sounds from un- dulatory currents passing through them. The type is the Bell telephone, which is formed of a plate of thin sheet-iron vibrating in front of a magnet, round which a coil of insulated conducting wire is wound. The 290 APPLICATIONS OF ELECTRICITY. vibrations of the plate produce induction currents in the coil. The strength and direction of the currents are directly connected to the move- ments of the vibrating plate. Many modifications in its form have been introduced, which in no way affect the principle discovered by Prof. Bell. BATTEEY TEANSMITTEES. Based on the variations of resistance of carbon under the influence of pressure, which was discovered by Du Moncel in 1856, and applied to telephony for the first time by Edison in 1877. The resistance of an imperfect contact was used for the first time by Hughes, in 1878, and the inventor named the apparatus the micro- phone. All transmitters now used are based on the variation of resis- tance of imperfect contacts, the contact being made to vary under the influence of articulate sounds. Carbon is the best substance to use, because it does not oxydise and is infusible, and also because it is of low conductivity, and its resistance decreases when heated. The different forms of microphones differ by the number of imperfect contacts, their arrangement, their grouping, the nature of the sounds to be transmitted, etc. It is impossible to give any definite rules, and, as Mr. Preece has justly remarked, " the microphone at present defies mathematical analysis." 1. In direct circuit, for short distances. 2. With induction coils. The undulatory current pa,sses through the primary coil of an induction coil ; the secondary circuit is joined to the receiver, which is thus affected by the induced currents. This last method alone is used for long lines and telephone systems. The resis- tance of the transmitter varies from 1 to 150 ohms. The resistance of the induction coils is also very variable, and no rule can be given, because of the secondary phenomena of self-induction, charging of the lines, etc. ^Lder's microphone, used by the Socie'te Generale des Telephones in Paris, has a, ineau resistance of 5 obms, the primary circuit of the coil 1-5 ohms, the secondary coil 150 ohms, and the receiver 75 ohms: tie flexible conductor about 4 to 5 ohms. The mean strength of the inducing current does not exceed a quarter of an ampere, or the twentieth of an ampere per contact. In Moser's experiments, with 24 transmitters in parallel arc, the current was 24 amperes, or one ampere per microphone, one-fifth of an ampere per contact. The plate of the receiver is -3 milli- metre thick, the wire of the coils '09 millimetre in diameter. The in- duction coil is made of wire, '5 millimetre for the primary and -14 millimetre for the secondary. For the telephonic system of Paris, the primary circuit is formed of the transmitter, the coil, and three Leclanche cells, with agglomerate plates, each arranged in series. TELEPHONY. 291 Receivers. The most used, in fact, the only ones used in practice, are: Magnetic receivers. The most simple and the best is the Bell telephone in its innumerable variations. Some are made with two poles, like the Siemens and Gower. The super- saturated telephone of Adcr and the concentric pole telephone of d? Ar&onval, Various receivers. Many other actions besides magnetic actions have been used in telephonic receivers. We will only cite the electromotograph of Edison, based on the variations of friction between chalk and plati- num, moistened by a saline solution, under the action of a variable current ; the mercury telephone of Anloine Breguet, based on electro - capillary actions; the heat telephone of Preece, based on the heating and expansion of a wire traversed by an undulatory current ; Dolbear^s electrostatic telephone, based on the reciprocal actions of two plates charged with variable quantities of electricity, etc. . With very few exceptions, an earth return should never be used for telephonic transmission. A double wire or metallic circuit should be used. An earth return may, however, be used where there is no fear of induction. Induction. The noise produced by the action of neighbouring circuits on a telephonic circuit is thus called. It often prevents direct conversation from being heard. When the telephonic circuit runs near many telegraph wires, it often sounds exactly like the boiling of a kettle. Induction may be diminished to a certain extent by the following devices : (1) By diminishing the sensibility of the receiver and increasing the transmitting currents, so as to weaken the external disturbances. (2) By establishing an induction screen between the telephone wire and the other wires, by using an insulated wire covered with a metallic coating connected to earth. (3) By modifying the causes of disturbance, by sending graduated currents instead of abrupt currents in the neighbouring circuits. (4) Neutralising the effects by means of counter-induction instru- ments. (5) Always employing a double or metallic circuit, placing the two wires close together; or, le';ter still, using insulated wire, and twisting them together. This last method is much the most efficacious and the most employed. L.OSSCS on the line. The use of a double wire demands perfect insulation on the line ; otherwise all exterior currents are felt in the instrument, especially when these external currents have an earth 292 APPLICATIONS OF ELECTRICITY. return. Telephonic lines with an earth return are also sensible to external disturbances, electric lighting, telegraphs, earth currents, storms, etc. Distance. "When all disturbing causes are carefully guarded against, it is possible to telephone to a distance of 700 kilometres, in per- fect silence and with an overhead line. Through submarine cables it has never been possible to exceed 180 kilometres, because of the electrostatic capacity of the cable. No more than 40 kilometres is possible with underground lines (January, 1883). Work done by batteries used with microphones (E. Reynier}. These figures have been calculated from the observed expenditure of zinc in the Leclanche batteries in the busiest offices oil the Paris telephone system (each office having a battery of 3 elements, one Ader microphone, and one induction coil). Mean strength of inducing current . . '084 ampere. Work given out by the battery when the microphone is in action -025 kilogramme tre per second. Annual work of a very busy office, the instru- ment being spoken through. 7 hours out of the 24 235,425 kgms. From Eeynier's calculations, the 3000 offices of the Paris system, each being supposed to be as busy as the central offices, would use daily 1,935,000 kilogrammetres, or one horse-power for about 7 hours and 5 minutes. With accumulators of efficiency 80 per cent., charged by dynamos of efficiency 80 per cent., a driving power of one horse-power working 12 hours per day would be ample for the work of the whole Paris system. Simultaneous telephony and telegraphy on the Same Wire. Van Rysselberghe's system (1883). After he had suc- ceeded in stopping the induction produced by telegraph wires on tele- phone wires by graduating telegraphic currents by the use of resistances, condensers, and electro-magnets, Van Rysselberghe was enabled to con- nect telephones directly to wires used for telegraphic communication, and use the wires for the simultaneous transmission of Morse signals and articulate speech. 