IN MEMORIAM 
 FLOR1AN CAJOR1 
 
ELECTRICITY 
 TREATED EXPERIMENTALLY 
 
ELECTRICITY 
 
 TREATED EXPERIMENTALLY 
 
 FOR THE USE OF SCHOOLS AND STUDENTS 
 
 BY 
 
 LINNAEUS GUMMING, M.A. 
 ii 
 
 LATE SCHOLAR OF TRINITY COLLEGE, CAMBRIDGE 
 ASSISTANT MASTER IN RUGBY SCHOOL 
 
 THIRD EDITION 
 
 LONDON 
 LONGMANS, GREEN, AND CO. 
 
 AND NEW YORK : 15 EAST i6TH STREET 
 1891 
 
PREFACE 
 
 THE author has endeavoured in this work to give the 
 substance of experimental lectures delivered to some of 
 the senior boys in Rugby School. 
 
 The course lasts for one school year, consisting of about 
 seventy lessons, each of one hour. Of these about ten 
 are devoted to testing the progress of the boys. 
 
 These lessons are educational, not technical; accord- 
 ingly, ample explanation and numerous experiments are 
 devoted to the principles of the science, while many appli- 
 cations claim but the briefest notice. 
 
 In every part of the subject quantitative measurement 
 has been kept in view, and attention has been directed 
 to the absolute system of measurement. 
 
 To understand certain instruments it is necessary to 
 assume results obtained from theory. Articles in which 
 such assumptions are made are marked with an asterisk (*), 
 and may be passed over at the teacher's discretion. It is 
 probably wiser, where possible, to defer them till the 
 learner has gained some acquaintance with the theory, 
 such as is afforded by the present author's Introduction 
 to the Theory of Electricity. 
 
 It is assumed that, in teaching the subject, the appa- 
 ratus is before the student, and not a mere diagram 
 
 91 S2B8 
 
vi Preface. 
 
 Articles referring to a few rather expensive pieces of 
 apparatus have been marked with an asterisk, to suggest 
 that they may be passed over in the absence of the 
 apparatus. 
 
 Every experiment described has been performed by the 
 author before his class with the apparatus shown, except 
 in cases where reference is made to an historical experi- 
 ment, not suited for class demonstration, or requiring 
 instruments of higher power than those commonly in 
 use. 
 
 The author wishes to record his thanks to his wife, and 
 to G. C. Eichards, Esq., of Balliol College, Oxford, who 
 have made drawings, from the apparatus actually in use, 
 for the woodcuts. His thanks are also due to his col- 
 league, G. Stallard, Esq., who has read the whole of the 
 proof-sheets and the MSS. of the portions referring to 
 Chemical Science, making many valuable corrections and 
 suggestions. 
 
 The numerical data are chiefly taken from S. Lupton's 
 Numerical Tables and Constants, a most valuable small 
 
 work of reference. 
 
 L. GUMMING. 
 
 RUGBY, 1886. 
 
PREFACE TO THIRD EDITION. 
 
 THE demand for a new Edition of this little work has 
 enabled the Author to make slight additions and altera- 
 tions which, he trusts, will bring the book more up to 
 date. Eemembering the advance during the last few 
 years in practical electricity, it is no wonder that what 
 was written nearly ten years ago fails to represent pre- 
 sent knowledge. A few Articles have been added on the 
 modern Dynamo, in which free use has been made of 
 Professor Sylvanus Thompson's work on Dynamo-Elec- 
 tricity. The Author wishes to record his thanks to Pro- 
 fessor Thompson, who in the kindest way gave him 
 permission to use a considerable number of diagrams 
 from that work. 
 
 L. GUMMING. 
 
 KUGBT Oct. 10, 1891. 
 
CONTENTS 
 
 BOOK I MAGNETISM. 
 CHAPTER I. MAGNETS. 
 
 [Pages 1-12.] 
 
 Definition of Magnetism Magnet Poles North and South Poles of a 
 Magnet Action of Magnetic Poles on each other Magnetism in- 
 duced in Soft Iron Induction by Induced Magnetism Steel 
 under Induction Hypothesis of Magnetized Molecules Magnetic 
 Substance. (SECT. 1 to 9.) 
 
 CHAPTER II. FIELD OF MAGNETIC FORCE. 
 
 [Pages 13-33.] 
 
 Definition of a Field of Magnetic Force Magnetic Force on a Pole at 
 a Point Lines of Force Strength of Magnetic Field of a Single 
 Pole, by Coulomb's Balance Strength of Field by the Method of 
 Oscillations Strength of Magnetic Field by Method of Devia- 
 tions Comparison of Strength of two Magnet Poles ^Meaning of 
 an Absolute System of Measurement * Absolute Unit of Magnetism 
 Theories suggested by Experiment. (SECT. 10 to 19.) 
 
 CHAPTER III. METHODS OF MAGNETIZATION. 
 [Pages 34-38.] 
 
 Quality and Temper of Steel Method of Single Touch Method of 
 
 Divided Touch Method of Double Touch Magnetic Battery 
 
 Magnetic Saturation Retention of Magnetism. (SECT. 20 to 26.) 
 
Contents. 
 
 CHAPTER IV. TERRESTRIAL MAGNETISM. 
 
 [Pages 39-66.] 
 
 Field of Terrestrial Magnetic Force Magnetic Elements of a Place 
 The Declinometer The Dipping Needle The Intensity *Gauss' 
 Method for Finding Intensity * Magnetic Moment of a Magnet 
 in Absolute Measure Magnetic Elements of Greenwich Changes 
 in Elements Variations in Declination Relation to Aurora 
 Borealis and to Solar Phenomena Other Variations Magnetic 
 Charts Isoclinal Chart Isodynamic Chart Isogonic Chart 
 Hypotheses of one or two Magnets The Mariner's Compass Effect 
 of iron masses in Ships Semicircular Variation Quadrantal 
 Varaition Magnetism of Steel-plated Ships Questions on Book I. 
 (SECT. 27 to 48.) 
 
 BOOK II. FKICTIONAL ELECTEICITY. 
 
 CHAPTER I. ELECTRIFICATION. 
 
 [Pages 67-80.] 
 
 Definition of Electricity Means of detecting Electricity Action of 
 Electrified Bodies on each other Vitreous and Resinous Elec- 
 tricity Conductors and Non-ConductorsEffect of Damp or Dry 
 Atmosphere Gold-Leaf Electroscope Development of the two 
 Electricities, simultaneous and in equal quantities The Electrical 
 Series Electrification by Pressure and Cleavage Pyro-Elec- 
 tricity. (SECT. 49 to 59.) 
 
 CHAPTER II. THE FIELD OF ELECTRIC FORCE. 
 [Pages 81-99.] 
 
 The Electric Field Coulomb's Torsion Balance Law of Action at 
 different Distances Law of Action with different Quantities 
 *Absolute Measure of Electricity Use of Proof Plane No 
 Electricity within a hollow Conductor Electrical Density 
 Cavendish's Proof of the Law of Inverse Squares Electrical 
 
Contents. xi 
 
 Potential Capacity of a Conductor Potential Experiments with 
 the Gold-Leaf Electroscope Electrical Force requires varying 
 Potential. (SECT. 60 to 71.) 
 
 CHAPTER III. ELECTRICAL INDUCTION. 
 [Pages 100-123.] 
 
 Electrification induced on an Insulated Conductor Induction on 
 a Body connected with the Earth Electroscope charged by 
 Induction Faraday's Ice-pail Experiment The Earth our Zero 
 of Potential *Potential in Absolute Measure * Absolute Measure 
 of Potential at a Point in the Field *Equipotential Surfaces 
 * Application to a Sphere Electrification of two Parallel Plates, 
 one initially charged The Leyden Jar Volta's Condensing 
 Electroscope *Discharge by Alternate Contacts Specific Induc- 
 tive Capacity Condition of the Dielectric in a Leyden Jar 
 Faraday's Theory of Induction. (SECT. 72 to 87.) 
 
 CHAPTER IV. ELECTRICAL MACHINES. 
 [Pages 124-151.] 
 
 The Cylinder Machine The Plate Machine The Electrophorus 
 The Voss Machine *The Holtz Machine Experiments with the 
 Electrical Machine Experiments with a Leyden Jar Battery 
 Chemical Decompositions by the Machine discharge. (SECT. 88 
 to 95.) 
 
 CHAPTER V. ABSOLUTE MEASURE OF ELECTRICITY. 
 [Pages 152-173.] 
 
 The Unit Jar, and Experiments with it *Theory of Thomson's Elec- 
 trometers *The absolute Electrometer *The Portable Elec- 
 trometer *The Quadrant Electrometer *The Gauge *The Re- 
 plenisher * Arrangements of the Electrometer ^Experiments 
 with the Quadrant Electrometer Questions on Book II. (SECT. 
 96 to 103.) 
 
xii Contents. 
 
 BOOK III. VOLTAIC ELECTEICITY. 
 CHAPTER I. THE BATTERY. 
 [Pages 174-194.] 
 
 Electrical Conditions of a Zinc-Copper Couple Chemical Conditions of 
 the Cell Thermal Condition of the Cell Source of Energy of the 
 Current Local Action Action of Evolved Hydrogen Smee's 
 Cell The Bichromate Cell Daniell's Cell Grove's and Bunsen's 
 Cells Leclanche's Cell Latimer Clark's Cell Becquerel's Cell 
 Electromotive Force Battery arranged in Simple Circuit 
 Battery arranged in Compound Circuit Frictional Electricity 
 obtained from a Battery Comparison of Frictional with Voltaic 
 Electricity Dry Piles. (SECT. 104 to 122.) 
 
 CHAPTER II. ELECTROLYSIS. 
 [Pages 195-219.] 
 
 Phenomena of the Current Direction of the Current Electrolysis of 
 Potassium Iodide Electrolysis of Water Electrolysis of Hydrogen 
 Chloride Secondary action in Decomposition of Sulphates, etc. 
 Potassium set free by Electrolysis Faraday's Terminology for Elec- 
 trolysis Quantity of Ions separated by the same current Electro- 
 Chemical Equivalents Battery obeys the Laws of Electrolysis 
 E.M.F. necessary for Electrolysis *E.M.F. measured thermally 
 Hypothesis of Molecular Electrification Grotthiis' Hypothesis 
 Polarisation of Electrodes Grove's Gas Battery, and Ritter's 
 Secondary Pile Polarisation the test of an Electrolyte Plante's 
 and Faure's Cells Electro-metallurgy Nobili's Rings The Lead 
 Tree. (SECT. 123 to 144.) 
 
 CHAPTER HI. OHM'S LAW. 
 
 [Pages 220-256. J 
 
 Ohm's Law Measurement of Resistance *Potential Gradient- 
 Oersted's Experiment: Galvanometers The Tangent Galvano- 
 meterSine Galvanometer Astatic Galvanometer The Mirror 
 
Contents. xiii 
 
 Galvanometer Magnetic action of a Current in a Liquid Units 
 employed in Voltaic Electricity Illustrations of Ohm's Law 
 Experimental Determination of Battery Resistance Resistance of 
 the Galvanometer To find the Resistance of a given Wire Coil 
 Relation of Resistance to Dimensions of Conductor: Specific 
 Resistance Application of Ohm's Law to Simple Circuit 
 Application of Ohm's Law to a Compound Circuit Application 
 of Ohm's Law to a Mixed Circuit * Arrangement of Battery for 
 the Greatest Current Method of changing rapidly the Battery 
 arrangement Measurement of E.M.F. by Galvanometer Laws 
 of Divided Currents Galvanometer Shunts Thermal Effects of a 
 Current in the Conductor *Measure of Heating Effect. (SECT. 
 145 to 169.) 
 
 CHAPTER IV. WHEATSTONE'S BRIDGE. 
 [Pages 257-265.] 
 
 *Theory of the Bridge *Use of the Bridge to find the Resistance of a 
 Coil *Method of Finding Galvanometer Resistance *Method of 
 Finding Battery Resistance *Method of Comparing the E.M.F. of 
 Cells. (SECT. 170 to 174.) 
 
 CHAPTER V. ELECTRO-MAGNETISM AND ELECTRO- 
 DYNAMICS. 
 
 [Pages 266-324.] 
 
 Bertins' Commutator Magnetic Field of a Straight Current Rotation 
 of a Magnet Pole round a Current Rotation of a Current round 
 a Magnet Pole Movement of Current in a Magnetic Field 
 Methods of Suspending Currents Effects of Terrestrial Mag- 
 netism on Moveable Currents Magnetic Properties of a Closed 
 Circuit carrying a Current *Distinction between a Voltaic Circuit 
 and a Magnetic Shell * Absolute Electro-magnetic Units Attrac- 
 tions and Repulsions of Parallel and Inclined Currents (Electro- 
 Dynamics) Action of an Infinite Current on another wholly on 
 one side Equivalence of a Sinuous and Straight Current *The 
 
xiv Contents. 
 
 Magnetic Field inside a Solenoid Electro-Magnets Paramagnetic 
 and Diamagnetic Substances Electro -magnetic Toys Electro- 
 motorsThe Electric Bell The Electric Telegraph The Line for 
 Land or Marine Telegraph The Battery The Single Needle 
 Telegraph Communicator The Single Needle Indicator Arrange- 
 ment of Apparatus at Telegraph Station Codes of Telegraph 
 Signals *The Morse Key *The Morse Indicator *The Morse 
 Relay *The Morse Sounder ^Electrostatic Induction in Cables 
 *Thomson's Marine Galvanometer * Thomson's Syphon Recorder 
 *Step by Step, or ABC Telegraph Telpherage * Ampere's 
 Theory of Magnetism The Magnetic Tick. (SECT. 175 to 210.) 
 
 CHAPTER VI. CURRENT INDUCTION. 
 [Pages 325-382. J 
 
 Work done in the Electro-Magnetic Field at expense of the Current 
 Theoretical Explanation of foregoing Experiment Induced Cur- 
 rents Induced Currents in a Wire Coil moving in a Magnetic 
 Field The Extra Current or Galvanic Spark Lenz's Law Cur- 
 rents induced in Solid Conductors moved in the Magnetic Field 
 Dead Beat Galvanometer Magneto-Electric Machines The Dy- 
 namo Continuous Current Machines Field Magnets Armatures 
 The Gramme Machine Alternating Current Machines The 
 Incandescent Electric Lamp The Arc Lamp Source of the 
 Voltaic Arc Arrangement of Lamps Theory of Self -regulation 
 of Lamps in Parallel Induction Coils Experiments with the 
 Induction Coil Discharge through rarefied Gas Graham Bell's 
 Telephone The Microphone Experiments on the Magnetic 
 Circuit Ammeters and Voltmeters Transmission of Electrical 
 Power : Transformers Questions on Book III. (SECT. 211 to 235.) 
 
 BOOK IV. THEEMO-ELECTEICITY. 
 
 [Pages 383-395.] 
 
 Definition of Thermo-Electricity Elementary Experiments The 
 Thermopile Thermo-electric Power and Diagram E.M.F. of 
 
Contents. xv 
 
 Thermo-electric Currents Thermo-electric Diagrams for Higher 
 Temperatures Thermo-electric Currents in Circuits of one Metal 
 *The Peltier Effect *Theoretical Measure of the E.M.F. of a 
 Thermo-electric Couple *The Thomson Effect Thermo-electric 
 Batteries Questions on Book IV. (SECT. 236 to 246.) 
 
 APPENDIX I. ABSOLUTE UNITS IN C.S.G. 
 SYSTEM. 
 
 [Pages 397-404.] 
 
 Units and Measures Fundamental Units Mechanical Units. (SECT. 
 247 to 249.) 
 
 APPENDIX II. 
 
 [Page 405.] 
 Table of Natural Sines and Tangents of Angles for each Degree. 
 
BOOK I. 
 MAGNETISM. 
 
 CHAPTER I. ; . r : 
 MAGNETS. 
 
 I. Definition of Magnetism. Magnetism is defined 
 as the property of attracting small masses of iron, possessed 
 by various compounds of iron which are called Magnets. 
 The ancients were acquainted with this property in a certain 
 iron ore obtained from Magnesia, in Asia Minor, whence the 
 name Magnetism is derived. This magnetic iron ore, or 
 Magnetite (denoted by the chemical formula Fe 3 4 ), occurs 
 very widely disseminated through the earth, and in various 
 parts, as in Sweden, forms massive beds, which are a very 
 valuable source of iron. Though always acted on powerfully 
 by other magnets, it does not itself always possess magnetic 
 power. The most powerful native magnets are obtained from 
 Siberia and from the Hartz Mountains. These magnets are 
 usually called natural, to distinguish them from artificial mag- 
 nets, which are made of tempered steel, magnetised either by 
 rubbing with a natural magnet, or by one of a variety of 
 methods described hereafter. These are in the form of 
 straight, rectangular or lozenge-shaped bars, or else of bars 
 bent into a horse-shoe form. 
 
Electricity. 
 
 [Book I. 
 
 2. Magnet Poles. If a natural magnet be sprinkled 
 with iron filings, the filings are observed to cling more abun- 
 dantly on two opposite faces than elsewhere. In the case 
 
 of a bar 'raa.grietj as in the figure, the iron filings remain 
 clinging onfy fco 'the ends, and to parts very near to the ends. 
 ! TJ^; '0)1(1$; of <t]fe bajr, in which the magnetic power seems 
 to be'coricentfateoi, are spoken of as the poles of the magnet. 
 The straight line drawn from pole to pole is the axis of the 
 magnet, and the plane which bisects the axis at right angles 
 is its equatorial plane, or equator. 
 
 3. North and South Poles of a Magnet. If either 
 a natural or artificial magnet be poised on a point, or sus- 
 pended by a silk fibre in a paper stirrup (Fig. 2), so as to 
 be free to move in a horizontal 
 plane, it will be observed always 
 to come to rest with its axis in a 
 certain definite direction. 1 Except 
 in very high latitudes, one (and 
 always the same) pole will point 
 more or less towards the north, and 
 the other towards the south. This 
 property leads us to a convenient 
 mode of distinguishing the two poles 
 of a magnet, calling that which is 
 directed towards the north the north (or better, the north- 
 
 1 This direction is called the Magnetic Meridian. 
 
chap, i.] Magnets. 
 
 pole and the opposite, the south or south-seeking 
 pole. They are also sometimes distinguished as blue and 
 red poles, or as positive and negative poles. This con- 
 stancy of direction in a freely-suspended magnet has led to 
 its use in Europe since the twelfth century, and from much 
 earlier times by the Chinese, for directing the course in navi- 
 gation. On this account the magnet is called the loadstone 
 (more correctly spelt lodestone), from an Anglo-Saxon word 
 denoting to lead. The poles in bar magnets are distinguished 
 by engraving either a line or the letter "N"near the north 
 pole (Fig. 3). 
 
 ( 3 *.\ 
 
 FIG. 3. 
 
 4. Action of Magnetic Poles on each other. We 
 
 have seen that the poles of a magnet differ from each other 
 in their behaviour under the action of the earth. We now 
 naturally inquire what is the action of the poles of two dif- 
 ferent magnets on each other. Suspend one magnet freely, 
 having marked its poles ; approach towards its poles (Fig. 4) 
 in succession one (say the north) pole of another magnet. 
 When the north pole is presented towards the north pole of 
 the suspended magnet it will be repelled, and if presented 
 towards the south pole it will be attracted. If, on the other 
 hand, the south pole be presented to the north pole of the 
 suspended magnet it will be attracted, and if the south pole 
 be presented to the south pole it will be repelled. Hence we 
 
Electricity. 
 
 [Book I. 
 
 learn that while both poles have the same power of attracting 
 soft iron, they behave in opposite ways towards the poles of 
 another magnet like poles repelling, but unlike poles attract- 
 
 FIG. 4. 
 
 ing each other. This property affords a delicate means of 
 detecting feeble magnetization. A long light magnet, sup- 
 ported in a paper stirrup and suspended by a few fibres of 
 cocoon silk (see Fig. 2), is easily deflected from its normal 
 direction. If on presenting the same part of a body to the 
 alternate ends we find one pole attracted and the other re- 
 pelled, we may conclude that the body is magnetized, the 
 magnet's behaviour towards it showing the name of the pole 
 used. 
 
 5. Magnetism induced in Soft Iron. If we take a 
 bar of annealed or soft iron and present it to the pole of a 
 
 \Svfbiron 
 
 PIG. 5. 
 
 magnet, the magnet, if sufficiently powerful, will pick it up 
 and support its weight, If while one end adheres to a pole 
 
chap, i.] Magnets. 
 
 of the magnet the other end be dipped in iron filings, they 
 will be found to cling to it, just as if it were a magnet 
 (Fig. 5). On removing the magnet the iron filings will 
 nearly all instantly fall off. This magnetism, which exists 
 temporarily in soft iron when in contact with a magnet, is 
 called induced magnetism, the magnet on whose influence it 
 depends being called the inducing magnet. It will be found 
 that actual contact is not necessary, as magnetism is induced 
 in the iron when the magnet is not in actual contact, but at 
 a considerable distance from the bar. The distribution of 
 induced magnetism is easily seen to be exactly similar to that 
 of ordinary magnetism in the magnet ; for if the iron under 
 induction of a magnet pole, at a small distance from one of its 
 
 1C 
 
 SOFT IRON 
 
 FlG. 6. 
 
 ends, be sprinkled with iron filings and be lifted up, the iron 
 filings will cling near the ends and fall off near the middle 
 (Fig. 6). It might easily be inferred from the attraction of 
 the magnet pole for the iron bar, that the pole nearest to 
 the inducing pole is of opposite name and the more remote 
 pole of the same name. That this is the case may be shown 
 (Fig. 7) by presenting one end of a long bar of soft iron (A) 
 to the north pole of a suspended magnet (B), placed at such a 
 distance as to produce merely a slight attractive deflection 
 from MM', the Magnetic Meridian. On presenting the north 
 pole of a magnet (C) to the more remote end of the iron bar, 
 the former attraction becomes a strong repulsion. This might 
 apparently be due to the repulsive action of the north pole (C) 
 itself, but on removing the iron bar (A), keeping the magnet 
 
Electricity. 
 