293 fi&fy $art. EECIPES, PROCESSES, ETC. Fusible alloys (Agenda du chimiste). IPArcefs alloy, fusing at 94 C. Lead Tin Bismuth Wood's alloy, fusing between 66 and 71 C. Lead Tin Bismuth Cadmium Fusible amalgam, fusing at 53 C. D'Arcet's alloy Mercury Alloys used for instruments: Tombac, or white copper ,, yellow ,, red Romilly's brass Copper. 86 to 88 91-66 70 5 parts. 3 8 , 2 parts. 4 7 to 8 Ito2 , 9 parts. 1 Zinc. Tin. 14 to 12 5'56 5-56 8'34 30 Aluminium bronze : Copper 90 parts. Aluminium Silvering: for curved mirrors: Tin Mercury 10 4 parts. 1 Alloy for nickel coins (Germany, Belgium, United States) Copper 75 parts. Nickel 25 294 RECIPES, PROCESSES, ETC. SOLDERS. 1 COPPER. ZINC. TIN. LEAD. Hard solder, yellow, high melting point . Hard solder, whitish yel- low, low melting point . Hard solder, yellowish white, very low melting point ..... 53-3 41 57-4 53-3 1-5 43-1 49-9 28 437 6 1-3 3-3 14-6 Bras 33 50 3 11 ,s 10 66 50 Hard solder, whitish yel- low, very strong Brass polder Plumber's solder Tinman's solder . LiOW temperature SOlder. For use when the parts to be soldered will not stand a high temperature. Finely divided copper (ob- tained by precipitating a solution of copper sulphate with zinc) is mixed with concentrated sulphuric acid in a porcelain mortar. 30 to 36 parts of copper are taken, according to the degree of hardness desired, and 70 parts of mercury are stirred in. When the amalgam has completely farmed, it is washed with hot water till all traces of acid are removed. It is then allowed to cool. When this composition is to be used it is heated until it is of the con- sistency of wax, so that the surfaces to be joined may be readily smeared with it. When cold they adhere very strongly. To give copper the appearance of platinum. Scale clean and dip in the following bath until the desired appearance is produced. Hydrochloric acid Arsenious acid Copper acetate Dry by rubbing with blacklead. 1 litre. 250 grammes. 45 Platinised Silver. Used in Smee's batteries. Dissolve a little bichloride of platinum in acidulated water, and decompose the solution by a current, taking a plate of platinum as the anode, and the silver plate to be platinised as the cathode. A rough deposit is thus obtained which facilitates the disengagement of the bubbles of hydrogen. AMALGAMATION OF IRON, ETC. 295 Platinised carbon (Walker']. The carbon plates are first purified by soaking them for some days in sulphuric acid diluted with three to four times its volume of water ; a tinned copper conductor is then fastened to it by tinned copper rivets. The carbon is then platinised by electrolysis, the carbon plate being used as the cathode, the anode being either a platinum or carbon plate. The solution used is thus prepared : sulphuric acid, diluted with ten times its volume of water, is taken, and crystals of chloride of platinum are added until the solution becomes of a beautiful straw yellow colour. After the current has passed for about twenty minutes the plate is finished ; it may be tested by using it as a cathode in the electrolysis of water ; it ought to allow the hydrogen to escape freely without sticking to it in the form of bubbles. Platinised iron.Patcrson dips the plate to be platinised into an acid solution of platinum in aqua regia. Amalgamation Of iron. The iron is steeped for some time in a solution of a mercury salt, or in mercury covered with very dilute sulphuric acid. Boettger heats the iron in a porcelain vessel with a mixture of 12 parts mercury, 1 zinc, 2 sulphate of iron, 12 water, and 1'5 hydrochloric acid. The simplest and quickest way to amalgamate iron is to clean it well with dilute acid, rinse in clean water, and then rub it with an amalgam of sodium or potassium (Nature). Amalgamation Of zinc. Put a little mercury in a plate or shallow dish, fill up with weak dilute sulphuric acid and water, and rub the zinc well with a pad of old rag, dipping the zinc from time to time into the mercury ; when the surface looks quite silvery, wash w ell with clean water, and stand the zinc edge downwards to drain, putting a dish under it to catch the excess of mercury, which will drain off. (This mercury contains much zinc.) To purify mercury. If one of the new low-pressure distilling apparatus be not at hand, put the mercury in a deep vessel, put plenty of dilute sulphuric acid over it, and place a piece of carbon (a bit of an electric light carbon answers very well) into the mercury, weight it or tie it down so that there is good contact with the mercury ; this arrange- ment sets up local action, and dissolves out all metallic impurities ; do not carry the action too far, as you may dissolve some of the mercury in the form of mercury sulphates. Silver black (A. Bailfeux).lst. Take nitric acid at 40, and dissolve silver (coins will do) in it until it is saturated. 2nd. Gently heat the object to be blackened, which ought not to be joined with tin 296 RECIPES, PROCESSES, ETC. solder. 3rd. Dip the object into the silver solution until it is cold, then replace it on the fire to dry. It is then black. Allow it to cool, then rub it with a softish brush and blacklead. Gilt plumbago (Tabauref). For giving a conducting surface to electrotype moulds, -10 gr. of chloride of gold is dissolved in one litre of sulphuric aether, 500 to 600 gr. of plumbago (in fine powder) is thrown in, the whole is poured out into a large dish, and exposed to air and light. As the aether evaporates the plumbago is stirred and turned over with a glass spatula. The drying is finished by a moderate heat, and the plumbago put by for use. Cyanide Of potassium. There are several qualities. No. 1 contains from 96 to 98 per cent, of pure cyanide. No. 2, for copper and brass platers, 65 to 70 per cent. No. 3, used by photographers, from 40 to 50 per cent. Chloride Of gold. 1 gramme of metallic gold corresponds to 1'8 grammes of neutral chloride, and to 2 or 2'2 grammes of the acid chloride such as is obtained from chemical manufacturers. Porous pots. Minimum leakage with distilled water at 14 C. 15 per cent, in twenty-four hours. Morse paper. Width : 1 centimetre. Weight: 53 grammes per 100 metres ; breaking strain : 1,300 grammes. Sulphate Of copper ought to contain less than 1 per cent, of iron, and 24 per cent, of pure copper (CuSO 4 -|- 5H 2 O). Ammonium chloride or sal-ammoniac (NH 4 C1) ought to contain less than 1 per cent, of impurities, and less than five thousandths of lead salts. Dextrine dissolved in four times its weight of water ought to produce complete adhesion between two pieces of paper in ten minutes without sensibly discolouring them. Black oxide of manganese. Without dust of the kind called needle manganese; it ought to contain at least 85 per cent, of manganese peroxide. Mean composition of commercial sulphate of Copper (Culley) : Crystallised copper sulphate .... 99'66to98'48 Iron sulphate '09 '12 Water '35 1-4 GILDER'S VERDIGRIS. 297 Mean composition of certain samples of com- mercial zillC Cnllei : Zinc C9-27 9876 97'85 Lead '67 T18 2'05 1'13 Iron -06 '06 '1 '02 The purest sample was Silesian zinc. Rolled or drawn battery zincs ought to contain at least 98 '5 per cent, of pure metal, and at most half per cent, of iron. Purification of common commercial sulphuric acid (d 1 ArsonvaT). It may be purified by merely shaking it up with common lamp oil in the proportion of 4 or 5 cubic centimetres of oil to the litre of acid. The foreign bodies which would attack the zinc, arsenic, lead, etc., are precipitated. Gilder's verdigris. Gilders call a bath of nitric acid in which they clean copper and its alloys, strong water. When the strong water is nearly saturated with copper it ceases to bite. It is refreshed by adding sulphuric acid, which forms an impure sulphate of copper improperly called verdigris, and sets the nitric acid free. The composition of this verdigris is rather variable. The following are the results of an analysis made by M. Van Heurck of a sample from a Paris shop. Water evaporable at 15 C. (moisture and water of crystallisation) 31'4 Substances volatile at a red heat (water of combination and a little nitric acid) 9'1 Oxide of copper 30'2 Sulphuric acid 29'3 Normal sulphate of copper contains : Water 36'3 Oxide of copper 32'32 Sulphuric acid 31'38 It may be seen that the verdigris may be used advantageously instead of sulphate of copper in batteries of the Daiiiell class. The more so because the impurities increase the conductivity of the fluid. The verdigris costs about 45 per cent, less than sulphate of copper. More than one hundred thousand kilogrammes per year are produced in Paris (.'. Meynier}. 298 RECIPKS, PROCESSES, ETC. Purification Of graphite (Pelouze and Fre-my). Graphite may be purified by reducing it to coarse powder, and mixing it with about one-fourteenth of its weight of chlorate of potash. The mixture is well mixed with twice as much concentrated sulphuric acid as graphite in an iron vessel, and heated in a sand bath until all the vapours of chlorous gas have ceased ; when cold it is thrown into water and well washed. The washed and dried graphite is then heated red hot; it increases considerably in volume, and falls into a very fine powder. To purify it completely it must be levigated. After this operation it may be considered to be pure graphite suitable for a number of commercial purposes. Magnetic figures may be obtained by placing a piece of -slightly gummed paper over a magnet, and throwing iron filings on to it, and tapping the paper. Much better figures are obtained with sheets of . glass covered with gum, and dried when the figure is formed ; if the glass be exposed to steam the gum softens, and on drying fixes the filings in place ; such glass plates may be used in the magic lantern for lecture ^purposes. \ Soldering Wires (CW%). To solder iron wires together dissolve chloride of zinc (or kill spirits of salts with zinc), add a little -hydrochloric acid (spirit of salt) to clean the wire. The rain soon washes off the excess of chloride of zinc. To solder iron and copper wires together the excess of chloride must be washed off, and the joint covered with paint or resin, or solder with resin. For unannealed wires solder at as low a temperature as possible. The zinc solution, or spirit of salt, should never be used except for overhead out- door lines. All joints in covered wire, whether run underground or above ground, and all joints within doors, either in covered or uncovered wire, should be made with resin. No spirit of salt, either pure or killed with zinc, should ever be allowed in an instrument maker's shop or dynamo factory. Workmen will use it, if not watched. Its presence may often be detected by holding an open bottle of strong solution of ammonia (liquor ammoniae) under a newly made joint, if it becomes surrounded with a slight white cloud or mist, spirit of salt in some form has been used. Joints of guttapercha-co vered wire (Culky}. Exact perfect cleanliness. Eemove the guttapercha for about 4 centimetres, clean the wire with emery paper, twist the wires together for about 2 centimetres, cut the ends off close so as to leave no point sticking out. Solder with resin and good solder containing plenty of tin. The gutta- SOLDER, VARNISH, ETC. 299 percha is then split, and turned back for about 5 centimetres, the soldered joint is covered with Chatterton's compound, and the guttapercha on each side of it is warmed and manipulated until the two sides join. The joint is finished with a hot soldering iron, taking care to smooth it off well, without burning it; it is then covered with another layer of Chatterton's compound. A sheet of guttapercha is then taken, warmed at a spirit lamp, and drawn out carefully so as slightly to diminish its thickness. "Whilst both guttapercha and Chatterton's compound are warm the sheet is laid on the joint, and moulded round it with the t thumb and forefinger. The joint is then trimmed with scissors ; the 3* ft edges kneaded in and smoothed down with a hot iron. When the joint ^S' is cold, another coating of Chatterton's compound is applied, and covered J.-} with a longer and broader piece of sheet guttapercha. The whole is thedKTI covered with a final coating of Chatterton's compound, spread with the*" iron, and polished by hand when cold, taking care to keep the hand well * moistened. It is indispensable to obtain intimate and perfect uniou^l between the new guttapercha and that which covers the wire. A much w neater and cleaner joint can be made by introducing the two wires into a ' little sleeve of tinned iron, fixing it to the wires by compressing it as metal tag is fixed to a lace, and afterwards soldering ; no points are thei left sticking out at the ends of the joint. Temporary joints in gnttapercha-covered A piece of indiarubber tube, fitting tightly to the wire, is slid some distance up one of the wires. The ends of the wires are cleaned, twisted together, and soldered in the usual way, and the indiarubber tubing sli down so as to cover the joint. Solder. Equal parts of lead and tin. Never solder with acids or chloride of zinc in instruments. It is impossible to clean them away, and they finally corrode the metal. Chloride of zinc never dries completely, so that if it gets on to wood or ebonite, it spoils the insulation. All instrument work, and all jointing of covered wire or any kind of wire not freely exposed to rain, should be done with resin. Red varnish. For wood, interior of electro -magnet coils, gal- vanometers, etc., dissolve sealing-wax in alcohol at 90 3 ; apply it with a pencil when cold in four or five coats, until the desired thickness is at- tained. It is better to use many coats than to make the varnish thick. Agglomeration Of wires. A process employed in con- structing coils for high resistance galvanometers. The wire is wound in layers, each one being covered with a pencil with a coating of a cold 300 RECIPES, PROCESSES, ETC. solution of gum copal in ether. It is baked, to dry it. The whole forms a sort of cake of considerable strength and high insulation resistance. Covering of the external wires of large electro- magnets. Large electro-magnets are generally wound with copper wire covered with a double layer of cotton. The outside layer is hardened by painting it with cold thick gum-lac varnish. It is gently roasted before a charcoal