 [Book I. 
 
 (C) in position, the suspended magnet will fall back almost 
 into its normal position. The large magnet (D) is placed to 
 steady the movements of the suspended needle in the experi- 
 ment. These two experiments prove that, under induction 
 of a magnet pole, the part of a soft iron bar nearest to the 
 inducing pole acquires polarity of opposite name, while the 
 part farthest away acquires polarity of the same name. This 
 
 FIG. 7. 
 
 can be illustrated by observing the behaviour, under induc- 
 tion, of pieces of iron of various shapes, with one or more 
 magnet poles variously disposed round them. If, for ex- 
 ample, a north magnet pole be presented to the middle of 
 a bar, the central part becomes a south pole, and each of 
 the ends a north pole (Fig. 8). If presented to the base of a 
 piece of iron shaped like the letter Y, the extremities of the 
 
Chap. I.] 
 
 Magnets. 
 
 fork become north poles. If presented to the centre of a star- 
 shaped piece of metal (Fig. 9), each point becomes a north 
 pole. The disposition of the poles is at once seen on dipping 
 
 FIG. 8. FIG. 9. 
 
 the body under induction into iron filings and lifting it out, 
 when the filings will be found clinging at each of the various 
 poles. 
 
 6. Induction by Induced Magnetism. It is easy to 
 show that induced magnetic poles have the power of inducing 
 magnetism in other iron bars brought under their influence. 
 If a series of iron bars be arranged end to end, in contact or 
 with space between them (Fig. 10), and a strong magnet pole 
 
 \ L 
 
 FIG. 10. 
 
 be brought near one end, the opposite end will be found to 
 be magnetic, having the power of picking up iron filings, and 
 of exerting attraction or repulsion on other poles. If a 
 magnet be drawn slowly through a number of short pieces of 
 iron wire or carpenter's brads (Fig. 11), they will be found 
 to arrange themselves in strings, end to end, each in turn 
 being a magnet, and inducing magnetism in the brad im- 
 mediately next to it. Of course the length of the string of 
 
Electricity. 
 
 [Book L 
 
 brads drawn after the pole depends on the strength of the 
 
 inducing pole. The same ex- 
 planation applies to the brush- 
 like appearance of the filaments 
 of iron filings round the poles 
 of a magnet, each filing being 
 a magnet and inducing mag- 
 netism in the one next it, the 
 terminal pole of each filament 
 being of the same name, and 
 therefore repelling all the other 
 terminal poles around it, thus 
 preventing the neighbouring 
 filaments from falling together. 
 
 7. Steel under Induction. If, instead of a piece of soft 
 iron we take a piece of unannealed iron, or better, a piece 
 of tempered steel, we notice a remarkable difference in its 
 susceptibility to magnetic induction. Choose, for example, a 
 piece of soft iron wire, and a knitting-needle of about the 
 same dimensions ; on dipping them alternately in iron filings, 
 and presenting the pole of a magnet to the opposite end, the 
 mass of iron filings lifted by the iron wire will be found to 
 be many times greater than the mass lifted by the knitting- 
 needle ; but on removing the inducing magnet all the filings 
 will fall away from the iron, while most of them will be re- 
 tained by the knitting-needle. Further, if the knitting-needle 
 be brought down on to the magnet pole with a smart tap, or 
 hammered when under induction, its magnetic power will be 
 very much increased, and will be almost wholly retained when 
 removed from the inducing magnet. This property of tern- 
 
Chap, i.] Magnets. 
 
 pered steel is usually expressed by saying that steel possesses 
 a coercive force which is absent in soft iron, in virtue of which 
 steel cannot at once take up the magnetic condition when 
 placed under magnetic induction, but having once taken it up 
 retains it for ever. Soft iron on the other hand, owing to the 
 absence of coercive force, takes up the magnetic condition 
 at once, and loses it as rapidly when the inducing magnet is 
 removed. It should be borne in mind that there is no such 
 thing in natural or artificial products as soft iron or hard steel 
 which strictly obeys the laws as stated above, all the varieties 
 of iron and steel being intermediate in their behaviour be- 
 tween those two ideal limits all soft iron retaining a fraction 
 of the magnetism induced in it, and all hard steel being to 
 some extent susceptible of temporary magnetization under 
 induction. 
 
 This explains the observation that the pole of a strong 
 magnet attracts either pole of a weak magnet when brought 
 sufficiently near to it. The strong magnet here acts by in- 
 duction on the weak, and the induced magnetism of opposite 
 name to the inducing pole overpowers the like permanent 
 magnetism, and converts repulsion into attraction. Hence in 
 experiments on weak magnetism, it is necessary to observe 
 the first movement of the suspended magnet, as the feeble pole 
 approaches it. The same explanation applies to the use of 
 armatures or keepers, that is bars of soft iron which are made 
 to lie across between opposite poles when magnets are packed 
 away (Fig. 12). Each armature becomes by induction a 
 magnet, and acts back by induction on the magnet poles to 
 which it owes its magnetic character, tending to prevent 
 their magnetism from dissipating under accidental jars or the 
 induction of neighbouring magnets. It is even possible to 
 
10 
 
 Electricity. 
 
 [Book I. 
 
 increase considerably the magnetism in a weakened horse-shoe 
 magnet by simply drawing the armature several times gently 
 across the poles, removing it at each stroke. 
 
 FIG. 12. 
 
 8. Hypothesis of Magnetized Molecules. We will 
 now inquire whether the two magnetisms developed at and 
 near the ends of a magnet are wholly confined to those parts. 
 To answer this question we will break a magnet in halves. 
 The knitting-needle magnetized in a previous experiment will 
 answer well, and can be at once snapped in two when held 
 in a pair of pincers. On performing the experiment, we find 
 
 S N 
 
 S N 
 
 FIG. 13. 
 
 S N 
 
 that each half has all the properties of a complete magnet ; 
 two new poles of opposite name having been developed on 
 opposite sides of the division. This experiment may be 
 repeated to an indefinite extent, and we shall still find the 
 smallest fragments into which a magnet can be divided to be 
 magnetic in the same direction as the original magnet (Fig. 13). 
 We infer that even the smallest molecules into which the 
 magnet can be divided will be magnetic also, and that a bar 
 
chap, i.] Magnets. 1 1 
 
 magnet is an assemblage of such molecules, each of which is 
 a magnet endowed with its opposite poles ; the poles of the 
 molecular magnet being arranged as in Fig 14, and the 
 magnetic properties of the magnet being due to the resultant 
 of such a system of magnetic forces. 
 
 MS NSNS MS /VS /VS #S /Y5 N 5 7VS NS 
 PIG. 14. 
 
 If we have two altogether equal magnets, and place their 
 opposite poles in contact, such an arrangement is exactly 
 equivalent to a magnet of double the length of either magnet ; 
 the two opposite poles when placed in contact each neutra- 
 lising the other's effect on all external magnetism. If we 
 apply this principle to the molecular magnets of Fig. 14, all of 
 which we suppose for a moment, of exactly equal magnetic 
 strength, we shall have equal and opposite poles in contact 
 along the whole length of the magnet mutually neutralising 
 each other, and free magnetism confined to the ends of the 
 magnet. l 
 
 If we next assume that the magnetic strength of the suc- 
 cessive molecules falls off as we get near the ends of the 
 magnet, we have the free magnetism distributed along the 
 magnet to some distance from the ends ; and that appears 
 to be at any rate a fair mental picture of the actual distribu- 
 tion of magnetism in a magnet. If we would form a picture of 
 the state of the magnet before magnetization, we may assume 
 either that the molecules are without magnetism till brought 
 under induction, or that the molecules already magnetized 
 
 1 By free, we mean magnetism not neutralised by opposite magnetism 
 in adjacent molecules, and therefore free to act on other magnetism 
 at a distance from it. 
 
1 2 Electricity. [Book i. 
 
 have their magnetic axes directed in all sorts of directions 
 (see Fig. 15), so as to neutralise each other's action. The 
 
 J \x\-x\ / \\x^- /xx 
 
 FIG. 15. 
 
 process of magnetization then consists in giving the molecules 
 a twist, which brings all their magnetic axes into the same 
 direction, namely that of magnetization. In the case of soft 
 iron this magnetic twist is brought about at once on applying 
 the Inducing Magnet; but in the case of steel there is a 
 greater molecular rigidity, which can only be overcome by 
 the magnetic force when the molecules are in a state of 
 vibration among themselves. This may be illustrated by a 
 glass tube containing iron or steel filings. If the pole of a 
 magnet be drawn along the tube always in the same direction, 
 several times, it will be found to have become a magnet, 
 showing polarity like a feeble bar magnet. On shaking up 
 the filings all trace of magnetism disappears. 
 
 These considerations however, belong to hypotheses in- 
 capable of direct verification by experiment, whose further 
 consideration had better be deferred till the student has 
 gained a more complete knowledge of experimental details. 
 
 p. Magnetic Substance. It has been shown by Fara- 
 day, with the help of very powerful magnets, that almost all 
 substances are susceptible of magnetic influence, but the only 
 substances besides the various compounds of iron, which show 
 magnetic properties under the action of our ordinary magnets, 
 are the metals nickel and cobalt. 
 
CHAPTER IL 
 FIELD OF MAGNETIC FORCE. 
 
 10. Definition of a Field of Magnetic Force. We 
 
 have seen that any body possessing induced or permanent 
 magnetism, when brought into the neighbourhood of a bar 
 magnet or any distribution of magnets, experiences mechanical 
 force. It is usual therefore to refer to the space surrounding 
 any distribution of magnetism as a Field of Magnetic Force. 
 
 We have also seen that every magnet has two kinds of 
 magnetism developed, each nearly concentrated in a pole. 
 The forces experienced by any magnetized body (suppose for 
 simplicity a thin bar magnet) will therefore usually consist 
 of two forces acting at its two ends, which may be combined 
 into a single resultant force and couple, on ordinary mechanical 
 principles. Before we can find this resultant we must know 
 the action on each pole, at its own place in th6 magnetic field. 
 To do this might seem impossible, as we cannot separate the 
 north pole from the south, and experiment with each sepa- 
 rately. We are able in effect to do exactly this, owing to the 
 fact that the force falls off rapidly as the distance increases, 
 so as to become almost or quite insensible at very moderate 
 distances. If then we choose a long magnet for exploring 
 the field, we can place its more remote pole in such a position 
 that the whole observed force is sensibly, though not accu- 
 rately, that due to the nearer pole. For we cannot observe 
 with absolute accuracy, and we can easily make the error 
 
 13 
 
14 Electricity. [Booki. 
 
 produced by the distant pole less than that inseparable from 
 our rough methods of observation. 
 
 ii. Magnetic Force on a Pole at a Point. Guided 
 by this principle, we proceed now to consider the force 
 experienced by a magnetic pole- placed in a given position 
 in a magnetic field. To define a force we require to know 
 three things the point of application, the direction of action, 
 and the magnitude. 
 
 1. The Point of Application. Since in any actual magnet 
 the free magnetism is distributed over a finite portion of the 
 magnet, it might seem that there was no point of application 
 of the magnetic force. If, however, we choose a thin and 
 evenly magnetized needle, there will be a certain centre of 
 magnetism very near to the actual end of the magnet, such 
 that the action of the field on the total magnetism is appreci- 
 ably the same as if it were all concentrated at that point. 
 This centre of magnetism should of course be defined as the 
 physical pole of the magnet. It is scarcely necessary to point 
 out its analogy to the centre of gravity of a material body. 
 We shall in future consider the force on a pole as acting on 
 the total quantity of magnetism concentrated in the pole. 
 
 2. The Direction. At each point in the field there will be a 
 certain direction in which a pole will be urged when placed 
 there, the directions being exactly opposite for a north and 
 south pole. These directions are spoken of as the Line of 
 Force through the point in the field, and we may conceive the 
 field mapped out into lines of force, the direction of the line 
 at each point showing the direction in which a magnet pole, 
 if placed at that point, would be urged. It is also clear that 
 two of these lines of force can never intersect (except in a 
 
chap, ii.] Field of Magnetic Force. 1 5 
 
 pole), since we should have in that case two directions in 
 which the force would urge the pole, and this we know to be 
 mechanically impossible. We may further define the positive 
 direction of a line of force as that in which a north (or +) 
 pole would be urged, and the negative direction as that in 
 which a south (or - ) pole would be urged. 
 
 3. The Magnitude. To determine this we must measure 
 the force with which a certain pole, which we choose as our 
 standard, is urged along the line of force. This may of 
 course be measured, like a statical force in pounds, grains or 
 grams, according to the system of weights and measures we 
 choose to employ. This force, when measured in suitable units, 
 is generally called the strength of the field at the given point. 
 
 12. Lines of Force. To exhibit the lines of force due 
 to a system of magnetic poles in one plane, the best method is 
 to lay a sheet of paper or thin card-board over the poles and 
 sprinkle it with iron filings from a sieve. On gently tapping 
 the paper or card the filings arrange themselves along lines 
 of force. Each separate filing becomes, under induction, a 
 magnet, and as the paper is tapped, it settles down with 
 its north pole in the + direction and its south pole in the 
 direction. These poles exercise their attractions on other 
 filings near them, and we have at last continuous strings of 
 filaments, giving us a vivid picture of the lines of force. 
 These pictures may be made permanent by pouring over 
 them a weak solution of gum, by which each filing is held in 
 its place ; or by a solution of potassium cyanide, which causes 
 under each iron filament a deposit of Prussian blue. For 
 this purpose the paper should be laid on a sheet of glass. 
 
 We may experiment with a single pole for magnetic system 
 
i6 
 
 Electricity. 
 
 [Book I. 
 
 by placing a long magnet vertical, using only its upper pole. 
 We then notice that the lines of force are in the form of 
 straight lines radiating from a point (Fig. 1 6). 
 
 FIG. 16. 
 
 In an ordinary bar magnet, laid horizontally under the paper, 
 the lines of force emanate chiefly from the poles (Fig. 1 7), 
 forming oval curves between them. Theoretically, in a simple 
 bar magnet we should expect all the lines of force to go 
 from one pole to the other, but in an ordinary magnet the free 
 magnetism along the edges causes some of the lines not to pro- 
 ceed directly from the poles, but always from north-polar to 
 south-polar magnetism, as may be seen on examining the figure. 
 
chap, ii.] Field of Magnetic Force. 17 
 
 In the system consisting of two poles of like name, the 
 lines emanate from each pole but do not intersect, all ap- 
 proaching towards the equatorial plane of the system without 
 meeting it this plane being, in mathematical language, an 
 asymptote to the system of lines. 
 
 FIG. 17. 
 
 In like manner can also be shown the polarity of an iron 
 bar under induction of two opposite or like poles near its ends. 
 Fig. 19 shows the lines of force in a system consisting of two 
 opposite magnet poles and a bar of iron between them. 
 
 If, as sometimes happens in a magnet, intermediate poles 
 
 B 
 
i8 
 
 Electricity. 
 
 [Book I. 
 
 by intention or accident have been developed, these are at 
 once shown by the behaviour of the iron filings. 
 
 It is instructive to notice that in all these cases the direc- 
 tion of the line of force is the direction of the resultant of a 
 system of forces acting from each pole of the system. Thus 
 
 in a single bar magnet, AB in Fig. 20, the line of force PF at 
 P will be found by compounding forces in the directions AP 
 and PJB, directed respectively from the north and towards 
 the south poles. 
 
 13. Strength of Magnetic Field of a Single Pole, 
 by Coulomb's Balance. We are now in a position to 
 
chap, ii.] Field of Magnetic Force. 1 9 
 
 compare the strength of the magnetic field at different points 
 in it. This was originally done by Coulomb for a single pole, 
 
 FIG. 20. 
 
 by means of the Torsion Balance (Fig. 21). It consists essen- 
 tially of three parts (1.) A long thin magnetic needle, -4, 
 
20 
 
 Electricity. 
 
 [Book I. 
 
 evenly magnetized and suspended, so as to swing in a hori- 
 zontal plane by a fine silver wire, which is attached above to a 
 Torsion Circle, B. A square of card is put on one end of the 
 magnet, the resistance of which against the air when swinging 
 tends to bring the needle rapidly to rest. (2.) The torsion 
 
 FIG. 21. 
 
 circle (shown enlarged on the right of Fig. 21) carries the 
 upper end of the wire coiled on the horizontal arm CD, 
 supported on the frame E, which can be twisted round the 
 vertical axis, the graduated limb FGr measuring the twist put 
 on to the wire in performing an experiment. (3.) The needle 
 swings in a glass case (HK), graduated on its surface, so as 
 to show the angular movements of the needle. The case 
 
chap, ii.] Field of Magnetic Force. 2 1 
 
 is perforated above, so as to allow of the introduction of a 
 magnetic needle (L) in a vertical position, whose lower pole 
 creates the magnetic field, whose strength is measured by 
 the pole of the moving needle. The effects of the more dis- 
 tant poles of L and A are neglected. 
 
 We assume at the outset that both the graduated torsion 
 circle (FG] has its pointer to zero, and that the needle points 
 to its zero of graduation on the case (HK), when the needle 
 is in the magnetic meridian, and the wire has no torsion ; 
 also that the magnet pole is introduced immediately opposite 
 the zero of graduation, so as to deflect the needle by its re- 
 pulsive action, the opposing poles being of like sign. This 
 adjustment is secured in practice by marking the magnetic 
 meridian by means of an independent magnet, and turning 
 the case until the and 180 of graduation are in a line with 
 it ; then, replacing the magnetic needle by a copper needle of 
 equal weight, twist the whole torsion circle until the copper 
 needle hangs in the magnetic meridian. On replacing the 
 magnetic needle, it will hang in the magnetic meridian, and 
 the wire will be free from torsion. 
 
 On introducing the vertical magnet there will be* repulsion, 
 and the needle will take up a position out of the magnetic 
 meridian, in which the repulsion between the two magnet 
 poles is balanced by the combined effect of the earth's direc- 
 tive force on the magnet and the torsion put on to the wire 
 by the deflection of the needle. 
 
 The latter of these is simply proportional to the angle 
 through which the wire is twisted, or to the deflection of the 
 needle ; and the earth's directive action can also be measured 
 in terms of the twist in the wire. The forces acting on the 
 needle, PP', in Fig. 22, when deflected from the meridian 
 
22 
 
 Electricity. 
 
 [Book I. 
 
 MM' will be two equal and opposite forces, whose magni- 
 tude we will call F, acting parallel to MM'. The effect of 
 such a pair of forces in twisting the magnet round C, back 
 again towards the meridian, will be measured by their 
 moment, or 2.Fx CGf. When the angle of deflection is small, 
 CG is very nearly equal to AP, the arc described by the pole 
 
 FIG. 22. 
 
 FIG. 23. 
 
 A in its deflection, and this is proportional simply to the angle 
 of deflection. 1 
 
 To find the action of the earth in terms of the torsion of 
 the wire, we must first find through how many degrees the 
 circle must be turned to give 1 deflection to the needle before 
 the magnet L is introduced. Take a plan of the instrument 
 
 1 The moment is really proportional to the sine of the angle of 
 deflection, and the sine for small angles is known to be proportional 
 to the annrle. 
 
chap, ii.] Field of Magnetic Force. 2 3 
 
 (Fig. 23) in which the smaller circle represents the torsion 
 circle, and the larger the graduated glass case. Suppose the 
 torsion circle turned from the magnetic meridian, MM', 
 through the angle EGA (=T), and the needle through the 
 angle PGA (=A), the torsion on the wire is (TA), and 
 this balances the deflection, A. Hence the torsion per degree 
 
 of deflection is ( ^ j , and we may assume that the direc- 
 tive action of the earth for any moderate deflection is found 
 
 T A 
 by multiplying the deflection by -^ 
 
 We can now express the force between the magnet poles in 
 any position in terms of the torsion of the wire alone, and 
 this is simply proportional to the angle of torsion in all ex- 
 periments with the same instrument. 
 
 We will now proceed to work out a particular numerical 
 experiment, in which we endeavour to compare the force 
 exerted on the moving by the fixed magnet pole, at two dis- 
 tances whose ratio is as 2 : 1. 
 
 (1.) Before introducing the second pole, twist the torsion 
 circle through 35; the needle is seen to deflect 5: and 
 therefore 30 of torsion balances the directive action of the 
 earth through 5 ; or the earth's directive action is measured 
 by 6 of torsion per degree of deflection. 
 
 (2.) Introduce the magnet pole which deflects the needle 
 40. Refer to the plan of the instrument (Fig. 24), in which 
 D represents the fixed pole, E the repulsive force which acts 
 in direction DP \ the effect in twisting the needle is measured 
 by the moment of E about (7, or GK x E. When the angle 
 of deflection is small, GK is nearly equal to GP ; and we shall 
 therefore assume that the moment is measured by E, the 
 
Electricity. 
 