brazier. The layer thus formed is extremely hard. It is filed smooth, polished with flax and fine pumice powder, and finally varnished. Cement for induction COilS. The proportions vary very much, but generally approximate to the following formula : Resin 2 parts. Wax 1 For hot countries, slightly increase the proportion of resin. Varnish for Silk. Six parts of boiled oil and two parts of rectified essence of turpentine. Varnish for insulating paper or tracing paper. Dissolve one part of Canada balsam in two parts of essence of turpentine ; digest in a bottle at a gentle heat, and filter before it grows cold. Application of an insulating mixture to the coils of electrical instruments. instructions issued to shops in which instruments are manufactured for the Indian Government, Tele- graph Department (Schwendler}. The empty reels are, first of all, care- fully dried for five hours at a temperature of at leaot 230 F. (110 C.). The moment they are taken from the oven they are plunged into a melted mixture at a temperature of about 350 F. (180 C.) ; this mixture is composed (by weight) of : Yellow wax 10 parts. White wax 1 Bubbles of air appear on each reel after it is immersed. When no more air comes off, the pot is taken off the fire, and allowed to cool very slowly. A little before the mixture sets, the reels are taken out and replaced on the fire so as to allow the excess of mixture to drain away. When they look quite clean they are taken off and cooled. They are now ready to receive the wire. When they have been wound, they are subjected to the same treat- ment, i.e. drying, immersion, and cooling. Practice has shown that the INSULATION OF WIRES. 301 coils must undergo this treatment at least three times in order to ensure their complete penetration by the mixture. Care must be taken during the successive heatings of the coils that the temperature does not rise too high; otherwise the mixture already present would run out instead of soaking into the coil. The drying temperature ought to be kept up to 230 F. (110 C.), and that of the insulating compound slightly diminished at each immersion. No paper should be used between the layers of wire. The evenness of the coil must be obtained by careful winding. Paper diminishes the magnetising effect of the coil, and prevents the composition from penetrating. Summary. It must be borne in mind that : 1. The preliminary drying of the reel and coils is necessary in order to get rid not only of moisture, but also of air, and so facilitate the pene- tration of the mixture. The temperature 230 3 F. (110 D C.) answers this purpose. 2. The immediate immersion of the reels and coils in the melted mixture is necessary in order to prevent the penetration of air and moisture. 3. The slow cooling is intended to make sure that only the mixture penetrates into the coil when contraction by cooling takes place. 4. The reels and coils must remain in the mixture until no more bubbles are formed, this being the only indication showing that the mixture has filled up pores and crevices. Oven. The same oven is used to heat the reels, coils, and mixture. It is formed of several copper receptacles arranged in a box of the same metal. The box is filled with hot oil, which produces a uniform tempera- ture in the receptacles in which the reels and coils are placed ; each receptacle is provided with a tin grating, on which the coils rest to prevent their touching the bottom. The earthen pot containing the mixture is heated directly on the open fire. Insulation of wires for telegraphy and tele- pliony (C. Wiedemami). Prepare a bath of potassium plumbate by dissolving 10 gr. of litharge in a litre of water, to which 200 gr. of caustic potash have been added, and boil for about half-an-hour ; it is allowed to settle, and decanted. The bath is now ready for use. The wire to be insulated is attached to the positive pole of a battery or electroplating dynamo, and dip a small plate of platinum attached to the negative pole also into the bath. The peroxide of lead is formed on the wire, and passes successively through all the colours of the spectrum. The insula- tion becomes perfect only when the wire assumes its last colour, which is a brownish-black. 302 RECIPES, PROCESSES, ETC. This perfect insulation may be utilised for galvanometers or other apparatus. Clark's composition. For covering the sheathing of cables. Mineral pitch 65 parts. Silica 30 Tar 5 It is mixed with oakum in the proportion of one volume of oakum to two of composition. Its density is about 1'62. The weight in kilo- grammes per nautical mile is obtained by multiplying the section in milli- metres by 3. Chatterton's Compound. For cementing together the layers of guttapercha in cable cores, an excellent insulator of fairly low inductive capacity. Stockholm Tar 1 part. Resin 1 ,, Guttapercha 3 ,, Is also used for filling up the interstices of shore-end cables. Its density is about the same as that of guttapercha, but its inductive capacity is less. Insulating 1 cement. The best, according to Harris, is good sealing-wax. Cement for insulators. Sulphur, lead, or plaster of Paris, mixed with a little glue to prevent its setting too rapidly. Muirhead'S Cement. 3 parts of Portland cement, 3 parts of coarse ashes, 3 parts of forge ashes, 4 parts of resin. Black cement. 1 pa,rt coarse ashes, 1 part forge ashes, 2 parts resin. Siemens' cement. 12 parts iron filings or rusty iron, and 100 parts sulphur. Marine glue. Used for battery troughs and generally as an insulating cement used at a high temperature, and, like common glue, with but little in the joint. It will stick together almost all materials, and form a strong joint. As, like pitch, it is a viscous solid and tends to flow, it should not be used thickly. One part of indiarubber is dissolved CEMENTS. 303 in 12 parts of benzine, and 20 parts of lac are added, the mixture being carefully heated. It may be applied with a brush. It is sold commer- cially in a solid form. It may either be redissolved or applied hot, using a rather high temperature and taking care not to allow it to burn, Cement to resist heat and acids. Sulphur ......... lOOpaHs. Tallow .......... 2 Resin .......... 2 ,, Melt the sulphur, tallow, and resin together until they are of a syrupy consistence and of a reddish-brown colour. Add sifted powdered glass until a soft easily -applied paste is produced. Heat the pieces to be joined, and use the cement very hot. Cement used by Gaston Plante for his secondary batteries is run hot on the corks and connecting strips of the secondary cells to prevent the acid from creeping. Turner's cement ........ 1,000 parts. Tallow, or beeswax ....... 100 ,, Powdered alabaster powder ..... 250 ,, Lampblack (to colour it black) . . . . . 2*5 Waterproofing wooden battery cells When the boxes are quite dry and warm, it is smeared over inside with a hot cement, composed of four parts of resin and one part of guttapercha, with a little boiled oil. Note by translator. The addition of boiled oil improves all substances used for this purpose which contain pitch, marine glue, or other viscous solid ; tending to prevent them from flowing. Cement for bone and ivory. A solution of alum, con- centrated to a syrupy condition by heat. Apply hot. Ebonite. Mixture of 2 to 3 parts of sulphur, with 5 parts of indiarubber, kept for some hours at a temperature of 75 C. under a pressure of 4 to 5 atmospheres. May be moulded into any desired shape. An excellent insulator, but becomes porous and spongy under the action of moisture, and loses its properties. To keep vulcanite in good order, it should be occasionally washed with a solution of ammonia, and rubbed with a rag slightly moistened with paraffin oil (Silvanus Thompson"}. 304 RECIPES, PROCESSES, ETC. Watertight decomposition cells for electro- typing* (E. Berthoud^.A. well-made vat of oak may last for twelve or fifteen years, if it be smeared inside with the following composition : Burgundy pitch. 1,500 grammes. Old guttapercha in small shreds . . 250 ,, Finely powdered puinice stone . . . 750 ,, Melt the guttapercha, and mix it well with the pumice-stone. Then add the Burgundy pitch. When the mixture is hot, smear the inside of the vat with it. Lay it on in several coats. Roughness and cracks are smoothed off with a hot soldering-iron. The heat of the iron makes the cement penetrate into the pores of the wood, and increases its adhesion. The vat will stand sulphate of copper baths, but not baths containing cyanide. Turner's cement. Used for fixing together pieces which have to be turned up to the same dimensions. It is thus composed : two- thirds brown resin and one-third beeswax. These proportions must be modified according to the temperature. In summer there must be less wax, and in winter less resin, so as to form a malleable cement, and tenacious enough to resist the friction of the tool on the material, also to resist the heating of the material, which is greater if it be used on a metal mandril. Wooden mandrils (of nutwood, for example) are better for this class of work. It is, however, necessary, when wooden mandrils are used, to pass the tool lightly over them, to make it smooth and of uniform thickness. A practical test of the quality of this substance is *o let a drop of the melted cement drop .on to a piece of metal ; when it is cold, chip it off and bend it between the finger and thumb. If it breaks, it requires the addition of more wax; if it is too plastic, of more resin. Experience alone can guide the workman to the right consistency (Oudinet, Principcs de la construction des instruments de precision"). Composition for cushions of frictional electric machines. Canton advises the use of an amalgam of zinc and tin. Kienmayer gives the following formula : equal parts of zinc and tin ; melt, and add twice the weight of alloy of mercury. When the rubbed plate or cylinder is of vulcanite, the amalgam must be softer than when it is of glass. In France they generally use mosaic gold (bisulphide of tin). The amalgam must be reduced to fine powder, and applied by the aid of a little hard grease. CLEANING COPPER, ETC. 305 Cleaning;, scaling*, and pickling of copper and its alloys. A very important series of operations, in which the surface of objects which are to be electro -plated is made chemically clean, so as to ensure the adhesion of the metallic surfaces : 1. Cleansing from grease. Heat the articles over a slow fire of coal- dust, baker's braise, or, better still, in an oven, up to a dull red heat. Delicate or soldered articles must be boiled in an alkaline solution of caustic potash, dissolved in ten times its weight of water. 2. Scaling. The scaling bath is composed of 100 parts of water, and 5 to 20 parts of sulphuric acid at 66 3 Baume. The articles may generally be dipped in the bath hot. Let them stop in the bath until they take a red- ochre colour. Articles cleaned from grease by caustic potash must be washed and rinsed with plenty of water before scaling. Henceforward the articles must not be touched with the hand. Copper hooks, or, better, glass hooks, should be used ; for very small objects, stoneware or porce- lain dishes. 3. Passing through old strong icater. This is nitric acid, weakened by former use. The articles are left in it until the red layer disappears, so that, when they have been rinsed, they only show a uniform metallic lustre. Rinse. Passing through quick strong water. The articles, after being well shaken and drained, are dipped in a mixture of Nitric acid at 36 (yellow) 100 volumes. Chloride of sodium 1 Calcined tallow (bistre) 1 The articles ought only to remain in the bath for a few seconds. Avoid heating, or the use of too cold a bath. Rinse in cold water. 5. Passing through brightening or mating strong ivater. Articles which are to show a high polish are dipped for one or two seconds (shaking them) in a cold bath of Nitric acid at 36 D 100 volumes. Sulphuric acid at 66 100 Copper salt, about 1 When a mat surface is wanted, the bath is composed of Nitric acid at 36 200 volumes. Sulphuric acid at 66 100 Sea salt 1 Sulphate of zinc 1 to 5 They should be left in the bath for from 5 to 20 minutes, according to the kind of surface required. They must then be washed for some 306 RECIPES, PROCESSES, ETC. time in plenty of water. The articles present an earthy, disagreeable appearance, which disappears on dipping them rapidly in the bright bath, and then rinsing them quickly. 6. Passing through nitrate of mercury. Dip the articles for one or two seconds into a bath of "VVater 10 kilogrammes. Nitrate of mercury 10 grammes. Sulphuric acid 20 ,, Shake before using. The bath should be richer in mercury if the articles are heavy, less rich if they are light. A badly cleaned and scaled article conies out of various colours and without metallic lustre. It is better to throw away a worked-out bath than to refresh it. After passing through the mercury bath, they must be rinsed in plenty of water, and then placed in the silvering or gilding bath. Cleaning articles for nickel-plating: (Gaife). Clean- ing from grease. Rub them with a brush dipped in a thin, hot paste of whitening, water, and carbonate of soda. The cleansing from grease is perfect when the articles are easily wetted by water. Scaling. Copper and its alloys are scaled in a few seconds by dipping them in a bath composed (by weight) of 10 parts of water, 1 part nitric acid. For unfinished articles a stronger bath is required, composed of : water, 2 parts ; nitric acid, 1 part ; sulphuric acid, 1 part. Steel, wrought and cast-iron (polished) are scaled in a bath composed of 100 parts of water and 1 part sulphuric acid. They are left in the bath until they become of an uniform grey colour. They are then rubbed with moistened pumice-stone powder, which lays the metal bare. Unfinished steel, wrought and cast-iron must remain in the bath for three or four hours, then be rubbed with well- sifted powdered stoneware and water. The two operations are repeated until the coating of oxide has completely disappeared. Deposition Of copper on g:laSS. The glass is varnished with a solution of guttapercha in turpentine or naphtha, or with wax dis- solved in turpentine. It is then brushed over with plumbago and put in the bath. The surface of the glass may be roughened by exposing it to the fumes of hydrofluoric acid, but this is rarely necessary. Tempering* of drills and tools for piercing and cutting hard or tempered steel, either in the lathe or machine, when the article can only be finished after it has been tempered, such as saiv-blades, etc. BRONZES. 