 [Book I. 
 
 force itself. Hence R is balanced by 40 torsion, together 
 with the earth's directive action through 40, which is equal 
 to 40 x 6 of torsion. 
 
 .*. R is measured by (40 + 6 x 40)= 280 of torsion. 
 
 (3.) Twist the torsion circle backwards, as indicated by the 
 arrow, through two complete revolutions, and about 260 in 
 
 addition, and you will find the needle at 20. If R' denote 
 the repulsion, we have R' balanced by (2 x 360 + 260 + 20) 
 = 1000 of torsion and the earth's deflective action, which is 
 equal to 20 x 6 = 120 of torsion. 
 
 .-. ^'=(1000 + 120)=1120 of torsion. 
 
 Observing that 11 20 = 4 x 280, we conclude that the force 
 is multiplied by 4 when the distance is halved. 
 
 By further experiment it will be found that the force, when 
 the reading is 13^, or one-third of 40, is 9 x 280, and at 10 
 it is 16 x 280, and so on. From these observations Coulomb 
 
chap, ii.] Field of Magnetic Force. 25 
 
 deduced the important law that where the distances of two 
 poles are made in succession proportional to 
 1, 2, 3, 4, ...... 
 
 the forces at these distances are proportional to 
 
 which is usually expressed by saying that the forces are in- 
 versely as the squares of the distances between the poles. 
 
 14. Strength of Field by the Method of Oscilla- 
 tions. The strength of the field may also be investigated by 
 means of the method of Oscillations. This depends on the 
 well-known dynamical law that a pendulum, when oscillating 
 through a small arc about its position of equilibrium, makes 
 isochronous oscillations i.e. oscillations whose time is indepen- 
 dent of the arc (supposed small) through which the pendulum 
 swings and that the force which is always drawing it back to 
 its position of rest is proportional to the square of the number 
 of oscillations made in a given time. 
 
 Now, a magnet, when freely suspended, is a double pen- 
 dulum, and, when disturbed, oscillates under the same laws 
 as a pendulum ; and, since it will continue to oscillate for five 
 or ten minutes, the number of oscillations in that time can be 
 counted within a fraction of a single oscillation. 1 
 
 If we place the south pole of another magnet in the 
 meridian, at a measured distance to the north of the suspended 
 magnet, it will increase the magnetic force on the needle, and 
 make the oscillations more rapid. If the suspended needle 
 be very short, compared with the distance of the magnet pole, 
 the forces on the two poles will be appreciably equal and 
 
 1 For rough experiments, the number of oscillations made in 30 
 seconds is sufficient. 
 
26 Electricity. [Booki. 
 
 opposite, and we have the oscillating magnet behaving as a 
 pendulum under the combined action of the earth and magnet 
 pole, whose effects are simply added together. 
 
 The experiment is performed by suspending by a single 
 silk fibre a magnetized needle about one centimetre (or half 
 an inch) long, supported in a paper stirrup (Fig. 25). In a 
 particular experiment this needle made 11 oscillations in 
 30 seconds under the action of the earth alone. If E repre- 
 sents the earth's magnetic force, E is measured by II 2 or 121. 
 
 T 
 
 JJ 
 
 FIG. 25. 
 
 On introducing the south pole of a , long magnet (about 40 
 centimetres in length) at a distance of 4 centimetres from the 
 point of suspension, the number of oscillations was 51 in 30 
 seconds. If then M represent the pull of the magnet at 4 
 cm., E + Mi is measured by 51 2 or 2601. Hence, M 4 is 
 measured by 2601 121 = 2480. On removing the pole to a 
 distance of 8 centimetres, the number of oscillations was 27. 
 Denoting by M 9 the force of the magnet at 8 cm., we 
 have E + M 8 measured by 27 2 =729, and therefore M a is 
 measured by 729 121 = 608. Hence M has to M B the ratio 
 2480 to 608, or the ratio 4 to 1 within the limit of errors of 
 observation. 
 
chap, ii.] Field of Magnetic Force. 27 
 
 The same method employed at other distances will confirm 
 the law of inverse squares, just as in Coulomb's method. 
 
 It should be noticed, in this and the following experiments, 
 that it must be the pole as defined in Art. 11, and not the 
 mere end of the magnet, which is to be placed at the given 
 distances from the suspended magnet. A few experiments 
 enable the experimenter to arrive at the true position of the 
 magnet pole, which in an ordinary bar magnet is about \ in. 
 from the end. 
 
 15. Strength of Magnetic Field by Method of 
 Deviations. Another method of great use in practical 
 magnetic measurements, is the method of Deviation. In this 
 
 M 
 
 method (Fig. 26) we employ a very short magnet PP (exag- 
 gerated in the figure), furnished with a long non-magnetic 
 pointer, by which the deflection of the needle from the 
 magnetic meridian may be measured. The deflecting magnet 
 is placed in a line east or west of the point of suspension of 
 
28 
 
 Electricity. 
 
 [Book I. 
 
 the needle as at M or N. Remembering that the magnet is 
 very short, and considering only one deflecting pole, the forces 
 acting on each pole will be a force along the magnetic meridian 
 (E) due to the earth's action, and a force at right angles to it 
 (F), due to the action of the deflecting pole. The magnet takes 
 up its position along the resultant of these two forces. Let 
 GOG' be a horizontal scale graduated both ways from (7; also, 
 let KCK' be a graduated scale placed in a vertical plane, both 
 being east and west of the meridian. If the line CP be pro- 
 duced, either by a pointer or by 
 sights attached to the magnet, 
 and moving with it, so that the 
 distance Q, at which the axis 
 of the magnet cuts the vertical 
 scale is known, the principle 
 of the parallelogram of forces 
 will apply, and we shall have 
 
 = But JBC and E are 
 
 FIG. 26A. 
 
 ment by the distance BQ. 
 proportional to 1, 2, 3, . . 
 respectively proportional to 1, J, 
 proof of the law of inverse squares. 
 
 fixed quantities for all obser- 
 vations, and hence we see that 
 F is measured in each experi- 
 If we choose distances for M 
 we shall find the distances BQ 
 . . . , thus giving another 
 
 The ratio -^ depends on the angle BOP, and is in fact 
 JjLf 
 
 simply the tangent of that angle. In the instrument called 
 the deflection magnetometer (shown in Fig. 26A), several 
 short needles are used parallel to each other, and the devia- 
 
chap, ii.] Field of Magnetic Force. 
 
 29 
 
 tion is read by means of a long glass pointer which moves 
 over a graduated card. The needle and pointer are shown at 
 G. The deflection is read off, and the tangent, taken from 
 Appendix II., gives the measure of the strength of field in 
 
 each experiment. 
 
 For since ^-=tan ; F=Eta,n (9, 6 being 
 Jb 
 
 the observed deflection. AB represents a metre rod attached 
 beneath the needle, by which distances E and W can be read. 
 
 16. Comparison of Strength of two Magnet Poles. 
 
 To compare two magnetic poles is simply to compare the 
 forces they respectively exert on the same pole when placed 
 at the same distance from it. 
 
 This comparison may be made by either of the above 
 methods, simply changing the one pole for the other of two 
 
 M' M 
 
 3E 
 
 /v 
 
 DTD) 
 
 FIQ. 27. 
 
 magnets to be tested, keeping the distance from the testing 
 magnet the same, or applying the law of inverse squares to 
 reduce the observations to a constant distance. A better 
 method is to place the two poles as at M and N y on opposite 
 
30 Electricity. [Book i. 
 
 sides of the short suspended needle of the last experiment, and 
 move one of them backwards and forwards till the suspended 
 needle remains in the meridian. The strengths of field at C 
 due to M and to N must then be equal, and we shall have 
 strength of pole M at distance CM equal to that of the pole 
 N at distance CN. Hence their strengths at the same dis- 
 tance would be in the ratio CM 2 to CN 2 . 
 
 If, now, m, m f be the strengths of the poles i.e. the forces 
 with which they urge a certain standard pole at unit distance 
 
 the strength of the field of m at distance r will be ^. Assum- 
 
 ing this we can easily correct the last result for the action of 
 the more distant pair of magnet poles. For if we assume MM' 
 and NN' (Fig. 27) to be the two magnets, the strength of field 
 at C due to the magnet MM' will be found by subtracting 
 the strength due to M' from that due to M, which gives 
 
 and that due to NN ' ** be - ; and 
 
 we have therefore, if the magnet remains undisturbed, 
 
 m (vJF~- CZp) =m '(cW>- CFV 
 from which the ratio m : m' is at once determined. 
 
 *I7. Meaning of an Absolute System of Measure- 
 ment. In speaking of magnet poles we have frequently 
 referred to a standard pole, but have used in place of it the 
 pole of any needle convenient for the particular experiment 
 we had in hand. No magnet pole can be made to retain its 
 magnetism without change for any length of time ; and it is 
 therefore useless to attempt, by means of a single magnet, to 
 
chap, ii.] Field of Magnetic Force. 3 1 
 
 compare the strengths of a field or of another pole at any 
 great interval of time. 
 
 To enable us to do this we make an absolute system of 
 units in which the strength of our pole must be determined, 
 absolutely at the time of each experiment. 
 
 For an account of the absolute system of units employed, 
 the student is referred to Appendix I. We only note here 
 that with three fundamental units (that of length being called 
 the centimetre ; of time, the second of our ordinary mean-time 
 clocks ; and of mass, the gram) we are able to express every 
 other unit required in physical investigation independently of 
 any new physical quantity. Premising that the absolute 
 unit of force is the dyne, we proceed to explain the absolute 
 units used in magnetism. 
 
 *i8. Absolute Unit of Magnetism. We know by our 
 experiments that two magnet poles of the same kind repel 
 each other with a force which may be measured in dynes or 
 absolute units of force. We can therefore conceive two equal 
 magnet poles which, when a centimetre apart, exert a force 
 of exactly one dyne on each other. These two would then 
 be called unit magnet poles, and the quantity of magnetism 
 in each of them a unit of magnetism. We make no assump- 
 tion here as to the nature of magnetism, referring only to its 
 action in the magnetic field. We should define the strength 
 of any other magnetic pole by the number of units of mag 
 netism it contains, or by the force exerted on a unit pole 
 placed at unit distance. We should also define the strength 
 at any point in a magnetic field, as the force with which a 
 unit of magnetism condensed in a point and placed there would 
 be urged along the line of force. 
 
32 Electricity. [Booti. 
 
 It follows from this definition, combined with the law of 
 inverse squares of the distance, that if we have a pole of 
 strength M the strength of the field at a distance D cm. from it 
 
 will be j- : and the force urging a pole of strength M' placed 
 
 at distance D cm., will be -~, both expressed in absolute 
 
 measure. 
 
 It will be convenient to give one or two definitions of terms 
 used in magnetism : 
 
 (1) Magnetic Moment. If a magnet have each of its poles of 
 strength M, and the distance between them be /, the product Ml 
 is called the magnetic moment of the magnet. Here the pole 
 should, of course, be taken as the physical pole defined above. 
 
 (2) Magnetic Density. If a pole of strength M be at the 
 
 end of a bar whose sectional area is A, the ratio is called 
 
 A 
 
 the magnetic density over the end of the bar. This is often 
 denoted by the symbol p, and we may write pA=M. 
 
 (3) Intensity of Magnetisation. According to the theory of 
 a magnet (Art. 8), any small bar cut out of a magnet along 
 the direction of magnetisation would have the same magnetic 
 density over its ends as the whole magnet ; but in the interior 
 the word density is inapplicable, and the term intensity of 
 magnetisation is used in place of it. If L = the length of the 
 small magnet, p the density on its end, A the area of either 
 end, and M the strength of either pole, we have p AL=ML. 
 Here AL is the volume of the magnet (V), and ML its 
 
 magnetic moment (G). Hence pV=G, or p = . Thus the 
 intensity of magnetisation is the ratio of the magnetic moment 
 
chap, ii.] Field of Magnetic Force. 33 
 
 of any portion of the magnet to its volume, or the magnetic 
 moment per unit volume. 
 
 19. Theories Suggested by Experiment. It will 
 naturally strike the student that by all our methods of 
 experiment, acknowledged everywhere to be rough and ap- 
 proximate only, we have given an altogether inadequate 
 proof of a law of such precision and generality. We must 
 remind him, however, that he has in this been only following 
 in the track of the discoverers, both of this and of every other 
 physical law. Such laws have been discovered by something 
 like a happy guess from very rough observations, while the 
 confirmation of the guess depends on methods of greater 
 refinement, which generally depend altogether on a know- 
 ledge of the law itself they are intended to prove. As an 
 illustration, we may notice that by help of the law just 
 enunciated we can determine the form of the magnetic curves 
 for a given distribution of poles, and can in many cases trace 
 the theoretical magnetic curves by graphical means, and so 
 compare the curves yielded by theory with those given by 
 experiment. 
 
CHAPTER II L 
 METHODS OF MAGNETIZATION. 
 
 20. Quality and Temper of Steel. To secure good 
 permanent magnets it is, first of all, necessary to have bars of 
 the best steel evenly tempered. The temper which gives the 
 best results is obtained by cooling the bars when brought to a 
 cherry-red the same temper as that for the best cutlery. 
 
 There are various processes of magnetization, but all depend 
 on overcoming the coercive force of the steel by vibrating its 
 molecules when under powerful external magnetic induction. 
 
 21. Method of Single Touch. The first method, 
 known as Single Touch, consists merely in rubbing the bai 
 to be magnetized several times lengthwise, and always in 
 the same direction, across the pole of 
 
 a strong magnet. In this, as in aU 
 
 cases, the end of the bar at which 
 
 the magnet pole leaves it becomes of 
 
 opposite name to the inducing pole. 
 
 This process is repeated five or six 
 
 times on both sides of the bar to be /v 5 
 
 magnetized, and gives a fairly strong Fl - 28 - 
 
 magnetism to a short thin bar, such as a piece of watch-spring 
 
 or small compass needle. The arrow shows the direction in 
 
 which the bar is rubbed across the pole to communicate the 
 
 poles shown by the letters N, S. 
 
chap, in.] Methods of Magnetization. 
 
 35 
 
 22. Divided Touch. The second method, that of 
 Divided Touch, consists in fixing the bar to be magnetized 
 between the opposite poles of two permanent magnets. 
 
 N S 
 
 FIG. 29. 
 
 N S 
 
 While under their induction the bar is stroked, each half 
 with the pole of another magnet of the same name as the 
 corresponding inducing pole, the stroking magnets being held 
 in the hands at an angle of about 30 degrees with the 
 bar ; the stroking beginning from the centre of the bar, and 
 the poles being lifted at the ends, in an arch, back again 
 to the centre. The stroking is repeated on the opposite 
 face of the bar. This method gives a strong and even 
 magnetism to moderately thin and long bars. 
 
 23. Method of Double Touch. The third method, 
 called that of Double Touch, consists in placing the bar to be 
 magnetized under the induction of two strong poles, as in the 
 last method. The stroking poles are placed at first over 
 
 FIG. 30. 
 
 the centre of the bar to be magnetized, but separated by 
 a small piece of wood. The stroking magnets, held at an 
 angle of about 15 degrees to the bar, are drawn along the bar 
 
Electricity. 
 
 [BOOK I. 
 
 steadily from the centre to the end, and back again to the 
 other end, several times, being taken off finally at the centre, 
 after each half has been passed over the same number of 
 times. The bar is turned over, and the same process repeated 
 on the opposite face. This is found to give a strong mag- 
 netism to thick bars, but is apt to develop consequent poles, 
 unless the rubbing be performed very steadily. 
 
 Some experimentalists prefer the use of a strong horse-shoe 
 magnet, whose two poles are placed on the bar at its centre, 
 
 7 f\ 
 
 
 S h 
 
 w 
 
 H 
 
 f Af j 
 
 FIG. 31. 
 
 and rubbed backwards and forwards, as in the last-named 
 method. When several bars require to be magnetized at 
 once, they are placed with their ends in contact, so as to 
 form a closed circuit, the angular spaces between their ends 
 being filled in with soft iron. The horse-shoe magnet is put 
 down at any part, and simply made to slide round the circuit, 
 always in the same direction, several times, by means of 
 which all the bars are magnetized strongly. Each bar is 
 magnetized in the same direction as the inducing magnet, 
 and the consecutive ends, acquiring opposite magnetism, 
 increase each other's power by mutual induction. 
 
 24. Magnetic Battery. It has been found that thin 
 bars can be magnetized much more strongly than thick ones 
 
chap, in.] Methods of Magnetization. 
 
 37 
 
 in proportion to their weight. In consequence, all large and 
 strong magnets are formed of bars each separately mag- 
 netized, and fastened together by screws 
 after magnetization (Fig. 32). In such a 
 magnetic magazine the power of the com- 
 bination is always less than the sum of the 
 powers of the separate bars, owing to their 
 induction on each other tending to weaken 
 the power of each, and especially of the 
 interior bars. 
 
 This relative weakness of thick bars 
 seems due to the magnetizing power not 
 penetrating far below the surface. This 
 has been proved by soaking magnetized 
 FIG. 32. bars in acid, by which the surface is slowly 
 
 eaten away. During this process the loss of magnetism is 
 found to proceed at a much higher rate than the loss of 
 weight. 
 
 25. Magnetic Saturation. The degree to which a 
 given bar is capable of magnetization depends on the manu- 
 facture and temper of the steel, and on the strength of the 
 inducing magnets. For each quality of steel, however, there 
 is a limit, beyond which the magnetism cannot be retained 
 permanently, and in this condition the bar is said to be satu- 
 rated. In making magnets it is best to magnetize beyond 
 saturation, and then allow the bar to sink back gradually to 
 saturation point, which may sometimes take a considerable 
 length of time. To test these changes in magnetism we have 
 only to place the magnet in the meridian at a constant dis- 
 tance from the same suspended magnet, and count the number 
 
38 Electricity. [Booki. 
 
 of oscillations in a given time. As long as these decrease in 
 number the power of the magnet is diminishing. Another 
 method commonly employed to test the power of a horse-shoe 
 magnet consists in suspending to the armature (Fig. 32) of a 
 fixed magnet a scale-pan, into which weights can be put, and 
 so determine its portative power. The amount the magnet 
 can support can be increased by adding small weights at 
 successive intervals, never allowing the weight to be sufficient 
 to separate the armature from the magnet. 
 
 The production of permanent magnets of small size, but 
 great magnetic power, is now a matter of great importance, 
 especially in telephone work, and great improvements have 
 been made in the manufacture of steel for this purpose. In 
 the Paris Exhibition of 1882 there was a magnet which could 
 support seventy-six times its own weight ; and the small 
 ordinary magnets now used in Gower-Bell telephones hold 
 up from fifteen to twenty-five times their own weight. (Mr. 
 W. H. Preece, F.E.S., in Report of Institute of Mech. Engineers, 
 Jan. 1883.) 
 
 26. Retention of Magnetism. < After a magnet has 
 been made, great care must be taken to preserve it from 
 accidental jars, by which the mass is set in vibration, the 
 effect of which, in the absence of strong external induction, 
 is to relax the molecular rigidity on which the magnetism of 
 steel depends. The same effect will be produced by heating 
 the magnet a red heat not only destroying all traces of mag- 
 netism, but making the metal quite indifferent to magnetism. 
 
CHAPTER IV. 
 TERRESTRIAL MAGNETISM. 
 
 27. Field of Terrestrial Magnetic Force. That 
 
 the earth, as a whole, is magnetic is proved by its influence on 
 a suspended magnet, which has already (Art. 3) been referred 
 to. Our only source of knowledge as to the nature of the 
 earth's magnetism is by observation of magnetic forces at 
 
 FIG. 33. 
 
 points in the earth's field of force. We must, therefore, find 
 for every place on the earth, where possible, the direction of 
 the line of magnetic force, and the strength of the magnetic 
 field. To find the direction of the line of force at a given 
 point, we have only to suspend a bar of steel so as to move 
 freely about its centre of gravity, and after magnetizing it, 
 
 39 
 
40 Electricity. 
 
 observe the position it assumes. This may be nearly fulfilled by 
 such a suspension as that of Fig. 33, in which the axis of a 
 needle swinging in a vertical plane is mounted on a pivot, 
 about which it can turn horizontally. Such a needle in Eng- 
 land at the present time will always come to rest in a plane 
 inclined 18 to 20 to the west of the astronomical meridian, 
 and will rest in that plane at an angle of 67 to 69 to the 
 horizon. This shows that within any very limited space the 
 lines of force are sensibly a series of straight lines parallel to 
 one another. 
 
 That these lines of force should remain straight lines to 
 considerable distances from the earth is very unlikely ; but 
 the linear dimensions of the earth are so great, compared 
 with any distances above it at which we can take observa- 
 tions, that we are not likely ever to be able to discover what 
 their true shape is. Their sensible parallelism for moderate 
 distances confirms us in our assumption (Art. 13) that the 
 earth's action on a needle consists of two equal and opposite 
 forces, since we cannot employ a needle so long that the field 
 of force at the two ends of it shows any sensible difference in 
 direction or intensity. This is all that is meant when the 
 earth's action on a needle is said to be directive only ; the 
 effect of a couple in mechanics being to twist a body round 
 without altering the position of its centre of gravity, until the 
 two forces constituting the couple are in the same straight 
 line. The needle in our experiment then takes up that 
 position in which the earth's pull consists of two equal and 
 opposite forces on its two ends, directed along it, and therefore 
 maintaining it in equilibrium. 
 
 This has been shown experimentally by supporting a 
 magnet on a cork float. In any vessel conveniently small 
 
c&ap. iv.] Terrestrial Magnetism. 41 
 
 the surface tension of the water will draw the cork to the 
 side, but at a point depending on the position on the surface 
 in which the float is placed, and in no way depending on 
 the direction of the earth's magnetism. 
 
 28. Magnetic Elements of a Place. The definitions 
 of the direction of the line of force and of the strength of the 
 earth's magnetic pull constitute what are called the magnetic 
 elements of the place. They are three in number. 
 
 1. Declination is the angle which the vertical plane through 
 the magnetic axis of a freely suspended needle makes with 
 the astronomical meridian of the place. This plane is com- 
 monly called the magnetic meridian of the place (see Art. 23), 
 and is the vertical plane which passes through the axis of an 
 ordinary horizontally suspended needle. The declination is 
 counted E. or W. as the north pole of the needle points to the 
 E. or W. of the astronomical meridian or vertical plane which 
 passes due north and south of the place of observation. 
 
 2. Inclination or Dip is the angle which the magnetic axis 
 of a magnet, freely suspended about its centre of gravity, 
 makes with the horizon of the place. This may be either 
 north or south according as the north or south end of the 
 needle dips below the horizontal plane. 
 
 3. Intensity is the force, expressed in absolute measure, 
 with which the earth's magnetism urges a unit magnet pole 
 at the place. 
 
 29. The Declinometer. To determine each of these 
 elements at any place requires a special piece of apparatus. 
 That for determining the declination is called a Declinometer. 
 This consists (Fig. 34) of a mounted telescope A, swinging on 
 two Y pieces B, B, the axis being levelled by the hanging 
 
4 2 Electricity. [Booki. 
 
 spirit-level. The Y's are mounted 011 a framework Z>, D, 
 having a circular limb which can be turned round in a hori- 
 zontal plane, and is graduated within. A horizontal magnet 
 needle, E, is pivoted at the centre of the graduations. The zero 
 of these graduations should be in the vertical plane through 
 the optical axis (or, more accurately, through the line of colli- 
 mation).of the telescope. If this adjustment is made and 
 the telescope is brought into the astronomical meridian, the 
 
 FIG. 84. 
 
 reading indicated by the end of the needle is the declination. 
 The framework DD carries a vernier and clamp F, which 
 slides over a horizontal graduated circle forming part of the 
 fixed base. This enables an observer with the telescope to 
 set it in the astronomical meridian. The base is supported 
 on levelling screws, by which the adjustments in level can be 
 made. 
 
 The magnet used for observing is usually a lozenge-shaped 
 magnet, and we read off the graduation corresponding to its 
 
chap, iv.] Terrestrial Magnetism. 43 
 
 pointed extremity. If the poles are not in the geometrical 
 axis of the magnet, this reading will be either too small or 
 too great. To correct this, the faces of the needle are usually 
 reversed, and the reading repeated, since then the declination, 
 which was before too small, will become too great, or vice 
 versd; the mean of the two readings correcting the error. 
 There may be also an error of centering the needle, by which 
 the pivot is thrown out of the centre of the graduations. This 
 is corrected by reading each time both ends of the needle. 
 The mean of the four readings so obtained will give the 
 true declination. 
 
 30. The Dipping Needle. The instrument for observ- 
 ing the inclination or dip is called the Dipping Needle. It 
 consists essentially of a magnetic needle swinging on a hori- 
 zontal axis, which passes through its centre of gravity, and 
 is at right angles to its magnetic axis. The needle swings 
 freely in pivots of agate to diminish friction, and the inclina- 
 tion is read off from a graduated limb, BB, which has the axis 
 of the needle at its centre. The whole is usually supported 
 on a horizontal framework movable about a vertical axis. 
 The frame carries a vernier and clamp, (7, which slides over a 
 circular graduated limb, fixed to the base of the instrument. 
 Levelling screws and small levels are attached for adjustment. 
 Where great accuracy is required, the positions of the ends 
 of the needle are observed by microscopes carried on an arm 
 whose extremities are made verniers for reading the limb. 
 
 To take an observation, it is necessary first to bring the 
 plane of movement of the needle into coincidence with the 
 magnetic meridian. The most convenient method for securing 
 this is to rotate the instrument in azimuth till the needle 
 
44 Electricity. [Book i. 
 
 shows an inclination of 90, i.e. stands vertical. The needle 
 must then be in the plane at right angles to the meridian, for 
 in this position the horizontal component of the earth's pull is 
 balanced by an increased pressure on the south and diminished, 
 pressure on the north bearing of the needle, while the vertical 
 component acting alone keeps the needle in a vertical position. 
 To eliminate the errors of centering, and of want of coinci- 
 dence between the geometrical and magnetic axes, the hori- 
 
 Fio. 35. 
 
 zontal circle is read, when each end of the needle points to 
 90, and also when the faces of the needle have been reversed, 
 either by turning the instrument through half a revolution 
 or by lifting the needle from its supports and reversing the 
 bearings. The mean of the four readings so obtained, 
 diminished by 90, will give the plane of the meridian. 
 
 When the needle is in the plane of the meridian, it is made 
 to vibrate slightly by bringing a magnet for a moment near to 
 it, and allowed to take up "its position of rest after the magnet's 
 
chap, iv.] Terrestrial Magnetism. 45 
 
 removal, when both ends of the needle are read. As it seldom 
 comes to rest twice over in exactly the same position, this 
 method is repeated about ten times. 
 
 As before, the faces of the needle are reversed, and the 
 same set of observations repeated. 
 
 There is a further error which occurs in the indications of 
 a dipping needle, due to the axis of rotation of the needle 
 not passing through its centre of gravity. If the centre of 
 gravity were ever so little towards the north end of the needle, 
 the weight acting through it would pull down the north end 
 and increase the dip, supposed north. If it were towards the 
 south end, it would pull down the south end, and therefore 
 diminish the dip. This error is neutralised by lifting out the 
 needle and reversing its magnetism, and again repeating the 
 two sets of observations on each end described above. The 
 mean of the eight means so obtained will give the true dip. 
 
 We have entered into details of the methods employed in 
 taking observations with the dipping needle, as an illustration 
 of the use of well-directed multiplied observations in using 
 physical instruments, and not because it is likely that such 
 methods could be usefully applied to the rough instruments 
 placed in a student's hands or used in a lecture experiment. 
 The need of such refinements only becomes apparent in instru- 
 ments brought to the highest perfection in construction, and 
 they would be as much out of place in a rough instrument 
 as a micrometer reading to thousands of an inch on a roughly 
 divided carpenter's rule, or a rider reading thousands of an 
 ounce on the beam of a grocer's balance. 
 
 31. The Intensity. To compare the magnetic intensity 
 at various places; we have apparently only to observe the 
 
46 Electricity. [Book i. 
 
 number of small oscillations made by the same dipping needle 
 in a given time about its position of equilibrium, the intensity 
 being simply proportional to the square of the number of 
 oscillations observed. This method would of course only 
 give us the intensity, referred to an arbitrary standard say 
 the intensity at some one place and not in absolute measure. 
 The dipping needle, however, is ill suited to observations on 
 oscillations, the friction on the supports bringing the needle 
 to rest in a comparatively small number of oscillations. For 
 this reason the dipping needle HORIZONTAL COMPONENT 
 was early abandoned in favour of 
 a horizontal needle suspended by 
 a few fibres of cocoon silk, whose 
 oscillations could be observed con- 
 tinuously for ten or fifteen minutes. 
 By this means the horizontal com- 
 ponent only is observed, but know- FIG. 36. 
 ing the horizontal component and the dip, the total intensity 
 is at once known (Fig. 36) by the law of the parallelogram 
 of forces. 
 
 The objections to this method will be obvious from what 
 we have stated as to the impossibility of preserving any 
 magnet from change in its magnetic power, or even of ascer- 
 taining any law of change. Gauss, however, introduced a 
 method which is independent of any magnetic quantities 
 whatever, and which, from suitable observations, gives us the 
 magnetic intensity in absolute measure. 
 
 *32. Gauss's Method for Finding Intensity. Let us 
 
 first consider the forces tending to bring back again a horizon- 
 
Chap. IV.] 
 
 Terrestrial Magnetism. 
 
 47 
 
 tally suspended magnetic needle displaced from the meridian. 
 Using absolute units, assume w to be the magnetic strength of 
 each pole of the magnet, and H the horizontal component 
 of the earth's magnetic intensity. The definition of H is the 
 pull on a unit of magnetism, and since at P there are by 
 supposition m units, the pull at P and P' will be two forces 
 Hm equal and oppositely directed. The moment of this 
 
 couple, tending to twist the magnet back to its position of 
 rest, is 2Hm x PM where PM is the arm of either force. This 
 
 maybe written Hm.PP' x when depends only on the 
 
 angle PGM, through which the magnet is deflected. The 
 quantity m x PP', or Magnetic Moment of the magnet 
 
48 Electricity. [Book i. 
 
 (Art. 18) may be denoted by G. The pull tending to 
 restore the needle to the meridian is therefore equal to 
 
 HG x -. It appears from Dynamics that the time T of 
 LiP 
 
 making a half oscillation of the needle is given by T=ir / -=^ 
 
 V -OCr 
 
 where M depends only on the mass and shape of the needle, 
 being its moment of inertia. If the needle used be long and 
 thin, such as a knitting-needle, whose mass is p. grams, and 
 
 Z 2 
 
 length I cm., then M=/x . And TT is the ratio of the circum- 
 12 
 
 ference to the diameter of the circle, equalling 3-14159, or 3^ 
 nearly. We then have HG=^ (1). 
 
 We employ next the needle of the foregoing oscillation 
 experiment, PP' t as deflecting needle in the magnetometer. 
 
 FIG. 3& 
 
 (Art. 15.) The forces urging the poles (of strength m') of the 
 magnetometer needle are Hm! along the meridian, and Fm' at 
 right angles to it, where F is the strength of field at C due to 
 
chap, iv.] Terrestrial Magnetism. 49 
 
 m at P, and m at P. Whence if 6 be the deflection of the 
 
 F 
 needle from the meridian, -^ = tan 6 also 
 
 _m m_ _ (CP-CP).(CP+CP) 
 
 ~ />2 n zx 2 m ' n D2 TTrv?! 
 
 PP 
 
 w < ^ CP + CP 
 
 We thus have - . / = tan 0, 
 
 Multiplying together equations (1) and (2) we obtain H 2 in 
 terms of magnitudes obtained by weighing and measuring 
 only, and independent of any magnetic quantity whatever. 
 
 *33. Magnetic Moment of a Magnet in Absolute 
 Measure. The method just described may be also used to 
 obtain G. For dividing, in place of multiplying, we have 
 G 2 in absolute measure. Hence the same method enables us 
 to express the magnetic moment, and hence the strength of 
 any magnet pole in absolute measure. 
 
 34. Magnetic Elements of Greenwich. The mag- 
 netic elements found for Greenwich in January 1884, were : 
 
 Declination, . 18 10' West. 
 Dip, . . . 67 30', 
 Intensity, . . '472. 
 
 35- Changes in Elements. No sooner had instru- 
 v ments of moderate accuracy been applied to determine these 
 
50 Electricity. [Book i. 
 
 elements, than it appeared that their value was different not 
 only for different parts of the globe, but that their values were 
 undergoing constant change at each place. To register these 
 small variations a specially constructed group of instruments 
 has been invented, which, by means of photography, give a 
 continuous chart of the movements of the magnets employed. 
 
 36. Variations in the Declination. On account of 
 the universal use of the declination compass, its variations 
 have been more studied than those of the other elements. 
 The chief variations in the declination needle are the fol- 
 lowing : 
 
 1. Secular Variation. This is a slow change in the magnetic 
 meridian of the place, which gradually moves in the course of 
 centuries, east and west of the astronomical meridian. The 
 following values of the magnetic declination of London for 
 the years given, will explain this variation : 
 
 Year. 
 
 1580, 
 1622, 
 1657, 
 1700, 
 
 This shows that before 1657 the declination was east. At 
 this date the magnetic and astronomical meridians coincided ; 
 after this the declination became west, reaching its maximum 
 west in 1815, since which date it has been slowly decreasing, 
 the present rate of decrease being about T per annum. 
 
 2. Annual Variation. From observations at widely dif- 
 ferent stations it appears certain that there is a variation of 
 small amount (about 1') depending on the sun's orbital posi- 
 
 Declination 
 
 Year. 
 
 Declination. 
 
 11 15' E. 
 
 1760, 
 
 . 19 12' W. 
 
 6 12' E. 
 
 1796, 
 
 . 24 O'W. 
 
 o o' ; 
 
 1815, 
 
 . 24 27' W. 
 
 9 40' W. 
 
 1820, 
 
 . 2411'W. 
 
chap, iv.] Terrestrial Magnetism. 5 1 
 
 tion ; the north end of the needle pointing to the east of the 
 mean position when the sun is north, and to the west when 
 the sun is south of the equator. 
 
 3. Diurnal Variation. The comparison of a series of hourly 
 observations of the declination at Kew, extending over several 
 years, shows that there is a variation in the declination, de- 
 pending on the sun's position in its daily path. 
 
 The needle occupies its mean position when the sun is 
 on the magnetic meridian about 10.30 A.M. Its maximum 
 easterly variation, amounting to 4', occurs three hours earlier, 
 and its maximum westerly, amounting to 6', about three hours 
 later. It again reaches the magnetic meridian about 6.30 
 P.M., and remains 1' or 2' east of it during the night, moving 
 eastwards again early in the morning. 
 
 4. Perturbations. These are irregular movements of the 
 needle, by which its regular advance is broken up into a series 
 of zigzags of greater or less amount. At some periods these 
 perturbations become comparatively very large, the needle 
 continuing to swing rapidly through several minutes of arc on 
 either side of its mean position. These are called Magnetic 
 Storms. 
 
 37. Relation to Aurora Borealis and to Solar 
 Phenomena. That these perturbations are not local dis- 
 turbances is proved by their occurring simultaneously at 
 stations very widely separated, and it is probable that they 
 have a common cause with the aurora borealis, brilliant displays 
 of which most frequently occur at the same time with the 
 magnetic storms. There is also evidence of a remarkable con- 
 nection between these magnetic perturbations and changes 
 in the sun's atmosphere. On 1st September 1859 Mr. Car- 
 
5 2 Electricity. [Booki. 
 
 rington, the astronomer, was taking observations on the sun's 
 spots in his Observatory at Redhill, when suddenly, within the 
 area of the largest group of spots, there broke out two patches 
 of intensely bright and white light, which, after increasing for 
 some seconds, gradually died away, the whole duration of the 
 phenomenon being not more than five minutes, during which 
 time the two patches traversed a space on the sun's disc of no 
 less than 35,000 miles. On visiting, a few days afterwards, the 
 magnetic Observatory at Kew, he learned that at the instant 
 he observed this phenomenon the three magnetic elements 
 were disturbed, the declination needle making a movement of 
 
 , , 13-2' to the west. 
 
 A further connection between the earth's magnetism and 
 
 '*the sun is shown by the apparent coincidence of the periods 
 of greatest frequency of sun-spots with a periodic maximum 
 disturbance of the magnetic needle. It seems pretty well 
 established, by observations extending over 150 years, that 
 there exists a periodic frequency of sun-spots, whose period 
 is from ten to eleven years. Accurate information on mag- 
 netic variation extends over a very much shorter period, but 
 there seems to be, at stations widely separated, a marked co 
 incidence between the periods of frequency of sun-spots, of 
 magnetic storms, and of a marked increase in the range of the 
 diurnal variation. These can hardly point to anything else 
 but a very marked influence exercised by the sun on the mag- 
 netism of the earth. 
 
 38. Other Variations. Such are the chief perturbations 
 in the magnetic elements, their character and amount changing 
 at different places on the earth. That others exist is highly 
 probable, and perturbations with a half-yearly period, and 
 
chap, iv.] Terrestrial Magnetism. 53 
 
 others depending on the moon, have been pointed out as 
 probable at least. These and many others may yet be de- 
 tected by careful comparison of the records continually accu- 
 mulating in the various magnetic observatories of the world. 
 
 39. Magnetic Charts. To get a connected view of 
 the main features of terrestrial magnetism, charts are con- 
 structed showing, by lines across the surface of the globe, all 
 places which have one of their magnetic elements the same. 
 Owing to the secular variation in all these elements, the 
 maps constructed for our epoch will require constant cor- 
 rection to bring them up to date. Those given are all for 
 the epoch 1840, and were prepared by Colonel (afterwards 
 General) Edward Sabine, E.A., from all the observations col- 
 lected during the preceding three years, the lines connecting 
 the stations of observation being supplied by Gauss's mathema- 
 tical theory of terrestrial magnetism. The lines on the isoclinal 
 map connect all places having the same inclination, on the 
 isodynamic map those which have the same intensity, and on 
 the isogonic map those which have the same declination, the 
 value of the element being denoted by figures above the lines. 
 
 40. Isoclinal Chart. Looking first at the isoclinal chart, 
 we see that the world is divided into two hemispheres, a north 
 magnetic in which the dip of the needle is to the north, and 
 a south magnetic in which the dip of the needle is to the 
 south, the lines of equal dip showing a rough parallelism 
 to the line of no dip, which is often called the Magnetic 
 Equator. This equator, however, is not a circle, and cuts the 
 equator at 2 E. long., and again in 170 W. long. 
 
 There are two points, one in the northern hemisphere and 
 one in the southern, at which the dip is 90, or the magnetic 
 
chap, iv.] Terrestrial Magnetism. 55 
 
 force is vertical. These points are called the Magnetic Poles 
 of the earth, though in a different sense to that in which we 
 have defined the poles of a bar magnet. The term Pole of 
 Verticity is sometimes applied to them. According to Captain 
 Ross, this pole in the northern hemisphere is in lat. 70 5' 17" 
 N., and long. 96 45' 48" W. In the southern hemisphere 
 the pole has not been reached, but in 1841 Captain Ross 
 found the dip to be 88 35' in lat. 76 20' S., and long. 
 165 32' E. 
 
 41. Isodynamic Chart. On comparing the chart of 
 isodynamic with that of isoclinal lines, we observe that the 
 two sets do not coincide, the line of least general intensity 
 not being the magnetic equator, and not being of equal in- 
 tensity throughout. By the line of least intensity, we mean 
 a line, such that the intensity increases as we pass off this 
 line on one side or the other. There exists a particular point 
 on this line at which the intensity is smaller than at any 
 other point in the world. This point, according to Erman, is 
 in lat. 20 S., and long. 35 12' W. 
 
 In the same way, by a point of maximum intensity, we 
 mean a point such that the intensity diminishes as we pass 
 from that point in any direction whatever. Of such points 
 there are two in the northern hemisphere, and probably only 
 one in the southern. The points are often also called magnetic 
 poles, but should be distinguished as Poles of Intensity. The 
 two poles in the northern hemisphere are not of equal in- 
 tensity, the stronger lying in North America to the south- 
 west of Hudson's Bay, about lat. 52 19' N., and long. 92 W., 
 and the weaker lying in North Siberia. The positions of 
 these poles are only known approximately, and that in the 
 
chap, iv.] Terrestrial Magnetism. 57 
 
 southern hemisphere with still less exactness, the point of 
 highest recorded intensity, according to the observations of 
 Captain Eoss, being in lat. 60 19' S., and long. 131 20' E.; 
 but he had certainly not reached the actual point of greatest 
 intensity, and was prevented by insuperable obstacles from 
 proceeding further towards it. 
 
 These remarks are sufficient to show that the poles of ver- 
 ticity and intensity do not coincide in the northern hemisphere, 
 and although their position is less certainly determined in the 
 southern hemisphere, enough is known to say that they are 
 not coincident. 
 
 42. Isogonic Chart. Eeferring lastly to the declination 
 chart, or chart of isogonic lines, we see that the line of 
 declination is not a great circle, but an irregular line passing 
 through the poles of verticity and astronomical poles in both 
 hemispheres. The lines of small declination follow its general 
 direction, but the lines of higher declination form a series of 
 loops in each hemisphere, connecting the pole of verticity with 
 the corresponding astronomical pole. 
 
 There is to be noticed a remarkable oval patch extending 
 over parts of North-East Siberia, China, and Japan, along the 
 margin of which the declination sinks to 0, and within it 
 becomes westerly, though surrounded by a region of easterly 
 declination. 
 
 There is also an area similar to this over the Pacific, in 
 which the declination shows a curious decrease, but does not 
 reach 0. 
 
 43. Hypotheses of one or two Magnets. The first 
 attempt to explain physically the phenomena of terrestrial 
 magnetism was the hypothesis of Bond (published in 1676), 
 
chap, iv.] Terrestrial Magnetism. 59 
 
 which assumed two magnet poles, one in the northern and the 
 other in the southern hemisphere, but not coincident with the 
 terrestrial poles. Of these poles the magnetic south was in 
 the northern, and the magnetic north pole in the southern 
 hemisphere. This hypothesis explained the general observa- 
 tion that in the northern hemisphere the north end of a 
 needle dips down, and in the southern hemisphere the south 
 end. It would require, however, the poles of verticity and 
 intensity to coincide, and the lines both of equal dip and of 
 equal intensity to be small circles round this common pole as 
 their centre. We have already seen that neither of these is 
 the case, and have no choice but to reject the hypothesis. 
 