307 Heat the tool to a cherry-red, then dip it in powdered resin ; replace it in the fire, and repeat the operation two or three times, then throw the tool into water at a temperature of 20' C. To use the tool turn slowly, and take care to keep both tool and work well moistened with essence of turpentine. If these directions be observed a good result can easily be obtained. Take care to give but little bevel to the tool ; if it is a drill, give it the shape of a conventional snake's tongue, like the ace of spades. bronze. A steel bronze can easily be put on copper by moistening it with a dilute solution of chloride of platinum, and slightly heating it. It may also be done by dipping the copper (well cleaned) into an acid solution of chloride of antimony (butter of antimony dis- solved in hydrochloric acid), but the colour is sometimes violet instead of black (Roseleur}. Green or antique bronze. Dissolve 30 gr. of carbonate or chloride of ammonium, 10 gr. of common salt, and the same quantity of cream of tartar and of acetate of copper in 100 gr. of acetic acid at 8 Baume, or 200 gr. of common vinegar, and add a little water. When thoroughly mixed, the solution is daubed over the copper article which is to be bronzed, which is then allowed to dry in the open air for f our-and- twenty or eight-and-f orty hours. At the end of this time it will be found to be completely verdigrised, but in different tints. The article is then brushed all over, and especially on the parts in relief, with a waxed brush, and if necessary the parts in relief are touched with colour. The green parts, which are to be made bluer, may be lightly touched with ammonia, and those where the tint is to be deepened, with carbonate of ammonium (Roseleur}. Medal bronze. The object being well cleaned, a thin paste of red oxide of iron and plumbago is applied with a pencil ; it is then strongly heated ; then when quite cold it is rubbed for a long time in every direction with a softish brush, which is very frequently passed over a piece of beeswax, and then over the mixture of red ochre and plumbago. This process gives a very brilliant reddish bronze, which is very effective on medals. Bronzing: iron. The articles to be bronzed, carefully cleaned, are exposed for about five minutes to the fumes of a mixture of equal parts of hydrochloric and nitric acids. They are then heated to a tempe- rature of 300 to 350 D , until the colour of the bronze becomes visible. After cooling they are rubbed with paraffin, and again heated until the paraffin begins to decompose ; this last operation is repeated six limes. 308 RECIPES, PROCESSES, ETC. If they are now again exposed to the fumes of a mixture of concentrated hydrochloric and nitric acids, tints of pale brown-red are obtained. Adding acetic acid to the other two acids, coatings of oxide of a fine yellow bronze colour are obtained. All gradations of colour from light-brown red to dark-brown red, or from light-yellow bronze to dark- yellow bronze, may be produced by varying the mixture of acids. Professor Oser has covered with oxide by this process some iron rods 1*5 metres long, and he asserts that after six months' exposure to the atmosphere of his laboratory, which is charged with acid vapours, they show no sign of being attacked (Dingier). Preparation of electric-liglit carbons. The problem is how to prepare carbon of higher conductivity than wood charcoal, and which, if not absolutely free from hydrogen, is at least free from all mineral substances. To attain this end three methods may be employed. 1st. The action of dry chlorine on carbon at a white heat. 2nd. The action of fused caustic soda. 3rd. The action of hydrofluoric acid in the cold on carbon cut into pencils immersed in it for some time. The use of chlorine answers perfectly for finely-divided carbon. By the double influence of chlorine and a high temperature the silica, alumina, manga- nese, alkaline oxides, and metallic oxides are reduced and transformed into volatile chlorides, and the hydrogen remaining in the carbon is trans- formed into hydrochloric acid, which is carried off with the chlorides. M. Jacquelain applies this method to solid carbon by directing a stream of dry chlorine for at least 30 hours on to a few kilogrammes of retort carbon cut into prismatic pencils, and heated to a white heat. This first operation leaves the carbon full of cavities, which have to be filled up, in order to restore as far as possible thd original conduc- tivity and feeble combustibility of the carbons; this is attained by submitting them, after the chlorine purifying process, to the action of a hydrocarbon which circulates slowly in the form of vapour for five or six hours over the pencils heated to a white red heat in a cylinder of refractory clay. The vaporisation of the hydrocarbon (heavy coal oil) must go on slowly, so that the decomposition may go on at the highest temperature, and so as to produce but a small deposit of carbon, other- wise all the pencils would be covered with a layer of hard carbon, thick enough to fix them all together into a solid block, and thus render them useless. The action of caustic soda with three equivalents of water fixed in vessels of sheet or cast-iron is more rapid, converting silica and alumina into alkaline silicates and aluminates; by repeated washing with hot distilled water, the alkali, which has soaked in, is removed together with the silicates and aluminates ; then by washing with very SOLUTION FOR CHEMICAL TELEGRAPHS. 309 weak hot hydrochloric acid and water all the iron oxide and earthy bases are removed ; and then a few washings with hot distilled water remove the remaining hydrochloric acid.. The operation of purifying retort carbon by hydrofluoric acid is most simple. The carbon pencils are immersed in hydrofluoric acid, diluted with twice its weight of water, and left for twenty-four to forty-eight hours, at a temperature of 15 to 25' C., in a rectangular covered leaden vessel. They are then washed in plenty of water, and then with distilled water, dried and carbonated for from three to four hours, if the earthy substances removed by the hydrofluoric acid are not in very great quantity. But the use of this acid even when diluted with twice its weight of water requires great care and precaution. Solution for paper for chemical telegraphs. One part saturated solution of ferrocyanide of potassium, one part saturated solution of nitrate of ammonium, two parts water. Translation of the Morse character into letters (Commandant Pereiti).The ingenious diagram below enables the letter corresponding to a Morse sign to be rapidly found. The diagram is thus used : V F U L A P J B X C Y Z QO Fig. 48. Diagram for translating the Morse Alphabet. CH In order to find what letter corresponds to a given sign, starting from the top of the diagram, each line is traced down to a bifurcation, taking the right hand line of each bifurcation for a dash, and the left hand line 310 RECIPES, PROCESSES, ETC. for a dot, and stopping when the dots and dashes are used up. Thus, for example, the signal leads us to the letter d, the signal to the letter/, and so on. Fixing electric bell-wires in houses. Copper wire f Jth of a millimetre