 The existence of two poles of intensity in the northern 
 hemisphere, inferred by Halley from his map of isogonic lines, 
 led him to the hypothesis (published in 1683) of two magnets, 
 of different strength, having their four poles at certain points 
 in the two hemispheres. This hypothesis (developed mathe- 
 matically by Hansteen in his Magnetismus der Erde, published 
 in 1819) was found to correspond with observation much more 
 nearly than that of a single magnet, but the discrepancies were 
 too great to allow of its being accepted as a full explanation 
 of the facts. 
 
 The German mathematician Gauss has developed a very 
 complete and satisfactory theory of terrestrial magnetism 
 from the very simple hypothesis that the earth as a whole is 
 magnetic, the northern hemisphere having an excess of south 
 polar magnetism, and the southern an equal excess of north 
 polar. The distribution of magnetic force is deduced from 
 observation of the elements at eight places widely scattered 
 over the earth. 
 
 Whether terrestrial magnetism is permanent, or the result 
 of cosmical induction, or partly both, we know not ; except 
 
60 Electricity. [Book i. 
 
 that observation justifies us in saying that some variations in 
 terrestrial magnetism, which depend on the position of the 
 sun in his daily and yearly course are likely to be due to 
 solar induction or to some less direct solar influence (such 
 perhaps as changes of temperature) ; while some remarkable 
 perturbations seem to be associated with outbursts taking 
 place in the solar atmosphere. 
 
 44. The Mariner's Compass. The practical interest 
 of terrestrial magnetism as applied to navigation is obvious. 
 
 FIG. 39. 
 
 The only element with which the mariner is directly concerned 
 in steering his vessel is the declination, and in parts of the 
 world where it is well known the course is directed by the 
 compass alone in all weathers ; astronomical observations 
 being used only to correct, from time to time, the calculated 
 position, derived from the rate and magnetic bearing. The 
 compass usually employed consists of a flat circular card, on 
 the under surface of which are secured four to eight light 
 
Chap. IV.] 
 
 Terrestrial Magnetism. 
 
 61 
 
 magnetic needles. The card swings in a compass-box on a 
 pivot placed at its centre, the box having a pointer which 
 corresponds to the direction of the ship's head. The box is 
 supported on gimbals (Fig. 39) an arrangement for preserving 
 the box horizontal while the ship is pitching and tossing. 
 The card is divided into thirty-two points by a star engraved 
 on it (Fig. 40), and it is by these points the course is steered. 
 
 FIG. 40. 
 
 45. Effect of iron masses in Ships. As soon as iron 
 entered largely into the construction of ships, errors in the 
 compass, depending on the terrestrial magnetic induction, 
 appeared. This effect is illustrated by holding a bar of soft 
 iron parallel to the dipping needle, when the lower end will, 
 on testing, be found to be a north pole, and the upper end a 
 south pole. If a piece of steel be held parallel to the dip and 
 hammered, it can be converted into a permanent magnet. In 
 this manner a fire-poker, which usually stands in a vertical 
 position, and is frequently struck down on the solid hearth, 
 is O'enerallv fonnrl to he a nfirma.npnt, rnao-npf 
 
62 Electricity. [Book i. 
 
 46. Semicircular Variation. The rudder-post is a 
 vertical mass of iron near the compass ; it will, under terrestrial 
 induction, always bring into existence a south pole nearly in 
 the plane of the compass. It is obvious from Fig. 41 that 
 the effect of this pole on the compass will be nil when it is in 
 the magnetic meridian, either north or south ; while to the 
 west of the magnetic meridian it will cause westerly varia- 
 tion in the north end of the compass needle, and when east 
 
 
 
 I 
 
 I 
 
 I 
 i 
 
 FIG. 41. 
 
 of the magnetic meridian an easterly variation. It is for 
 this reason called the Semicircular Variation. 
 
 This variation can be neutralised by placing a smaller rod 
 of iron on the opposite side of the compass-box, also in a 
 vertical position. Its exact position must be found by ex- 
 periment when the ship's head is east or west. 
 
 47. Quadrantal Variation. A horizontal mass of iron 
 in the ship such as the guns and iron armour in an old man- 
 
Chap. IV.] 
 
 Terrestrial Magnetism. 
 
 of- war, or even a cargo of iron and steel produce by their 
 transient magnetism another variation in the compass. Each 
 mass of iron becomes a magnet, always having its magnetic 
 axis parallel to the meridian. The effect is seen on inspect- 
 ing Fig. 42. In the four positions, A,B, C, D, of the mass 
 
 
 /v 
 
 
 
 T ' 
 
 
 tv 
 
 
 
 FIG. 42. 
 
 i.e. at the four cardinal points of the compass the variation 
 vanishes. When the magnetic mass is between^ and B i.e. 
 in the northwest quadrant the influence of the induced south 
 pole on the north pole of the needle preponderates, and the 
 variation of the north pole is west. Between B and C the 
 north polar influence preponderates, and the variation is east. 
 Between C and D, in the south-east quadrant, it is again 
 west, and between D and A, or in the north-east quadrant, it 
 
64 Electricity. [Book i. 
 
 is east. This variation, from changing its direction at each 
 quadrant, is called quadrantal variation. It follows that two 
 masses of soft iron fixed in the ship on opposite sides of the 
 compass always increase each other's disturbance of the needle, 
 but if placed so that the lines joining them to the compass 
 subtend a right angle, they tend to neutralise each other's 
 effect. To correct this variation a mass of soft iron must be 
 fixed near the compass in a direction at right angles to that 
 of the centre of the resultant disturbing mass. 
 
 48. Magnetism of Steel-plated Ships. As soon as 
 ships were constructed of iron plates riveted together, it was 
 found that the hammering of the plates during construction 
 converted them into permanent magnets, the total effect of 
 which on the ship's compass was very large and very irregular : 
 so much so that in one ship the compass varied 50 east in one 
 position of the ship's head, and 50 west in another. It was 
 found by theory, and confirmed by experiment, that the total 
 permanent magnetism could always be resolved into two 
 magnets, one along the ship's length, and the other trans- 
 verse to the ship. Each of these was separately corrected 
 by a permanent magnet fastened on the deck of the vessel. 
 
 After the first few voyages of an iron ship a considerable 
 amount of the magnetism obtained during construction is 
 lost, probably by beating about with the waves, and it is in 
 consequence necessary, while the ship is young; to make a 
 new correction for magnetism after each voyage. Very soon, 
 however, the ship acquires a permanent magnetic condition, 
 after which no further readjustment is needed. 
 
 The magnetism lost during the first few voyages is called 
 sub-permanent, and that retained always permanent magnetism. 
 
QUESTIONS ON BOOK I. 
 
 1. Draw a rough sketch of the lines of force for three equal and 
 similar magnet poles placed at the angles of an equilateral triangle. 
 
 2. Draw the lines of force for two magnet poles of the same sign, 
 but one stronger than the other. 
 
 3. On twisting the torsion circle in Coulomb's balance, through 40, 
 the needle is deflected from the meridian 5. Find the torsion equi- 
 valent of the earth's directive action on the magnet. 
 
 ANS. 7. 
 
 4. The earth's directive action being measured by 5 of torsion, 
 how far must the torsion circle be twisted round to bring the needle 
 to 10? 
 
 ANS. 60. 
 
 5. The influence of the earth in Coulomb's balance being neutralised 
 by external magnets, so that the needle is under torsion only; when 
 the magnet pole is introduced the needle deflects 40. How much 
 torsion must be applied to bring the needle to 20 and to 10 ? 
 
 ANS. 140 and 630 respectively. 
 
 6. The directive action of the earth being 5, the introduction of 
 the magnet causes a deflection of 40. How much torsion must be 
 put on to bring the reading to 20 ? 
 
 ANS. 840. 
 
 7. A short magnet needle suspended horizontally, and oscillating 
 under the earth's action only makes 21 oscillations in a minute ; when 
 another magnet pole is distant 4 inches it makes 27 oscillations in the 
 same time. Calculate the number of oscillations it will make when 
 the second pole is distant 2 inches. f^f ^ 
 
 ANS. 40 per 1' nearly. 
 
 8. A short suspended magnet, oscillating under the earth's force, 
 makes 35 oscillations in a minute ; when a south pole is placed in the 
 meridian to the north of it, it makes 45 oscillations in the same time. 
 How many oscillations per minute will it make if the pole be placed 
 at the same distance to the south of it ? 
 
 ANS. 21 per 1' nearly. 
 
 E 
 
66 Questions on Magnetism. 
 
 9. A needle makes 29 oscillations per 1' when a south magnet pole 
 is 8 inches to the south of it, and 50 oscillations when the same pole is 
 4 inches to the north of it. Find how many oscillations the needle will 
 make when under the earth's influence only. 
 
 ANS. 34 oscillations per 1' nearly. 
 
 10. Two magnet needles of equal size and weight, freely suspended, 
 under the earth's action, make 40 and 36 oscillations respectively in 
 the same time. Compare their magnetic strength. 
 
 ANS. Ratio of 1 to -81. 
 
 11. Two magnets 14 and 16 centimetres long, placed east and west 
 of a suspended needle, with their nearer poles 7 and 8 centimetres 
 respectively from the point of suspension, just balance each other. 
 Compare the strengths of their poles. 
 
 ANS. 49 to 64. 
 
 12. Two equal magnet poles, placed 3 centimetres apart, exert on each 
 other an attraction of 4 units. Find the strength of the poles in 
 absolute measure. 
 
 ANS. Each of strength 6. 
 
 13. Two magnet poles, whose strengths are in the ratio 3 to 2 when 
 placed 10 centimetres apart, exert a force of 24 units. Find the 
 strength of each pole in absolute measure. 
 
 ANS. 60 and 40. 
 
 14. Two magnets, the strengths of whose poles are 8 and 12, are 
 placed in the same straight line, with opposite poles facing each other, 
 at a distance of 4 centimetres. If the magnets are respectively 12 
 and 16 centimetres long, find the magnetic attraction between them. 
 
 ANS. 5 '5 units nearly. 
 
 15. The same magnet needle, suspended horizontally under the 
 earth's action, makes at two places 101 and 103 oscillations in the 
 same time. Compare the horizontal component of the earth's mag- 
 netism at those places. 
 
 ANS. 1 to 1-04 nearly. 
 
 16. A short magnet, suspended horizontally, makes 29 oscillations 
 in a minute ; when a south pole is placed 4 centimetres from it on the 
 north side, it makes 39 oscillations in the same time. Compare the 
 strength of this pole with the horizontal component of the earth's 
 magnetism. Explain fully what is meant by this comparison. 
 
 ANS. 12-9 to 1 nearly. 
 
BOOK II. 
 FRICTIONAL ELECTRICITY. 
 
 CHAPTER L 
 ELECTRIFICATION. 
 
 49. Definition of Electricity. There are certain bodies 
 which, when warm and dry, acquire by friction the property 
 of attracting feathers, filaments of silk, or indeed any light 
 bodies towards them. This property is called Electricity, 
 and bodies which possess it are said to be electrified. The 
 ancients were acquainted with it only in amber, the Greek 
 name for which (r/AeKT/oov) is the origin of the term Electricity. 
 Dr. Gilbert, physician to Queen Elizabeth, seems to have been 
 the first who noticed the same property in other bodies, and 
 we shall see reason to believe that any two bodies whatever 
 of different structure, when rubbed together, develop elec- 
 tricity to a greater or smaller extent 
 
 To exhibit this property all the apparatus employed must 
 be kept warm and dry, With this precaution, absolutely 
 necessary in all experiments on the present subject, it is easy 
 to exhibit electricity in a very great variety of bodies. Glass 
 rubbed with silk, sealing-wax rubbed with flannel, vulcanite 
 or ebonite rubbed with any woollen material, or with silk, 
 
 67 
 
68 Electricity. [Book n 
 
 common writing-paper well warmed and rubbed with a bristle 
 clothes-brush all manifest electricity by picking up feathers, 
 scraps of paper, silk fibre, or other light materials. 
 
 50. Means of detecting Electricity. If we present 
 an electrified body to a pith-ball pendulum that is, a pith 
 
 ball suspended by a silk thread it is 
 first drawn towards the excited body, 
 and, immediately after contact, repelled, 
 for a reason which we shall see pre- 
 sently. A skeleton-ball pendulum (Fig. 
 43) made of narrow strips of gilt paper, 
 or a small disc of tinfoil, will answer 
 equally well. A light lath (Fig. 44), 
 about a metre long, poised on the con- 
 vex surface of an egg or a watch-glass, 
 will follow the movements of the excited 
 body round a complete circle. These 
 and other arrangements described later for detecting the 
 presence of electricity are called Electroscopes. 
 
 If the body electrified be very light, it will cling to other 
 bodies to which it is presented. The paper excited by a 
 clothes-brush will be found to cling with some force to the 
 table on which it was laid while being excited by brushing ; 
 on removal it clings to the hands of the operator, and may 
 be made to cling to the walls of a room, or any other flat 
 surface. 
 
 51. Action of Electrified Bodies on each other. 
 
 To investigate the action of electricity on other electricity, we 
 will excite by friction a rod of sealing-wax, and either poise it 
 on a convex surface, like the lath electroscope, or suspend it 
 
Chap. I.] 
 
 Electrification. 
 
 6 9 
 
 in a paper stirrup (Fig. 45), like the magnet in Art. 3. If we 
 bring towards its end another rod of sealing-wax, also excited, 
 
 Fro. 44. 
 
 we shall find repulsion between the two rods. If, on the other 
 hand, we bring towards it an excited glass rod, we shall find 
 
 A 
 
 FIG. 45. 
 
 attraction. If instead we take an excited glass rod, and 
 suspend it in a paper stirrup, or poise it on a point by means 
 
7O Electricity. [Book n. 
 
 of a dimple blown in its surface (Fig. 46), we shall find it 
 attracted by excited sealing-wax, but repelled by excited 
 glass. 
 
 52. Vitreous and Resinous Electricity. This 
 teaches us that there are two different kinds of electricity : 
 
 FIG. 46. 
 
 one developed in glass when excited by silk, called Vitreous 
 or Positive electricity (written + E.) ; another developed in 
 sealing-wax when excited by flannel, which is called 
 Resinous or Negative electricity (written K). The experi- 
 ments also show that like electricities repel, but unlike 
 electricities attract, each other. 
 
 The suspended glass and sealing-wax rods when excited 
 may be used to detect the kinds of other electrifications ; for 
 a body, if unelectrified, will attract both rods when presented 
 to them in turn, but an electrified body will attract one and 
 repel the other, as its electricity is of the opposite or of the 
 same name. Thus paper electrified by rubbing with india- 
 
chap, i.] Electrification, 71 
 
 rubber will be found to have a charge of vitreous electricity, 
 and the india-rubber will have a charge of resinous electricity. 
 If a silk ribbon (Fig. 47), a foot or a foot and a half long, 
 after being rubbed several times over a glass rod, is folded 
 in the middle, the two halves repel each other, being similarly 
 excited by the glass, and, if suspended, 
 remain for some time divergent. This 
 may be used as an electroscope, for on 
 bringing near from below a negatively- 
 electrified body (an excited rod of sealing- 
 wax, for instance), the ribbons diverge 
 further, they being negatively electrified ; 
 and, conversely, on bringing near a 
 positively electrified body they collapse. 
 In the same manner, if a sheet of paper, before it is excited, be 
 cut up into narrow strips, only held together along one edge, 
 after excitement the strips show a violent repulsion, curling 
 up away from one another. 
 
 53. Conductors and Non-Conductors or Insulators. 
 
 --There is a class of bodies, of which the metals are the best 
 
 Fid. 48. 
 
 examples, which do not show any sign of electrification when 
 excited by friction. This is the case with a brass rod held in 
 
72 Electricity. [Bookii. 
 
 the hand, and rubbed with a cat's fur or a silk handkerchief. 
 If, however, the brass rod be supported on a handle of glass 
 (Fig. 48) or ebonite, we shall find that, holding it by its handle, 
 and rubbing it, it is immediately excited, and on testing is 
 found to be charged with negative electricity. On touching 
 the excited brass with the finger, or with another metal body 
 in connection with the earth, all signs of electricity instan- 
 taneously disappear. We see therefore that the metal is 
 capable of excitement like the other bodies we have con- 
 sidered ; but the reason we do not observe it when held in 
 the hand and excited is, that the electricity is drawn away by 
 the hand as fast as it is generated. Bodies such as these are 
 called Conductors ; while other bodies, such as glass and seal- 
 ing-wax, which do not carry away the electricity as fast as it 
 is generated, are called Non-conductors or Insulators. These 
 latter, which can be excited when held in the hand, used to 
 be called Electrics, and those like the metals, which were not 
 so excited, were called Non-electrics. These terms, however, 
 are now misleading, and had better be abandoned. 
 
 Different bodies have very different powers of conducting 
 electricity, all being intermediate between an ideal perfect 
 conductor and perfect non-conductor. The best conductors 
 are the metals, and the best solid non-conductor is said to be 
 gum-lac. For our present purpose it will be sufficient to notice 
 that such bodies as the following are, next to metals, the best 
 conductors : Charcoal, graphite, water, mineral and vegetable 
 substances (chiefly owing to the large amount of water they 
 contain), and linen and cotton fibres. The best non-conduc- 
 tors or insulators after gum-lac are sealing-wax, glass, resin, 
 sulphur, silk, dry paper, and caoutchouc. These are roughly 
 in order of their powers of conduction and insulation respec- 
 
chap. i. ] Electrification . 7 3 
 
 tively. It is doubtful how far air and gases are conductors 
 in the proper sense of the word, but it is important to notice 
 that dry air acts as an insulator of ordinary charges, while 
 damp air allows the charge to pass away, though this effect is 
 probably due to the film of moisture formed on the surface of 
 the insulating supports of electrified bodies, and this liquid 
 film is certainly an excellent conductor. In the case of liquids 
 also mercury and the fused metals conduct well, and just 
 like the metals ; aqueous solutions of acids and salts are fair 
 conductors ; pure water, alcohol, ether, are semi-conductors ; 
 while carbon bisulphide is a good non-conductor, though in 
 these, excepting the metals, it is doubtful how far conduction 
 is separated from another action (electrolysis), which we 
 shall discuss later on. 
 
 Conduction in bodies is also affected by temperature. Some 
 bodies which are insulators when cold become conductors when 
 heated to fusion, or even considerably below fusing-point. 
 This is the case with glass. 
 
 54. Effect of Damp or Dry Atmosphere. We can 
 
 now understand the necessity for drying and warming our 
 apparatus, insisted upon above. Warming the air of a room in 
 which experiments are performed dries the air, by removing 
 it further from its dew-point, while warming the apparatus 
 above the temperature of the air prevents the formation of 
 the film of water on the insulating supports. Paper, being 
 very hygroscopic, must be thoroughly dried by holding it 
 before the fire for a minute or so, in order to drive out the 
 moisture before it can be electrified. 
 
 55. Gold-leaf Electroscope. The instrument most 
 
74 
 
 Electricity. 
 
 [Book II, 
 
 FIG. 49. 
 
 commonly used for investigations in electricity is the Gold- 
 leaf Electroscope. This consists of a brass 
 rod (A) fastened to the centre of a brass 
 circular cap (B), and having at its other end 
 two strips of gold leaf (0(7), which, when 
 the instrument is unelectrified, hang down 
 parallel to each other. This apparatus is in- 
 sulated by supporting the cap on a glass 
 tube (D\ well varnished, which surrounds 
 the brass rod. The tube is cemented into 
 the top of a glass bell-jar (E). Two strips of 
 tinfoil (FF) usually run from the base of 
 the glass bell up to the level of the gold 
 leaves. The base is of wood, sometimes 
 covered with tinfoil, and usually supports a cup of 
 sulphuric acid, or calcium chloride, to maintain dryness in 
 the air. 
 
 On touching the cap of the electroscope with excited glass 
 or sealing-wax, we communicate a charge which causes the 
 gold leaves to diverge exactly like the excited silk ribbons in 
 Art. 52. Otherwise a negative charge can be communicated 
 by simply napping the cap slightly with a silk handkerchief, 
 affording another illustration of the electrification of an insu- 
 lated conductor by friction. Further, when we have charged 
 the electroscope, say with positive electricity, on bringing an- 
 other positively electrified body near to its cap, we observe 
 that the leaves diverge further : this is because the posi- 
 tive electricity tends to repel like electricity from the 
 cap into the leaves, causing further divergence. In the 
 same manner, on bringing a negatively electrified body 
 near, the leaves are observed partly to collapse. In this 
 
chap, i.] Electrification. 75 
 
 manner we use the electroscope to distinguish even very 
 feeble charges of electricity. 1 
 
 56. Development of the two Electricities, simulta- 
 neous and in equal quantities. It will now be easy to 
 
 show that these opposite electricities are always developed 
 together; that where the glass was charged with positive 
 electricity, the silk used for the rubber carried off negative elec- 
 tricity, and that where the sealing-wax was charged negatively 
 the flannel used as rubber carried off positive electricity. 
 
 FIG. 50. 
 
 This can be shown (Tig. 50) by taking a plate of window- 
 glass, and a rubber made of leather covered on its flat surface 
 with silk (better if amalgamated, as for the electrical machine), 
 and furnished with a glass handle. On simply turning the 
 rubber round on the plate a few times, the friction develops 
 electricity ; but on presenting the plate and rubber in contact 
 to the previously charged electroscope, no indication of elec- 
 tricity appears. On presenting them separately, however, 
 the glass is found to be positively and the rubber negatively 
 
 1 For a similar reason to that noticed in Magnetism, we must 
 observe the first movement of the leaves as the electrified body 
 approaches the electroscope. 
 
76 Electricity. [Boot n. 
 
 charged. Similarly, if a rod of sealing-wax (Fig. 51) be fur- 
 nished with a flannel cap extending three inches down it (with 
 a silk thread attached by which it can be drawn off), by 
 twisting the rod round and round inside the cap electricity is 
 generated ; but on presenting them together to the electro- 
 scope, no trace of electrification is observed. When, after 
 drawing off the cap by the silk thread, they are presented 
 separately, the sealing-wax is found to be negatively and the 
 flannel cap positively electrified. 
 
 PIG. 51. 
 
 This shows that tne two electricities are always separated 
 together, and since, while the two bodies are held in contact, 
 there is no trace of electrification, the two quantities sepa- 
 rated are always such as just to neutralise each other's attrac- 
 tive and repulsive effect on external electricity. This leads 
 us also to say that the two electricities are separated in equal 
 quantities. This statement we shall find to be of universal 
 application ; and we can no more develop a quantity of posi- 
 tive electricity without an equal (or complementary) quantity 
 of negative electricity, than we can have a north magnetic 
 pole without somewhere an equal south pole. 
 
 57. The Electrical Series. The kind of electrification 
 developed on a body depends not only on the body itself, but on 
 the substance with which it is rubbed. Thus glass is positive 
 
chap, i.] Electrification. 77 
 
 when rubbed with silk, and negative when rubbed with the - 
 fur of the living cat. Minute differences in the surface texture 
 of the substances rubbed leads to an electrical separation on 
 rubbing. Thus white and black silk, when rubbed together, 
 show a separation of electricity ; probably due to a difference 
 in surface caused by the dye ; rough and smooth glass, when 
 rubbed together, leave the smooth positively and the rough 1 
 negatively electrified ; and even two pieces of ribbon cut from 
 the same piece, if drawn over each other, the length of one 
 across the breadth of the other, will show a separation of 
 electricities. The fur of the living cat, and, according to 
 Clerk-Maxwell, that of the living dog, is found to be positive 
 to a dressed cat's fur. 
 
 If we have any three substances (A, B, C), and find by, 
 experiment that A carries away positive electricity when 
 rubbed with B, and B positive electricity when rubbed with 
 C, we shall always find A positive to C when they are rubbed 
 together. In performing the experiment care should be takeif 
 that all the bodies are neutral, to begin with. Suppose, for 
 instance, that A, on being rubbed by B, left B with a high 
 charge of negative electricity, the effect of rubbing B and C 
 might then be only to divide B's charge between B and C, 
 which would then both be found negative. 
 
 On this ground it is possible to arrange any given sub- 
 stances in an electric series, such that each member of the 
 series is positive to all that come after it, but negative to all 
 that go before it. From what we have just said, it will be 
 clear that the order of the series will not be the same for all 
 samples of nominally the same substance, and thus irregu- 
 larities occur. Thus it is generally stated that cat's fur stands 
 at the head of this series, but the present writer has found 
 
78 Electricity. [Book n. 
 
 certain cleavage planes in calcite to be positive to the fur 
 of at least one living cat, and has found specimens of glass 
 positive to some dressed furs. The series given by different 
 authors consequently differ a good deal ; that which we 
 supply here must therefore be understood as only true in a 
 general way, with such limitations as we have noticed. It 
 is that obtained with the substances generally used by the 
 present writer. 
 
 Catskin. 
 Smooth Glass. 
 The Hand. 
 Paper. 
 Flannel. 
 Silk. 
 
 Koughened Glass. 
 Cork. 
 
 Metal. 
 Caoutchouc. 
 Planed Dealboard. 
 Ebonite. 
 Sealing-wax. 
 Sulphur. 
 
 Vulcanised India- 
 rubber. 
 
 58. Electrification by Pressure and Cleavage. 
 
 There are other methods besides friction of causing electrical 
 separation. We do not at present refer to electricity de- 
 veloped by contact in metals, or by chemical decomposition, 
 or by heating the junction of two metals. If two non-con- 
 ductors be simply pressed together, and suddenly separated, 
 they will be found to be electrified. This is easily shown by 
 pressing a cork supported on a glass handle down on to a 
 piece of indiarubber, or even on to a piece of orange-peel. 
 Many minerals show an electrical separation on cleavage. 
 If a block of j&ka be held by two insulating handles, and 
 separated along cleavage planes, the flakes will be found to be 
 
c&ap. L] Electrification. 79 
 
 electrified. The same thing appears on breaking up roll- 
 sulphur. If the sulphur be supported on an insulating pad, 
 a piece of india-rubber for instance, and be broken over an 
 electroscope by smart taps of a hammer, the fragments which 
 fall on the cap will generally make the leaves diverge. For 
 the same reason, lump sugar, when broken in the dark, often 
 shows a phosphorescence, due to the reuniting of the electri- 
 cities separated by the fracture. 
 
 59. Pyro-Electricity. There is also another mode in 
 which electricity is developed, namely, when certain badly 
 conducting minerals are heated or cooled. This is termed 
 pyro-electricity. It is most strongly shown in tourmaline 
 
 Fio. 52. 
 
 crystals which have the facets at the opposite ends of the 
 crystal differently arranged (Fig. 52). The specimen should 
 be suspended in a stirrup of fine wire over a metal plate 
 warmed by a spirit lamp. Very soon one end will show 
 positive, and the opposite negative, electricity, and this will 
 continue as long as the temperature rises, till it reaches a 
 temperature of about 350 C., when all trace of electricity 
 ceases. On removing the plate, and passing the lamp flame 
 over the crystal to discharge its electricity, and then allowing 
 it to cool, that end which was positive when being heated 
 becomes negative while being cooled, and -vice versa. The end 
 
8o Electricity. [Book n. 
 
 which is positive while being heated is called the analogue, 
 and the opposite the antilogue, pole of the crystal. Suitable 
 crystals are rare, but specimens in the form of long needles 
 may be met with, which show pyro-electricity faintly, and 
 especially while cooling. Observation can be more easily 
 made by help of the Quadrant Electrometer described later. 
 In Fig. 52 the left-hand drawing showing the terminal 
 with fewest facets is the analogue, and the right-hand draw- 
 ing is the antilogue pole. 
 
 No physical theory has yet been propounded to account for 
 the electrical separations we have noticed. We may, per- 
 haps, point out that they all seem dependent on a molecular 
 strain in the molecules of different bodies when brought into 
 very close contact by friction or pressure. The electrification 
 by cleavage or heating in crystals may be referred to a similar 
 cause, if we remember that in many crystals the arrangement 
 of the molecules is such that their expansion by heating and 
 all physical properties are different in different directions. 
 In these, either cleavage or heating may establish a state 
 of molecular strain which is accompanied by a separation of 
 electricity. If the crystal is a conductor, the separated 
 electricities of course immediately unite again, and the phe- 
 nomenon cannot be observed. 
 
 We have, as in Magnetism, purposely avoided all reference 
 to the various one and two fluid hypotheses, which were useful 
 only in the infancy of those sciences. 
 
CHAPTER II. 
 THE FIELD OF ELECTRIC FORCE. 
 
 60. The Electric Field. We must now proceed to 
 consider the laws of attraction and repulsion of electrified 
 bodies, just as we did in Magnetism. We have seen that if we 
 have a distribution of electricity, and an electrified body be 
 brought near it, this latter will experience mechanical force. 
 Just, then, as the air space round a magnet showed us a field 
 of magnetic force, so the air space round an electrified body 
 shows us a field of electrical force. To the air or other 
 medium across which electrical forces are displayed, Faraday 
 gave the name dielectric. It will simplify matters if we 
 use for exploring the field of force a very small sphere, 
 carrying always the same charge of electricity, and we may 
 then assume that the action on this sphere is the same as if 
 all the electricity were collected at some point within it, 
 probably near its centre. We will suppose this an unit charge, 
 and assuming the electrification positive, we will call it a 
 plus unit (written + unit). At every point in the field of 
 force there will be a certain definite direction in which the 
 + unit put there will be urged, and this direction is called 
 the line of force through that point. The whole field may 
 therefore be mapped out into lines of force, which, as in 
 Magnetism, cannot intersect each other. There will also be 
 a certain force with which the + unit is urged along the line 
 of force at each point in the field, and this force is called the 
 
 F 
 
82 
 
 Electricity. 
 
 [Book H. 
 
 strength of the field at that point. We may also define the 
 positive and negative direction of a line of force as the direc- 
 tion in which a + or unit respectively would be urged. 
 
 6l. Coulomb's Torsion Balance. We have no means, 
 similar to the magnetic curves, for exhibiting to the eye the 
 form of the lines of force. We may assume, however, that 
 
 PIG. 
 
 the lines of force for a small electrified sphere proceed out 
 round it in all directions, and can then investigate the strength 
 of the field at each point as depending (1) on the distance, 
 (2) on the quantity, of electricity present. This was done by 
 Coulomb, using a torsion balance very similar to that used 
 by the same experimenter for magnetic forces. 
 
chap. iL] The Field of Electric Force. 83 
 
 The torsion balance (Fig. 53) consists of a glass needle (A) 
 carrying at one end a gilt ball (B), and at the other a counter- 
 poise, suspended by a fine wire ((7), which is often a single 
 capillary fibre of glass, attached to a torsion circle (D) above, 
 the circle having a graduated rim by which the twist put on 
 to the wire may be measured. The needle moves in a glass case 
 (E), whose surface is graduated, the suspension of the needle 
 being in the centre of graduations : by its means the movement 
 of the needle may be read. In the upper part of the case there 
 is a hole through which an insulated gilt ball (F) (the carrier 
 ball), of the same size as the needle ball, may be introduced 
 and placed in contact with the needle ball. Another in- 
 sulated gilt ball (G-) (the divided-charge ball), equal to the 
 carrier and needle balls, and supported on an insulating stem, 
 is required in the course of the experiment. The base is 
 supported on levelling screws, by which the suspension of the 
 needle is brought to the centre of the graduations on the case. 
 Within the case is placed a vessel with drying material as in 
 the gold-leaf electroscope. 
 
 When the whole system is unelectrified, the needle ball 
 rests in the place which the carrier ball will occupy when in 
 position ; the wire being without torsion, and the needle and 
 pointer each at its zero of graduation. 
 
 62. Law of Action at different Distances. On 
 
 electrifying the carrier ball, and introducing it, there is at 
 first attraction, but after contact repulsion, of the needle ball. 
 We will suppose it to be repelled, and to come to rest at 72. 
 The torsion on the wire is also 72. To bring the needle back 
 to 36, it will be found necessary to turn the torsion circle 
 backwards through about 250. The repulsion at 36 will 
 
84 Electricity. [Book n. 
 
 then be 250 + 36 = 286, which we notice to be very nearly 
 4 x 72. Thus we learn that the repulsion at 36 is four times 
 that at 72. To bring the needle to 24, we must still turn 
 the torsion circle backwards through one complete revolution, 
 and 260 additional. The total torsion is then 360 + 260 + 
 24 = 644, which is nearly 9 x 72. 
 
 This will be sufficient to suggest the law of inverse squares, 
 as that holding between two small electrified spheres placed 
 at different distances from each other. In most instruments 
 the torsion, when the needle and carrier balls are within 20 
 of each other, becomes less than this theory requires, the 
 reason being that the electricities on the two balls mutually 
 repel each other towards the more remote sides of the balls, 
 and they in consequence act on each other at a distance some- 
 what greater than the distance of their centres. 
 
 We may infer that the strength of the electrical field, due 
 to a quantity of electricity condensed in a point, is inversely as 
 the square of the distance from the electrified particle, i.e. if 
 distances be taken respectively as 1, 2, 3, . . . etc., the forces 
 at those distances will be as 1, J, , . . . etc. 
 
 63. Law of Action with different Quantities. We 
 
 have seen nothing at present enabling us to measure quantities 
 of electricity, but if we have two equal spheres, one charged 
 with electricity, and the other insulated and neutral, we 
 may assume that on bringing them into contact the charge 
 will be divided equally between them. Thus, in the above 
 experiment, when the carrier ball touched the needle ball 
 the charge was equally divided between them, and we 
 were therefore investigating the force between two equal 
 charges. After turning back the torsion circle to its 0, let us 
 
chap, ii.] The Field of Electric Force. 85 
 
 remove the carrier ball, and halve its charge by simple contact 
 with the equal divided-charge ball. Reintroduce it into the 
 instrument, carefully avoiding contact with the needle ball 
 (this may be done by turning the torsion circle through 
 about a quarter of a revolution), and regulate the torsion 
 circle till the needle again stands at 72. It will be found 
 that the torsion circle stands at 36, and the torsion on the 
 wire is (72 36) = 36. Hence we see that the repulsive 
 force is halved on halving the charge in the carrier ball. 
 If we halve again the charge in the carrier ball, the torsion 
 circle must be twisted through 54, and the torsion is there- 
 fore (72 -54) = 18, which is one fourth of its first value 
 when the charge of one of the balls is divided by four. Lastly, 
 take out the carrier ball, and discharge by contact with the 
 finger. On reintroducing it, the needle ball is attracted, and 
 divides its charge with the carrier ball, so that each ball has 
 half of its original charge. We shall then find that the torsion 
 necessary to keep the balls at 72 is 18, or ^x^of that 
 when each charge was unity. 
 
 From these experiments we may infer that the force at 
 equal distances between two charges of electricity condensed 
 in points is proportional to the product of the quantities, and 
 that the strength of the field at a given distance from a charge 
 condensed in a point is proportional to the charge. 
 
 *64. Absolute Measure of Electricity. We may now 
 
 explain how electrical quantities may, like magnetic, be 
 measured in terms of the absolute system of units, explained 
 in Appendix I. Thus we shall assume one absolute unit of 
 electricity to be such a quantity that, when condensed in a 
 point, it exerts unit force on another equal quantity placed at 
 
86 Electricity. [Book n. 
 
 unit distance. We can then express the force between two 
 quantities q and q' condensed in points at distance D cm. apart 
 
 t>y > an d the strength of field at a distance Z>from a quan- 
 
 tity q condensed in a point by 
 
 Coulomb, by vertical stops which prevented the needle 
 swinging back to zero, showed identically the same laws to 
 hold for the attraction between two quantities of electricity 
 of opposite sign. 
 
 65. Use of the Proof- Plane. Returning to our funda- 
 mental experiment of the attraction and subsequent repulsion 
 by an electrified body of any light conducting body, we can 
 
 o 
 
 FIG. 54. 
 
 see that if we insulate by a glass handle a small gilt ball or 
 paper disc, and apply it to the surface of an electrified body, 
 it will, on removal, carry away some of its electricity, which 
 may be tested by a charged electroscope at a distance. We 
 may, in this manner, test the electrification of a body too 
 feebly electrified to show directly attractions and repulsions. 
 Such an instrument was called a Proof-Plane by Coulomb, and 
 has since his time been widely used in testing electrification. 
 It may be noticed that what we test by the proof-plane is 
 really the strength of the electric field close to the point on 
 the conductor at which it is applied, for this, and this only, 
 determines the quantity of electricity which shall be repelled 
 
chap, ii.] The Field of Electric Force. 
 
 on to the proof-plane when brought into contact with the 
 conductor, the flow continuing till the charge on the proof- 
 plane and that on the conductor exercise equal and op- 
 posite repulsions. Assuming, then, that the proof-plane is 
 so small that it can be charged from the conductor without 
 
 FIG. 55. 
 
 sensibly weakening its charge, or altering the distribution on 
 it, the proof-plane carries away a charge proportional to the 
 strength of the field of force close to the conductor at the 
 point where it is applied. 
 
 66. No Electricity within a hollow Conductor. 
 
 We will employ the proof-plane to show that there is no 
 electrical force inside a charged conductor, or, as it is usually 
 
88 
 
 Electricity. 
 
 [Book II. 
 
 expressed, that electricity resides only on the outside of a con- 
 ductor. 
 
 Let us take an insulated hollow sphere (Fig. 55), or con- 
 ductor of any shape, with a small circular aperture, through 
 which the proof-plane may be easily introduced. Charge the 
 conductor, 1 and charge with the same kind of electricity a 
 gold-leaf electroscope at a distance. On testing with the 
 proof-plane we find indications of a charge, on any external 
 point, but on any part of the interior surface no charge what- 
 ever. 
 
 FIG. 56. 
 
 Otherwise take an insulated sphere (A), having two in- 
 sulated hemispheres (BC), which envelop A, but are separated 
 from it by an air-space (shown in section in Fig. 56) Let A 
 be charged, and the hemispheres adjusted carefully without 
 
 1 In this and the following experiments the charging of the con- 
 ductors, but not of the electroscope, is done from an electrophorus. 
 
Chap. II.] The Field of Electric Force. 89 
 
 contact with A ; then lift by its silk thread the metal wire D, 
 and drop it through the aperture E in B, until it just rests on 
 A, and then remove it again. On removing B and (7, A will 
 be found to be completely discharged, the charge having been 
 by contact transferred to the external hemispheres. 
 
 Again, if we test the outside and inside of a hollow electri- 
 fied cylinder, we shall find the inside charge insensible every- 
 where except very near to the edge. This will be true even 
 if the cylinder be made of wire gauze with very large meshes. 
 Faraday used an insulated cotton gauze bag, similar to a 
 
 FIG. 57. 
 
 butterfly-net, fitted to a wire rim for support, and fastened on 
 to a glass stem, the end of the bag being furnished with a 
 silk thread passing through both sides, by which the bag 
 could be turned inside out at pleasure. After charging he 
 showed by the proof-plane that there was no sensible electri- 
 fication on the inside. He then by the silk thread turned 
 the bag inside out, showing again that there was no trace of 
 electrification on the inside surface. 
 
90 
 
 Electricity. 
 
 [Book II. 
 
 Faraday also constructed a cubical chamber, twelve feet 
 wide, formed of a slight wooden framework, with copper wires 
 passing along and across it in various directions, and then 
 covered it with paper in close proximity to the conducting 
 wires, and pasted bands of tinfoil over it in every direction. 
 This chamber was insulated, and put in connection with a 
 
 FIG. 58. 
 
 powerful electrical machine, which was worked for some time. 
 He then says: "I went into the cube and lived in it, and 
 using lighted candles, electrometers, and all other tests of 
 electrical states, I could not find the least influence upon them, 
 or indication of anything particular given by them, though all 
 
chap, n.] The Field of Electric Force. 9 1 
 
 the time the outside of the cube was powerfully charged, and 
 large sparks and brushes were darting off from every part of 
 its outer surface." 
 
 We may imitate this experiment by placing a metal wire 
 cage over a gold-leaf electroscope supported on a metal plate, 
 which is insulated with a pad of india-rubber (Fig. 58). We 
 may either leave the electroscope free or connect its cap by a 
 wire with the outside surface of the cage ; but on electrifying 
 the cage, the leaves of the electroscope will not diverge, as we 
 have seen they always do when the instrument is placed in a 
 field of electric force. 
 
 (X- 
 
 67. Electrical Density, These experiments show us 
 that the field of force only exists in the dielectric surrounding 
 electrified conductors, and does not extend inside them. 
 They show not only that there is no electricity within the 
 conductor, but also that the external electrification is so dis- 
 tributed that the resultant force at every internal point 
 vanishes. The older theorists, assuming that electricity was 
 of the nature of a material but weightless film investing the 
 conductor, set themselves to discover the law of density of 
 such a film that the condition thus stated might be true, and 
 there came into use the term Electrical Density at a point on 
 a conductor. We may use the term to denote the quantity 
 of electrification per unit area on a charged conductor, and this 
 implies no material idea of electricity, while our definition of 
 quantity implies none. The term, moreover, is convenient, 
 since we can clearly have the same quantity of electricity on 
 a sphere of one inch or of one foot radius, and the densities 
 of the distributions must thus be inversely as the surfaces of 
 the spheres, or as 144 to 1. It follows, too, theoretically, as a 
 
Electricity. 
 
 [Book n. 
 
 consequence of the general law of distribution stated above, 
 that the force close to any point on an electrified conductor is 
 proportional only to the density of the electrification at that 
 point. 1 Hence for our purpose it matters little whether we 
 speak of the force near a point on an electrified conductor, or 
 the density of the electrification at the point. 
 
 Although we cannot lay down the law of density of distri- 
 bution on a conductor, we can show the more general laws by 
 
 FIG. 59. 
 
 the proof-plane and gold-leaf electroscope. If we test a sphere, 
 we shall find that its electrification has the same density at 
 every point, as might have been expected from its shape. 
 For other conductors it will be found that the density at points 
 and angles is very high ; that at the flatter portions small ; 
 while within hollows and cavities it almost wholly disappears. 
 1 Cumming's Introduction to the Theory of Electricity, Art. 62. 
 
chap, n.] The Field of Electric Force. 93 
 
 If for the density we substitute depth of a liquid film 
 supposed homogeneous, we may represent to the eye the 
 depth of the imaginary electric stratum by the diagrams (Fig. 
 59), which show it approximately for a sphere, a cone, and a 
 hollow hemisphere. 
 