in diameter is generally used for the wires from the battery, and wires of ^th or 1 millimetre in diameter for the branches to the pushes. Insulated wire should always be used. One of the best bell- wires is covered with indiarubber, over which is a layer of braided cotton soaked in paraffin ; guttapercha wire is very good, but simple cotton - covered wire is usually all that is wanted ; nothing, indeed, is better in dry places, if it be given a coat of shellac varnish after it is put up. The wires should always be kept an inch or two apart ; it is unadvisable, in passing through walls, door frames, etc. , to put both wires through the same hole, even if guttapercha wire be used. The wires may be fixed with small staples, but care must be taken that these are not hammered in so tightly as to cut through the insulation. Wherever joints have to be made, resin alone should be used for soldering, and the joint be covered with gutta- percha tissue or several coats of shellac varnish. Bells. The best are mounted on bed plates of metal, which avoids the disarrangement of their adjustment, due to the play of wooden frames. They should be fitted with a set screw to prevent the contact screw from getting out of adjustment. They should never be fixed directly to a damp wall; whenever the wall is damp, a slab of wood painted with oil colour should be interposed. Static induction machines. These machines give a continuous current, like batteries and magneto and dynamo machines ; the current is very small, but the electromotive force is vjry high. Thus the ordinary laboratory type of Holtz machine has a constant e. m. f . of about 50,000 volts at all speeds, but the current strength increases in proportion to the speed of rotation; at 120 revolutions per minute its internal resistance is 2,180 megohms, at 450 revolutions it falls to 646 megohms. According to Kohlrausch's experiments the maximum current furnished by a Holtz machine can only decompose '0035 nrcrogramme of water per second, which corresponds to a current strength of about 40 microamperes. Ink for writing on glass. Dissolve at a gentle heat 5 parts of copal in powder in 32 parts of essence of lavender, and colour it with lampblack, indigo, or vermilion. Ink for engraving on glass. Saturate commercial hydro- fluoric acid with ammonia, add an equal volume of hydrofluoric acid, COPPERING BY IMMERSION. 311 and thicken with a little sulphate of barium in fine powder. A metal pen may be used ; the ink bites almost instantaneously. The glass then only requires to be washed in water. Spray producer. A common spray producer, which may be bought at any chemist's for a few pence, is very handy for fixing magnetic figures on gummed paper or glass. Coppering by simple immersion. The following process is often used in order to protect iron and steel articles from rust, and give them the appearance of copper, when it is not required to obtain a lasting deposit or perfect adhesion. Prepare the articles by brushing them hard with petroleum, and wiping them in hot sawdust, then dip them for one minute only into a saturated solution of sulphate of copper, to which half its volume of acidulated water has been added. Take them out and wash them quickly by dipping them in boiling water and wiping them with hot sawdust. Very small articles can often be coppered by rubbing them well in sawdust well moistened with an acidulated solution of sulphate of copper. Another process, which is especially suited for cast-iron articles, consists in using a solution of 10 parts nitric acid, 10 parts chloride of copper, and 33 parts of hydrochloric acid. The articles are dipped several times, and wiped after each immersion with a woollen rag. When iron wire is thus coated it should be afterwards re-drawn so as to consolidate the layer of copper, and make it adhere better. . To coat large articles such as statues, candelabra, etc., the following solution is used : Water 25 litres. Potassic tartrate of soda 8 kilog. Caustic soda 3 ,, Sulphate of copper 1'25 ,, The mixture is carefully stirred, and time given for the complete solution of the ingredients ; the articles should be dipped in the solution by zinc wires. The work goes on slowly. Five hours are required for a uniform deposit. After being taken out of the bath the articles are carefully washed and dried (H. Fontaine}. 312 BIBLIOGRAPHY OF THE PRINCIPAL WORKS CONSULTED BY M. HOSPITALIER. PEEIODICALS. Annales telegraphiqiies. La lumiere electrique. L'Elec- tricien. L' ' Electricite. Bulletin de la Societe franc,aise de physique. Journal de physique. Annales de physique et de chimie. Comptes rendux de V Academic des sciences. Revue scientijique. Revue industrielle. La Nature. Le Genie civil. Journal telegraphique. Archives des sciences physiques et naturelles de Geneve. Telegraphic Journal and Electrical Review. Journal of the Society of Telegraph Engineers and Electricians. The Electrician. Philosophical Magazine. Proceedings of the Royal Society. Nature. Engineering. The Engineer. Elektrotechnische Zeitschrift. Centralblatt fur Elcktrotechnik. GENERAL TREATISES. Traites de physique, by Jamin, Daguin, Angot, Ganot. Traite d'electricite, by De La Rive. Traite d' electricite et de magnetisme, by A. -C. Becquerel. Traite d' electricite et de magnetisme, by J. G. H. Gordon (French translation by M. J. Raynaud). Traite d'elec- tricite statique, by M. Mascart. Traite d' electricite et magnetisme, by MM. Mascart and Joubert. Traite pratique d'electricite, by C. M. Gariel. Cours d' electricite, by E. Duter. Recherches sur Velectricite, by M. G. Plante. Electricity and Magnetism, by J. Clerk-Maxwell. Elec- tricity and Magnetism, byFleeming Jenkin. Elementary Lessons in Elec- tricity and Magnetism, by Silvanus Thompson. The Student's Text-book of Electricity, by Noad and Preece. Electricity, by Dr. Fergusson. Magnetism and Electricity, by Dr. Guthrie. UNITS. Grandeurs electriques, by E. Blavier. Units and Physical Constants, by Everett. Expose sommaire de la mesure electrique en unites absolues, by J. Raynaud. Sur la mesure pratique des grandeurs electriquex, by W. H. Preece. Les mesures electriques, by T. Rothen. Reports of the Committee on Electrical Standards of the British Association, edited by Fleeming Jenkin. BIBLIOGRAPHY. 