 67a. Cavendish's Proof of the Law of Inverse 
 Squares. The fallowing proof of the law of inverse squares 
 of distances as applied to electrical actions, which is infinitely 
 more rigorous than any deduction from experiments with the 
 torsion balance, was given by Henry Cavendish more than 
 100 years ago. He assumes the two results of experiment 
 referred to in the two preceding articles. 
 
 1st. There is no electrical force within a hollow insulated 
 spherical conductor. 
 
 2d. The distribution of electricity over a spherical con- 
 ductor, far removed from other conductors, is of uniform 
 density. 
 
 Now it was proved by Newton that a uniform shell of 
 attracting matter (the attraction being according to the law 
 of the inverse square of the distance) causes no attraction on 
 a material particle within it. The law of inverse squares of 
 the distance, for electrical actions, is therefore consistent with 
 both experiments referred to. Cavendish inquired whether 
 any other law could give the same perfectly balanced attrac- 
 tion on an internal particle, and he found that no other law 
 whatever satisfied this condition. (Cumming's Theory of 
 Electricity, Art. 56.) 
 
 68. Electrical Potential. We will now take a long 
 piece of copper wire, connecting one end with the electroscope 
 
94 
 
 Electricity. 
 
 [Book II. 
 
 cap, and attaching the other to a proof plane, or else support- 
 ing it towards the end on a rod of sealing-wax or glass, by 
 which the free end can be brought to any point on a con- 
 ductor. Electrifying any of the conductors we have been 
 experimenting upon, we pass the proof-plane or wire end over 
 its surface, and observe that there is a certain fixed diverg- 
 ence of the electroscope leaves, which remains the same 
 whether we touch the conductor at a place of high or low 
 density, ami whether we touch it within or without. 
 
 FIG. (50. 
 
 It will now be convenient to define by some term the 
 electroscope indication, and we will call it the potential of 
 the electroscope. If the leaves diverge with + E, we shall 
 speak of the indication as positive potential, which will 
 be low when the divergence is small, and high when the 
 divergence is large. Similarly we have negative potential 
 when the leaves are negative. 
 
chap, ii.] The Field of Electric Force. 95 
 
 The preceding experiment enables us to say that the poten- 
 tial of a conductor is the same, all over within and without 
 as the potential indicated by a distant electroscope attached 
 to the conductor by a long wire. Thus the electroscope, 
 which primarily indicates the potential of its own cap and 
 leaves, will also, from the proved property of a conductor, 
 indicate the potential of any conductor which is connected 
 with it by a conducting wire. 
 
 It must next be noticed that the potential of an electro- 
 scope or other conductor depends not only on the charge of 
 the body itself, but also on the charges of all surrounding 
 bodies. Thus when an uncharged electroscope is approached 
 by an electrified rod of glass, the leaves diverge, showing a 
 positive potential, though no charge has been communicated 
 to it. Thus we see that an insulated conductor acquires a 
 positive potential from the mere presence of a + electrification 
 near it. If the electroscope were first charged +, the poten- 
 tial is increased by bringing near to it a body with a -f- 
 electrifi cation. If an excited rod of ebonite be approached 
 towards a + charged electroscope the leaves at first collapse, 
 showing a lowering of potential by the approach of E. 
 If the E be brought nearer, the leaves completely collapse 
 (when we may for convenience call the potential zero), and 
 on further approach still they diverge with E, showing 
 therefore negative potential. Thus we see that a body whose 
 own charge is + may acquire a negative potential owing to 
 the presence of E near to it. Similar results with oppo- 
 site signs follow if we first charge the electroscope with E. 
 We may- then generalise and say that the potential of a body 
 is always raised by bringing + E near, and always lowered by 
 bringing E near. We must understand raised and lowered 
 
96 Electricity. [Book n. 
 
 here in their algebraical senses : thus a negative potential is 
 lowered when the leaves increase their divergence, and raised 
 when they partially collapse. 
 
 If a conductor connected with the earth, such as the hand, 
 be brought near a positively electrified conductor, its poten- 
 tial is lowered. This will be explained in the chapter on 
 Induction. 
 
 69. Capacity of a Conductor. Take the hollow sphere 
 having an aperture in its surface, and connect it with the 
 distant electroscope. If we bring successive charges by means 
 of a small insulated sphere or proof-plane, and introduce them 
 through the aperture, on touching the inner surface the charge 
 is given up to the sphere, and the proof-plane can be with- 
 drawn uncharged. We now observe that the potential shown 
 by the divergence in the gold leaves goes on rising with the 
 charge, and we shall assume that the potential is proportional 
 to the charge, so that for each conductor there is a fixed ratio 
 between the charge and the potential, which fixed ratio id 
 called the Capacity of the Conductor. If, then, we are able 
 to obtain a numerical measure of the potential in terms of a 
 suitable unit ; if Q represent the charge, F the potential, and 
 
 C the capacity of a given conductor, we have ^ = (7, or 
 
 Q=CF. The capacity may therefore be defined as the 
 quantity of electricity required to bring the conductor from 
 zero to unit potential. 
 
 The capacity, so far as a conductor insulated in a large room 
 is concerned, depends only on the shape and size of the con- 
 ductor. That the capacity depends on the form, and not 
 only on the size of the conductor, may be shown by choosing 
 
chap. iL] The Field of Electric Force. 97 
 
 two conductors of the same surface and very different forms ; 
 a sphere composed of two separable hemispheres (see Fig. 56), 
 and one of the separate hemispheres answers well, since in 
 the hemisphere both the outer and inner hemispheres become 
 external. Charge one hemisphere and test its potential by 
 connecting it with a distant electroscope. Then bring up the 
 second hemisphere, and fit the two together without discharg- 
 ing, and you have the same quantity of electricity as before 
 distributed over the same surface, the inner surface now not 
 being electrified. It will be found, nevertheless, that the 
 gold leaves have collapsed somewhat, proving that for equal 
 charges the potential of the sphere is lower than the hemi- 
 sphere, or that the capacity of the sphere is greater than that 
 of a hemisphere of the same total area. 
 
 It will also be inferred from the last article that the capa- 
 city of a conductor depends also on the neighbourhood of 
 other conductors, electrified or not. 
 
 70. Potential Experiments with the Gold-Leaf 
 Electroscope. We can now examine more fully the 
 action of the Gold-leaf Electroscope, especially with reference 
 to the function of the tinfoil strips, which are attached to the 
 glass case opposite to the gold leaves. We will at present 
 assume that the whole base is covered with tinfoil in contact 
 with strips, and that it extends outside the glass case by 
 passing under it, as shown in section in Fig. 61. We will 
 now insulate the electroscope, and connect the cap with the 
 base by wires outside the case (Fig 62). We shall now find, 
 however highly we electrify the cap, there is no divergence of 
 the gold leaves. The effect of joining, by a conductor, the 
 base and the cap is to bring them all to the same potential. 
 
Electricity. 
 
 [Book II. 
 
 We learn, therefore, that the leaves will not diverge unless the 
 base and cap are at different potentials. To illustrate this 
 further, remove the connecting wires, and charge say 
 with + electricity the base, leaving the cap uncharged ; the 
 leaves now diverge with electricity. Next give a charge 
 to the cap, and if it be of the right strength, the leaves 
 collapse, since the base and cap are brought to the same 
 potential. If the last charge be too strong the leaves diverge 
 with + electricity. By giving alternate charges to the base 
 and cap we shall find that the leaves may diverge with -f- or 
 electricity, though both cap and base are charged posi 
 
 FIG. 61. 
 
 FIG. 62. 
 
 tively, just as the potential of the cap is higher or lower 
 than that of the base. 
 
 71. Electrical Force requires varying Potential. 
 
 These experiments teach us that we can only have electrical 
 force exhibited in a region in which the potential changes 
 as we go from one part to another. In the last experiment 
 the mechanical force which caused the leaves to diverge was 
 
chap, ii.] The Field of Electric Force. 99 
 
 exerted because a positive electrification tends to move from 
 places of higher towards places of lower potential \ and vice 
 versa, negative electricity tends from places of lower towards 
 places of higher potential. Every field of force therefore is a 
 region of varying, potential, but the space inside an electrified 
 conductor, in which, as we have already seen (Art. 66), no 
 divergence in the leaves of an unelectrified electroscope takes 
 place, must be a region of uniform potential. 
 
 We may point out two useful analogies which these experi- 
 ments suggest. First, that of temperature, in which a flow of 
 heat takes place from hotter to colder bodies, i.e. from bodies 
 at higher towards those at lower temperature. In this case 
 heat is analogous to electricity, and temperature to potential, 
 no exchange being apparent if the bodies are at equal tem- 
 peratures. Secondly, that of level in gravitation a liquid 
 (water, for example) always tends to flow when a channel is 
 opened from places of higher towards places of lower level, in 
 which case level is analogous to potential, and water to elec- 
 tricity, there being no flow of water between two reservoirs 
 at the same level. 
 
CHAPTER III. 
 ELECTRICAL INDUCTION 
 
 72. Electrification induced on an Insulated Con- 
 ductor. If we introduce an insulated unelectrified body into 
 a field of force, we find a separation of electricities by induc- 
 tion similar in general character to magnetic induction. 
 
 Pro. 63. 
 
 Thus if A (Fig. 63) be a body electrified, say positively, 
 and BC an insulated unelectrified body, we shall find on testing 
 EC with a proof-plane that there is a charge of negative 
 electricity at B and of positive electricity at C. If we pass 
 from B or C, testing with the proof-plane at each step, we 
 shall easily see that the density diminishes continually, 
 
 until at an intermediate point it vanishes. Such points of 
 100 
 
Chap. III.] 
 
 Electrical Induction. 
 
 101 
 
 neutral electrification form a neutral lin$ rpund;JB!C. j 
 see that the electrification of A acts on "the conductor C, 
 separating its electricities, drawing electricity; of ^opposite naii'e 
 towards B, and repelling electricity of like name towards C. 
 
 We infer that every electrical charge tends to separate 
 electricity in all surrounding conductors, drawing to the parts 
 nearest to it electricity of opposite name to its own, and 
 repelling to the most remote part electricity of like name. 
 
 FIG. 64. 
 
 It is easy to see that these induced charges are able to 
 cause fresh separations by induction in other bodies, as may 
 be seen if we bring DE (Fig. 64) near to <7, when we shall 
 find negative electricity towards D and positive towards E. 
 
 If BG be divisible into two parts by a plane through its 
 middle (Fig. 65), enabling us to separate B and (7, while 
 keeping them insulated, we shall find that B carries away a 
 negative charge and C a positive charge. 
 
 We thus see that from a given electrical separation we can 
 by induction make fresh separations in other conductors 
 without limit, and this principle is used in many machines 
 
IO2 
 
 Electricity. 
 
 [Book II. 
 
 fo^ generating electricity. It might at first sight appear 
 that in obtaining an unlimited amount of electrical sepa- 
 raoion from a smalJ initial separation we have a breach of 
 the general law of conservation of energy. Such is not the 
 case, however, since, in separating B and G in the foregoing 
 illustration, just as much energy is expended as would have 
 produced in any other way the separation in question. 
 
 FIG. 65. 
 
 If, while EC is under induction, we test in the manner of 
 Art. 68 its potential, we shall find it to be the same through- 
 out, just as for a charged body. This potential is found to 
 be lower than that of the charged body A, but nearer to A 
 the nearer BO is brought to A. The function of the induced 
 negative charge at B is to keep down the potential where it 
 would be too high, and that of the + charge at G to keep up 
 the potential where it would be too low. 
 
 We can now see that the attraction of light bodies in our 
 earliest experiments was itself a consequence of induction. 
 These bodies had a charge developed in them by induction 
 opposite to that of the inducing body on the side next 
 
ciiap. in.] Electrical Induction. 103 
 
 to it. The attraction between the opposite electricities 
 caused the first attraction of the bodies. By contact the 
 induced charge was neutralised, and the original charge dis- 
 tributed over both bodies, and then repulsion between the 
 like electricities caused the observed repulsion between the 
 bodies. 
 
 In the same way, in every case in which an electrical dis- 
 charge takes place, that charge is preceded by induction, and 
 may be regarded as a consequence of the increased inductive 
 action as the bodies approach more and more near. 
 
 73. Induction on a Body connected with the Earth. 
 
 If EG be touched for an instant with the finger, the leaves 
 of an electroscope attached to it collapse. The reason is, that 
 the human body, the floor, walls, and furniture of the room, 
 are on the whole conductors, and through them the cap and 
 base of the electroscope are brought into conducting contact, 
 and, as we have seen, the leaves in that case collapse. The 
 conductor SO, however, is not discharged, but retains an 
 induced negative charge, which can be either tested by the 
 proof-plane, or becomes sensible to the attached electroscope 
 on the removal of A, the inducing body. 
 
 74. Electroscope charged by Induction. We can 
 
 in this manner charge a body by induction with a charge 
 opposite to that of the inducing body. This method is fre- 
 quently employed for charging a gold-leaf electroscope (Fig. 
 66). Present to it an excited glass rod, charged + (Fig. 66a), 
 and the leaves will diverge, owing to the inductive separa- 
 tion of electricities, + E. going to the leaves, and E. to the 
 cap, the potential of the leaves and cap, owing to the induc- 
 tion, being higher than the earth. Touch the cap with the 
 
IO4 
 
 Electricity. 
 
 [Book II. 
 
 finger (Fig. 666), thus bringing the cap and leaves to earth 
 potential, or the potential of the tinfoil strips, the leaves 
 will collapse, the cap and leaves retaining a bound negative 
 
 FIG. 66. 
 
 charge. Remove first the finger, and next the inducing 
 body (Fig. 66c), and the electroscope leaves diverge with 
 their negative charge now set free. 
 
 75. Faraday's Ice-pail Experiment. To find the total 
 amount of inductive action of which an electrified body is 
 capable, Faraday adopted the following method, which is 
 generally called the Ice-pail Experiment, from the use of an 
 ice pail in the original experiment. Take a metal pail (A), 
 closed at bottom, and open at the top, and support it on an 
 insulating stand (Fig. 67). Connect its outside with an electro- 
 scope (B) at a distance. Electrify a brass ball ((7), suspended 
 by a silk thread, and lower it into the pail. The leaves 
 will of course immediately diverge by induction, but after 
 the ball has been lowered a third of the depth, no further 
 divergence is perceptible as it is lowered further. And even 
 after contact with the base of the pail, the leaves still retain 
 
Chap. III.] 
 
 Electrical Induction. 
 
 105 
 
 the same divergence. On removing the ball by its silk thread, 
 it is of course found to be completely discharged. 
 
 
 \ 
 
 
 . 
 
 
 
 
 
 
 
 - 
 
 
 - 
 
 
 1- - 
 
 H-(C 
 
 :)+ - 
 
 -1 
 
 
 - 
 
 _ 
 
 /T51TS 
 
 PIG. 67. 
 
 We see by this experiment that the brass ball, as soon as 
 it was pretty well under cover of the pail, induced on the 
 pail a certain definite quantity of electricity, negative on 
 the inside, and of course an equal quantity of positive on the 
 outside. By contact with the base of the pail, the ball was 
 discharged, just neutralising the induced negative charge 
 on the inside, leaving the positive charge on the outside quite 
 unaltered. Thus we see the original induction on the surface 
 of the pail was equal to the body's own charge, and this 
 must be the expression of a universal law of induction. 
 
 Faraday repeated the experiment with a series of ice pails, 
 one inside the other, but separated by insulatirfg pads (Fig. 
 68). The result was precisely the same. When he lowered 
 the electrified ball into the innermost pail (No. 1), the same 
 effects were observed as before in the outermost (No. 4). On 
 connecting 1 and 2 together by an insulated wire, there was 
 still no change in the electroscope. On now removing No. 1 
 
io6 
 
 Electricity. 
 
 [Book II. 
 
 by silk threads there was still no change perceptible, every 
 experiment only tending to confirm the preceding conclu- 
 
 o 
 
 Fio. 68. 
 
 sion of the equality under all conditions of the charge, and 
 the induced charge developed on surrounding conductors. 
 The ice-pail method may be used with advantage to detect a 
 feeble electrification. The pail is connected with an electro- 
 scope and charged. The electrified body is then lowered into 
 it, and its electrification can be detected by the movement in 
 the leaves. 
 
 76. The Earth our Zero of Potential. If we make 
 electrical separations in an ordinary room, the foregoing ex- 
 periments show us that the complimentary distributions are 
 bound across the air of the room to the distributions on the 
 insulated conductors within. Outside the room there will be 
 no electrical force due to the separation made inside. The 
 earth, being a conductor, is at the same potential throughout, 
 
chap, in.] Electrical Induction. 107 
 
 that potential being independent of any electrical separa- 
 tions made in cavities within it. This makes the earth a very 
 convenient standard as a zero of potential. This zero of 
 potential is as arbitrary as the zero of a thermometer scale. 
 Whether the earth's potential is high or low we cannot tell; 
 but since all potentials we observe are ultimately compared 
 with it, and its own potential can never be altered by any 
 electrical separations we make within it, we choose it as our 
 most convenient standard of reference, or our zero. 
 
 *77. Potential in Absolute Measure. We have at 
 present only referred to potential as the electroscope indica- 
 tion. We have proved by experiment these laws : (1) The 
 potential at every point of a charged conductor is the same ; 
 (2) The potential of a conductor rises with its charge j (3) 
 Electrical force requires a region of varying potential ; (4) 
 Positive electricity tends to fly from places of higher towards 
 places of lower potential. We may choose as our measure of 
 potential any physical quantity which satisfies these four 
 conditions. Now it is proved in works on the Theory of 
 Electricity that these are all satisfied by measuring potential by 
 the work done against electrical forces in carrying a + unit from 
 the earth up to the point at which potential is measured. For 
 it is shown (1) the work done in carrying a + unit up to any 
 point on or within a charged conductor is the same ; (2) the 
 work done is proportional to the charge, thus confirming our 
 assumption that there exists a constant ratio between the charge 
 and the potential, which ratio we defined to be the capacity of 
 the conductor ; (3) the electrical force urging a -f unit in any 
 direction whatever is measured by the rate of change of the 
 potential in that direction, thus showing that electrical forces 
 exist only in a region of varying potential ; (4) that the -f 
 
 is nrorp.rl hv flip, fnrnp.s a.r.fino' in flip. plp.rvhnV. fip.lrl frnm 
 
io8 Electricity. [Bookii. 
 
 places of higher towards places of lower potential, since work 
 is done when the + unit is carried in the opposite direction. 
 This shows that we may measure the potential of a con- 
 ductor absolutely by the work done on a + unit in carrying 
 it from the earth to the conductor. Should work be done in 
 carrying the + unit from the conductor to the earth, the 
 potential of the conductor is negative. 
 
 *78. Absolute Measure of Potential at a Point in 
 the Field. We can clearly take, for the absolute measure 
 of the potential at a given point in the field, the work done 
 on a + unit brought up from the earth to the given point, 
 and it can be proved that this is quite independent of the 
 path pursued in carrying up the + unit. The difference of 
 potential between any two points in the field thus becomes 
 measured by the work done in carrying the + unit from one 
 point to the other, that being at higher potential to which 
 the + unit is carried. This work done between the two 
 points is also independent of the path pursued. Thus each 
 point in the field has its own potential. 
 
 To connect this with our electroscope indication, we may con- 
 ceive a very small insulated conductor placed at the point, and 
 connected with an electroscope so charged that no electricity 
 passes between the electroscope and the conductor to alter its 
 charge. The electroscope indication would then give the 
 potential at that point in the air. Otherwise assume a burning 
 match placed at the point, and connected with the electroscope. 
 Unless the match and electroscope are at the same potential 
 as the point in the air, electricity tends to be thrown off, and 
 the smoke and products of combustion fly off with their own 
 charges of electricity until equilibrium is established. The 
 electroscope indication is then the potential at the point. 
 
chap, in.] Electrical Induction. 109 
 
 *7p. Equipotential Surfaces. There is no force on a 
 + unit, and therefore no change of potential, if it is carried 
 along a line which cuts lines of force at right angles. There- 
 fore any surface drawn cutting all lines of force at right 
 angles has the same potential throughout, and is called an 
 equipotential surface. One such surface passes through every 
 point in the field between the conductor and the walls of the 
 room, both of which are also equipotential surfaces. 
 
 Again, there is no force inside a charged conductor. This 
 shows that the whole space within the conductor is equi- 
 potential, and not merely the surface. We pointed this out 
 experimentally (Art. 66) when we saw that a gold-leaf electro- 
 scope did not show divergence when placed in a wire cage 
 highly charged. There was, at least, no difference of potential 
 between the cap and base of the instrument, however placed, 
 and therefore presumably no change of potential anywhere 
 within the conductor. 
 
 *8o. Application to a Sphere. It is a useful exercise 
 to consider the case of an electrified sphere supposed to be 
 suspended in a large room. The lines of force emanate from 
 it at right angles, and we will assume that they are straight 
 lines (the room being very large), and that the equipotential 
 surfaces are spheres concentric with the conductor (Fig. 69). 
 Since the electrification has uniform density, the force exerted 
 by the charge on the sphere can be proved the same as if it 
 were condensed in its centre. Thus, if the charge be Q, and 
 the radius JR, the force on a + unit at a distance D from the 
 
 centre is yp, and that just outside the surface is ^- The 
 is = ' which shows that the den ' 
 
no 
 
 Electricity. 
 