313 INSTRUMENTS AND METHODS or MEASUREMENT. Manuel d'electro- metrie industrielle, by R. V. Picou. Electric Testing, by H. K. Kempe. Testing Instructions, by Schwendler. Epreuves electriques des cables telegraphiqucs, by W. Hoskiaer. APPLICATIONS. Expose des applications de Velectridte, by Th. du Moncel. Les principales applications de V electricite, by E. Hospitaller. Z' 'electridte et ses applications, by H. de Parville. Electricity : its Theory, Sources and Applications, by JohnT. Sprague. Traite de la pile electrique, by A. Niaudet. Traite theorique et pratique des piles electriques, by A. Cazin and A. Angot. Guide pratique du doreur, de Vargenteur et du galvanoplaste, by A. Roseleur. Electro- Metallurgy, byG. Gore. Electro- plating, by Urquhart. Machines electriques, by A. Niaudet. Die Magnet und dynamo-elektrischen Maschinen, by Dr. H. Schellen. ISelec- tricite comme force motrice, by Th. du Moncel and Frank -Geraldy. Electric Transmission of Poivcr, byPaget Higgs. Eclairage a V 'electridte, by H. Fontaine. IS eclair age electrique, by M. Th. du Moncel. La lumiere electrique, by Alglave and Boulard. Electric Illumination, by J. Dredge. Electric Lighting, by Sawyer, Schoolbred. Traites de tele- graphic electrique, by MM. Mercadier, Blavier, Th. du Moncel, Breguet, Gavarret. Le siphon-recorder, by Ternant. Systemes telegraphiques, by Ch. Bontemps. Electricity and the Electric Telegraph, by G. B. Prescott. Manuel de telegraphic pratique, by R. S. Culley. ANNUALS, POCKET-BOOKS, AND TABLES. Electrical Tables and For- mulce, by Latimer Clark and Robert Sabine. Annuaires du bureau des longitudes et de Vobservatoire de Montsouris. Agendas du chimiste, des posies et telegraphes, d'Oppermann. Garnet de Voffider de marine. Rules and Tables, by Rankine. Formulaire de Vinyenieur, by Ch. Armengand. VARIOUS. Comptes rendus des travaux du Congres international des electriciens. Proces-verbaux de la reunion Internationale des electriciens. Les phares electriques, by E. Allard. Note sur les appareils photo- electriques employes par les marines militaires, by MM. Sautter and Lemouuier, etc., etc. Dept. Meeli, Bng. INDEX TO TABLES. Acceleration due to gravity and the length of the seconds pendu- lum, Values of, 36. Area, Units of, 35. Ayrtou arid Perry's motors, 251. B. Barometer, Mean height of, 155. Batteries, Constants and work of some known forms, 203. , E.m.f. of amalgams of potassium of zinc, 200. , of Grove's cell, 200. , of some two-fluid cells, 202. , of various, 201. , Porous pot, 192. - , Testing, 206. Birmingham wire gauge, 172. Bronze-phosphor and silicium, Pro- perties of, 177. Brush machine, 242. Burgin machine, 242 C. Caudles, electric, Tests of, 268. Capacities, Specific inductive, ] 79. Capacity, Units of, 34. Carbon (Cylindrical), resistance r er metre, 165. Carbons, Experiments with bare and plated, 264. Chemical and electro-chemical equi- valents, 212. Coefficients of expansion of some solids, 157. Conductivity (relative) of copper, 163. of metals, 164. of solutions, 166. Conductors, Diameter and resistance of some, 178. , Loss of energy in, 227. Copper, Conductivitj r (relative) of, 163. , Eesistance of pure, at C., 174. sulphate, Densities of solutions of, 155. , Specific resistance of, 167. Current strength, Units of, 46. D. Densities of solutions of common salt, 154. of copper sulphate, 155. of nitric acid, 153. of zinc sulphate, 153. Diamaguetic substances, 180. Diameter and resistance of some con- ductors, 178. Duprez's experiments, 256-7. Dynamo-electric machines : Brush, 242. Burgin, 242. Edison, 240. Edison-Hopkinson, 241. Elphinstone-Vincent, 242. Ferranti-Thomson, 243. Gramme, 178. 316 THE ELECTRICIAN'S POCKET-BOOK. Dynamo-electric machines (contd.) : Gulcher, 237. Beinrichs, 237. Meritens, 244. Schnckert, 238. Siemens, 237, 240, 243. Dynamo- electric machines, Size of wire for, 235. machines. (See also Machines.) E. Ed'son-Hopkinson machine, 241. Edison's lamp, 271. machine, 240. Electrical resistance, Units of, 45. Electric candles, Tests of, 268. light carbon, Resistance of, 165. Electrification, Influence of length of time of, 170. Electro-chemical equivalents, 212. magnetic units, 41. E.m.f. of amalgams of potassium and zinc, 200. of some two-fluid cells, 202. of various cells containing only one electrolyte, 201. Electrotyping : coppering baths, 218. , weight of deposit per hour and strength of current, 217, 221. Elphinstone- Vincent machine, 242. Energy, heat, and work, Units of, 51. , Loss of, in conductors, 227. F. Ferranti-Thomson machine, 243. Force and weight, Units of, 38. French and English units of length, 33. units of volume and capacity, 34. G. Gases and vapours, Specific gravity of, 154. Geometrical formulae, 137. Gramme and Siemens motors, 251. machine, 236. and projectors used in the French navy, 267. Gravities, Specific, 148-152. Grove's cell, E.m.f. of, 200. Gulcher machine, 237. H. Heat disengaged by the combination of gramme with chlorine, 159. by the oxydation of gramme , 159. , work, and energy, Units of, 51. Heinrichs machine, 237. J. Jauge carcasse, 173. Lamps, incandescent Edison, Tests of, 271-2. , Tests of, 272. , Tests of Siemens and Halske's, 272. (See Edison, etc.) Length, Units of, 33. Logarithms, 135-6. M. Machines and lamps, Tests of con- tinuous current, 266. (See Dynamo-electric machines.) Magnetic substances, 180. Melting and boiling points of common substances, 158. Meritens machine, 244. Metals, Conductivity of, 164. Motors, Ayrton and Perry's, 251. Gramme and Siemens, 251. INDEX TO TABLES. 317 N. Nitric acid, Densities of solutions of, 153. , Resistance of, 167. Numbers, their reciprocals, etc., 131. P. Phosphor-bronze, Properties of, 177. Polygons, Radii and areas of regular inscribed, 138. Pressure, Units of, 50. R. Radii and areas of regular inscribed polygons, 138. Relay, Schweudler's experiments on a Siemens polarised, 285. Resistance : List of common bodies in order of decreasing conduc- tivity, 161. of common metals and a^oys, 162. of cylindrical carbons per metre, 165. of nitric acid, 167. of solutions of copper sulphatp, 167. of fculphuric acid, 167. of zinc sulphate, 168. of wires of pure annealed copper at C., 174. , Specific, of water and ice, 168. , Strength of received currents and equivalent insulation re- sistances, 278. , Units of, 45. . (See also Conductors.) S. Salt, common, Densities of solutions of, 154. Schuckert machine, 238. Siemens machines, 239, 240, 213. and Halske's incandescent lamps, Tests of, 272. Silicium bronze, 177. Sines and tangents, 139. Solders, 294. Solids, Cubic coefficients of expan- sion of, 157. Solutions, Conductivity of, 166. Specific gravities, 148-152. gravity of gases and vapours, 154. inductive capacities, 179. Submarine cables, Details of some, 282. Subterranean cables with seven con- ductors, 280. Sulphuric acid, Specific resistance of solutions of, 167. T. Temperature, 158. , Measurement of, 156. (See Melting and boiling points of common substances.) Temperatures, Determination of high, 157. Testing batteries, 203. Tests of continuous current machines and lamps, 266. Thermo-electric powers for calcula- ting, 225. Thermometer, 49. scales, Fahrenheit and Centi- grade, 156. Transmission of power, 254. , Duprez's experiments, 256-7. Triangles, Solution of, 142. Trigonometrical formulae, 140. U. Units, Electro-magnetic, 41. of area, 35. of current strength, 46. of electrical resistance, 45. of energy, heat, and work, 51. 318 THE ELECTRICIAN'S POCKET-BOOK. Units of length, 33. of pressure, 50. of volume and capicity, 34. of weight and force, 38. of work, 39. V. Values of the acceleration due to gravity and the length of the seconds pendulum, 36. Volume and capacity, Units of, 34. W. Water and ice, Approximate specific resistances of, 168. Weight and force, Units of, 38. Wire-gauge, Birmingham, 172. jauge carcasse, 173. , Size of, for dynamo-electric ma- chines, 235. Work, heat, and energy, Units of, 51. , Units of, 39. Z. Zinc sulphate, Densities of solutions of, 153. , Specific resistance of solu- tions of, 168. fOJUTBKSITT; 03T UNIVERSITY OF CALIFORNIA i BERKELEY Books not returned on time are ; per volume after the ^third^ day is made before expiration of OCT 1 period. 1955 LU 20m-ll,'20 n UNIVERSITY OF CALIFORNIA LIBRARY I m m