 [Book II. 
 
 sity is proportional to the force just outside the sphere. It 
 can be proved that the work done in bringing up a + unit to 
 
 Q 
 a point at a distance D is - , which therefore measures the 
 
 FIG. 69. 
 
 potential at distance D. Hence the potential close to the 
 surface is ^ = V suppose. Hence Q= FB, and therefore R 
 
 measures the capacity of the sphere, or the charge per unit 
 potential (Art. 69). 
 
 81. Electrification of two Parallel Plates, one 
 initially charged. As an instructive example of the 
 foregoing principles, we will consider the problem of the 
 induction of one charged plate on another thin un- 
 charged plate parallel with it, whose distance from the 
 
Chap. III.] 
 
 Electrical Induction. 
 
 i ii 
 
 first plate can be varied at pleasure. The arrangement is 
 shown in Fig. 70 
 
 FIG. 70 
 
 (1) Let the charged plate (A) (Fig. 71) be connected with 
 
 FIG. 71. 
 
 the cap, and the insulated but uncharged plate (B) with the 
 
112 
 
 Electricity. 
 
 [Book II. 
 
 base of the same electroscope. When B is brought up very 
 near to A, but without actual contact, the leaves collapse, 
 showing that the unelectrified plate is sensibly at the same 
 potential as the electrified plate, but on moving it further away, 
 the difference of potential goes on increasing, A of course being 
 at higher potential than B. The potential at any point in 
 B will be due to the three distributions, namely the + on A, 
 and the + and distributions on opposite sides of B. The 
 two latter, from their symmetry, will neutralise each other's 
 potential everywhere within B, and the potential of B will be 
 that due only to A. When B is close to A, its potential will 
 therefore be the same as that in air close to A, and as it 
 retreats from A its potential will decrease just as the potential 
 in air 
 
 PIG. 72. 
 
 (2) Let us now test the potential of A and B relatively to 
 the earth, connecting A with the cap of one electroscope, and B 
 with that of another (Fig. 72). When they are close together, 
 the two electroscopes indicate the same potential. As we 
 separate them, we find that the potential of B constantly de- 
 creases, that of A remaining unaltered. The explanation is, 
 
Chap. III.] 
 
 Electrical Induction. 
 
 that the equal and opposite induced charges on B are so 
 nearly at the same distance from every point on A, that 
 their inductive effects on A are equal and opposite, and their 
 potentials at every point of A are equal and opposite, and 
 therefore do not affect the potential of A, which is still that 
 due to its own charge. 
 
 FIG. 73. 
 
 (3) Keplace B by a thick plate (Fig. 73) a hollow plate 
 with two opposite flat metallic surfaces will do. We shall 
 now find that the potential of A diminishes as B is moved up 
 to A . Here the opposite charges called up by induction are 
 not at the same distance from A, the negative charge being 
 the nearer, and in consequence the potential of A is lowered. 
 
 (4) Replace the thin plate and touch it with the finger 
 (Fig. 74). The potential of A at once falls, and the nearer 
 B is to A the greater the fall in A's potential. This is due 
 to the large negative charge induced by A, which, from its 
 nearness to A, lowers A's potential. In other words, on 
 bringing up the -l-^mjt to A, the work is almost nil, for B's 
 attraction nearly equals A's repulsion. 
 
 
Electricity. 
 
 [Book II. 
 
 (5) Place B at a certain distance from A, touch B, and 
 connect it with an electroscope. The leaves of course 
 collapse. On separating the plates further, however, the 
 leaves of B's electroscope are seen to diverge with E., but 
 on bringing them nearer together they diverge with + E. 
 
 FIG. 74. 
 
 EARTH 
 
 These are obviously the effects of increased and diminished 
 induction, owing to the change in B's position. It shows also 
 that a body having a charge may have a + potential, 
 owing to the presence of + E. near to it. 
 
 82. The Leyden Jar. These experiments show us that 
 the capacity of a charged body depends not only on the geometry 
 of the body considered, but also on the presence of other con- 
 ductors. Since the potential of the charged body in the pre- 
 ceding experiment was lowered by bringing near to it a body 
 connected with the earth, it follows that the capacity of the 
 conductor was raised in the same proportion. This principle is 
 used in the Leyden jar. This consists of a glass jar (Fig. 75), 
 coated outside to about two-thirds of its height with tinfoil, and 
 the inside is either coated with tinfoil or filled with sulphuric 
 
Chap. III.] 
 
 Electrical Induction. 
 
 acid, or any conductor. A brass rod passes inside, in con- 
 nection with a brass knob on the outside. To understand the 
 action of the jar we will first insulate the 
 outer coat by standing it on an indiarubber 
 pad. Connect the rod with an electroscope; 
 when one or two charges, carried by a proof 
 plane from an electrophorus, will give a 
 considerable divergence to the leaves. 
 
 Uninsulate the outer coat by placing 
 the jar on the table, and it will be found 
 that a dozen charges may be brought from 
 the electrophorus without at all visibly 
 affecting the leaves. In fact, several sparks 
 may be given to the knob direct from the 
 electrophones without making the diver- 
 gence as great as that observed in preceding 
 experiment. 
 
 This shows that the quantity required to 
 raise the jar to a certain potential (or its capacity), is enor- 
 mously increased by connecting the outer coat to earth. 
 
 It may be remembered that the capacity is in direct pro- 
 portion to the area of coated surface, and in inverse propor- 
 tion to the thickness of the glass, supposing the glass to be 
 always of the same kind. 
 
 When a jar is charged by a machine, the discharge should 
 be made with a pair of tongs whose ends are brought into 
 contact with the inner and outer coats. The discharge is then 
 accompanied by a bright spark and sharp report. If taken 
 through the body it gives a violent shock. 
 
 83. Volta's Condensing Electroscope. On the same 
 
 principle depends the condensing electroscope of Volte. The 
 
 FIG. 75. 
 
1 1 6 Electricity. [Book n. 
 
 cap of the electroscope is ground perfectly plane, and another 
 plane disc of brass with a glass handle is made to fit accurately 
 on to it. The two are then separated by a thin layer of shellac 
 varnish, which, when dry, forms an insulating layer of di- 
 electric between the plates. It is only useful in cases where 
 a large quantity of electricity is available, but of too low 
 potential to be sensible to the ordinary electroscope. Connect 
 the upper or condensing plate with the source of electricity, and 
 the cap with the earth by touching it with the finger. There 
 will be a large accumulation of electricity on the Leyden jar 
 principle across the very thin layer of shellac. On removing 
 the finger, the charge called up by induction is insulated, and 
 
 FIG. 7t>. 
 
 on lifting the cap becomes free, causing the leaves of the electro- 
 scope to diverge with electricity of opposite kind to that of the 
 source. We shall illustrate the use of this apparatus hereafter. 
 
chap, in.] Electrical Induction. 117 
 
 *84. Discharge by Alternate Contacts. Returning 
 to the two plates in given position (Art. 81), A charged and 
 B uncharged, we notice generally that the charge of A is 
 divided, part on the side facing B, and part on the side away 
 from B ; while on B there is a charge opposite to A, and an 
 equal + charge on the other face. To the opposing charges, 
 + on A and on B, Faraday'^ ice-pail principle is applicable, 
 showing that these charges are equal and opposite. These 
 are frequently spoken of together as a bound charge. The 
 charges on the outsides of A and B might be treated in 
 the same way, they being bound to equal and opposite 
 charges on surrounding conductors, only we assume surround- 
 ing conductors to be so distant that their effect on the distribur 
 
 FREE CHARGE 
 
 A 
 B 
 
 I- BOUND CHAI 
 
 - 71 77! Q = FREE CHARGE 
 FIG. 77. 
 
 tion is inappreciable, and these charges are spoken of as the 
 free charges of A and B respectively. Each of these systems 
 will have its own capacity that for the bound charge de- 
 pending on the shape, size, and nearness of the plates, and 
 that for the free charge only on the form of the external 
 surfaces. If we call these and G' respectively, every 
 charge communicated to A will be divided between the free 
 and bound charges in ratio of C' to (7. If the whole charge on 
 
 G' 
 A be Q, the free charge will be . .. Q=nQ suppose, 
 
Electricity. 
 
 [Book II. 
 
 and the bound charge - . Q=mQ suppose; where of 
 G + C 
 
 course m + n=I. 
 
 (1) At first charging, the charges will be, as in the first 
 diagram of Fig. 77, 
 
 on A, free charge =nQ; bound charge =mQ; 
 and on B, bound charge = mQ. 
 
 \f . FIG. 78 
 
 (2) Insulate B, and touch A, thus bringing its potential to 
 zero. The bound charge on B is now divided in ratio G' : C y 
 and we have, as in the second diagram, 
 
 on B, free charge =mnQ; bound charge = w 2 $; 
 and on A, bound charge = +m 2 $. 
 
 (3) Insulate A, and touch B ; the bound charge on A will 
 now be divided in same ratio, and we have 
 
chap, nil Electrical Induction. 119 
 
 on A, free charge =7im 2 Q, and bound charge=m 3 Q; 
 and on B> bound charge =m 3 Q. 
 
 (4) By similar reasoning we see that after p contacts with 
 the alternate plates the free charge will be 
 
 db nm p ~ l Q t and the bound charge m?.Q. 
 Since m is a fraction near to unity, m p will be a considerable 
 fraction when p is a large number, and hence in the discharge 
 by alternate contacts the charge is dissipated very slowly indeed. 
 
 This is illustrated in various ways, as by attaching a bell 
 to the knob of the Leyden jar (Fig. 78), and placing another 
 in connection with the earth in such a position that a small 
 metal weight, suspended by a silk thread may strike first 
 one bell and then the other, the motion being kept up by the 
 successive attractions and repulsions between the metal and 
 either bell. This arrangement will continue ringing for a 
 considerable time if the jar be first charged by a machine. 
 
 85. Specific Inductive Capacity. Returning once more 
 to the parallel plates, let A (Fig. 79) be charged as before, and 
 B be connected with an electroscope. Touch B with the finger, 
 bringing its potential to zero. Take now a plate of solid 
 paraffin larger than the plates, and whose thickness is a little 
 less than the distance between the plates. On carefully in- 
 troducing it between the plates without contact with either, 
 the leaves of B's electroscope will be found to diverge slightly, 
 showing, on testing, positive electrification, that is, just the 
 same effect as if the plates were brought nearer together. 
 (Great care is necessary to prevent the electrification of the 
 paraffin, by accidental friction with the hands or clothes, in 
 which case the resulting divergence would be negative, since the 
 paraffin becomes negative by friction. ) This shows that indue - 
 tion depends on the nature of the dielectric. This phenomenon 
 
I2O 
 
 Electricity. 
 
 [BookIL 
 
 was discovered by Faraday, who experimented by constructing 
 exactly equal Leyden jars, in one of which air was the dielec- 
 tric, and in the other a substance like sulphur or shellac. On 
 charging one, and then dividing the charge with the other 
 jar, he found in the case of shellac that the jar having shellac 
 retained two-thirds of the divided charge, and that with air 
 only one-third. Since they were at the same potential, he 
 
 FIG. 79. 
 
 inferred that the capacity of the jar with shellac as dielectric 
 was just double that with air. This he expressed by saying 
 that the inductive capacity of shellac was double that of air. 
 He found dry air a convenient standard, since he found no 
 sensible difference on either rarefying or condensing it, or 
 on substituting for it any of the permanent gases. There were 
 few solid substances in which the insulation was good enough 
 to admit of Faraday's method of experiment. The only ones 
 with which he expresses himself satisfied are sulphur and 
 flint glass, in both of which he showed the specific inductive 
 capacity to be greater than double that of air. 
 
chap. HI.] Electrical Induction. 121 
 
 86. Condition of the Dielectric in a Leyden Jar. 
 
 That all electrical actions belong to the dielectric, and not to 
 the conductor, is also shown by the Leyden jar with moveable 
 coatings (Fig. 80). Charge this jar in the usual way, and place 
 it on an insulator. Lift out the inner coat, and this will be 
 found to carry away only a small fraction of the charge. Lift 
 the jar out of the outer coat, which will also retain hardly a 
 trace of the charge. The glass can now be handled inside and 
 out, a slight discharge being perceptible when the outside 
 and inside are touched at the same time ; but on fitting up 
 the jar again, and discharging in the usual way, there will be 
 nearly as strong a spark as if the discharge had immediately 
 followed the charge. 
 
 Fio. 80. 
 
 This shows that every electrification is not one of con- 
 ductors in the field, but rather one of the field itself, the 
 function of the conductor being only to determine the limits 
 of the field. 
 
 Another illustration is given by the residual charge in a 
 Leyden jar. Of whatever dielectric the condenser be made, 
 except it be a gas, a short time after the first discharge has 
 
122 Electricity. [Book IL 
 
 passed, another feeble discharge can be obtained, and this may 
 be repeated several times in succession. This appears due to a 
 want of homogeneity in the dielectric, and a partial conduction 
 through it, causing a storing up of electricity within the sub- 
 stance of the dielectric, which begins to be conducted back 
 again only after the primary discharge has passed. 
 
 87: Faraday's Theory of Induction. Faraday has 
 laid down a theory of induction agreeable to this conception, 
 and this was the first step towards a true physical conception 
 of electrical actions. He satisfied himself that induction was 
 not due to action at a distance between the electrified body 
 and the body under induction, and he substituted for it an 
 action through the dielectric from molecule to molecule only. 
 He assumes that every dielectric consists of molecules, each 
 
 !> 
 
 FIG. 81. 
 
 of which acts as a conductor, but which are separated from 
 each other by a non-conducting medium, or, at least, non-con- 
 
chap, in.] Electrical Induction. 123 
 
 ducting up to a certain limiting strain among the molecules. 
 The electrification of the surface bounding the field (or of 
 the conductor, if we choose still to speak of it) separates the 
 electricities in the layer of molecules next to it. These act 
 on the next layer, and so on through the field. The lines of 
 force define the direction in which the separation takes place, 
 the quantity separated being always equal to that in the 
 proximate layer of molecules. Thus the electrification will 
 consist of a flow of electricity equal to the original charge 
 across each equipotential surface ; but instead of being a flow 
 through a finite space, it is only a flow across the molecules 
 which lie in that surface. This may be represented in a 
 diagrammatic way, as in Fig. 81, supposing shaded parts to 
 represent positive electricity. 
 
 Of a higher order is the theory of Faraday developed by 
 Clerk-Maxwell, in which he regards the electrification as a 
 state of molecular strain in the dielectric. In support of that 
 theory is the observation of Sir William Thomson, that on 
 charging and discharging a large condenser a peculiar noise 
 is emitted, just as might be expected in a medium taking 
 up or losing suddenly a strained condition. More recently it 
 has been proved that the discharge consists of a rapid series 
 of discharges backwards and forwards, just like the oscillations 
 observed in an elastic body when suddenly released from a 
 state of strain. 
 
CHAPTER IV, 
 ELECTRICAL MACHINES. 
 
 88. The Cylinder Machine. There are two classes of 
 electrical machines; that is, machines by which large quantities 
 of electricity at high potential may be rapidly obtained, one 
 depending on simple friction, and the other on an initial 
 electrification by friction, from which an indefinite amount 
 of electricity may be developed by induction. 
 
 FIG. 82. 
 
 The simplest form of friction machine is that known as the 
 cylinder machine (Fig. 82). It consists of a cylinder of glass 
 (B) fitted in a frame which allows it to rotate about a spindle 
 running along its axis. The extremity of one horizontal 
 
 124 
 
chap, iv.] Electrical Machines. 125 
 
 diameter is pressed by a leather pad (A) coated with silk, on 
 which is smeared an amalgam of mercury and tin, the pressure 
 being increased by a spring controlled by a screw. The pad 
 is usually insulated and furnished with a brass knob, from 
 which negative electricity can be collected. Towards the 
 opposite side of the cylinder points a comb, consisting of a row 
 of very sharp brass points (G) attached to a large brass globe 
 or cylinder (D), called the Prime Conductor, on which the 
 positive electricity collects. This is always insulated by being 
 supported on glass legs. A flap of silk attached at one edge 
 to the rubber passes nearly over the upper half of the cylinder, 
 and prevents the deposit of dust on the cylinder, by which 
 the electricity would be dissipated. 
 
 On turning round the cylinder, the friction with the rubber 
 separates electricity, the positive on the glass and the negative 
 on the rubber. The glass with its positive charge is carried 
 onwards till it is opposite the brass comb on the opposite side. 
 Here it acts inductively on the points, and E. is drawn 
 off, neutralising the + E. on the cylinder, and causing a charge 
 of free + E. on the conductor. On turning the handle round 
 this process constantly goes on, till the difference of potential 
 between the prime ( + ) and negative ( ) conductors is equal 
 to that which can be obtained by the friction between glass 
 and amalgamated silk. Sparks of positive or negative elec- 
 tricity can be obtained from the respective conductors. The 
 difference of potential actually attained will always be less 
 than the limit indicated, because of dust and moisture in the 
 air, and also because of the want of perfect insulation in the 
 glass supports. The advantage of a warm and dry state in 
 the atmosphere is obvious. 
 
 In the ordinary working of the machine it is usual to con- 
 
126 
 
 Electricity. 
 
 [Book II. 
 
 nect the negative conductor with the earth by a metal chain. 
 If this precaution were omitted and the insulation of the rubber 
 were perfect, we should, on drawing sparks from the prime 
 conductor, at last reach a stage at which the potential of the 
 negative conductor would be below the potential of the earth 
 by the whole available potential difference, and then the prime 
 conductor would be at zero potential, and no sparks could be ob- 
 tained from it. The machine would apparently cease to work. 
 Again, the body which draws sparks from the machine is 
 generally at the potential of the earth, and therefore the poten- 
 tial difference available for giving 
 sparks is that between the earth and 
 the prime conductor. But if the 
 negative conductor be at a negative 
 potential, this available difference is 
 not the full potential difference of 
 the machine, or the machine is prac- 
 tically not working to its full power. 
 On connecting the negative conductor 
 with the ground the potential of the 
 positive conductor at once rises. The 
 same effect may be gained by simply 
 connecting the negative conductor 
 with the apparatus by which sparks 
 are to be drawn, keeping all insulated. In a fairly insulated 
 machine the difference is well seen (1) by drawing a succession 
 of sparks from the prime conductor while the rubber is insu- 
 lated ; (2) by drawing sparks, while standing on an insulating 
 stool, and touching with one hand the negative conductor ; 
 (3) by drawing sparks, standing on the ground with the 
 rubber to earth. 
 
 FIG. 83. 
 
Chap. IV.] 
 
 Electrical Machines. 
 
 127 
 
 The prime conductor is frequently furnished with an elec- 
 trometer, consisting of a vertical metal rod, from which is 
 suspended, by a thin wire or linen thread, a pith ball (Fig. 83). 
 The divergence is shown by a small graduated quadrant 
 attached, which indicates the degree to which the machine is 
 working. This is called Henley's Quadrant Electrometer 
 an unfortunate term, as the Quadrant Electrometer is an 
 instrument of Sir William Thomson's, described hereafter. 
 
 89. The Plate Machine. The Plate Machine (Fig. 84) is 
 a circular vertical plate (A) of glass or ebonite, which is turned 
 
 FIG. 84. 
 
 by a spindle through its centre. Two rubbers (BE) are 
 attached at opposite extremities of the vertical diameter, each 
 made double, and pressed by a screw clamp on opposite 
 
128 Electricity. [Book n. 
 
 sides of the plate. Along a horizontal diameter are two 
 combs ((7(7), each formed in shape of the letter U, so as to 
 act on the two surfaces of the plate. These are connected by 
 metal rods with the prime conductor, which is well insu- 
 lated on a glass support. Flaps of silk (EE) extend over the 
 quadrants from the rubbers nearly to the combs. 
 
 The action is identical with that of the cylinder machine. 
 Its advantages are rather greater compactness, and the possi- 
 bility of substituting ebonite for glass. The ebonite is as 
 good in its electrical properties, but is less hygroscopic, and 
 therefore the action is not quite so dependent on weather. 
 Also the double action on opposite sides of the plate increases 
 the rate at which electricity can be obtained. 
 
 pO. The Electrophorus. Of instruments depending on 
 induction the simplest is the electrophorus (Fig. 85). It consists 
 
 
 
 i.- A 
 B 
 
 DEARTH 
 ...C 
 
 Pro. 85. 
 
 of a cake (A) resting on a metal form or sole (5), and of a 
 
chap, iv.] Electrical Machines. 129 
 
 cover (0). The cake used to consist of a resinous compound 
 melted and poured into the form, but is now more commonly 
 a plate of ebonite, with a brass plate or a sheet of tinfoil on 
 its under surface forming the sole. The cover is a flat metal 
 plate, having attached to it a glass handle, by which it can 
 be raised and lowered. The charging of the electrophorus is 
 done by rubbing or flapping the ebonite plate with a cat's fur 
 (Fig. 85, i) by which a charge of E. is developed on its 
 upper surface. This acts inductively through the cake, and 
 binds by induction a charge of + E. on the sole. By this 
 means the charge on the cake is increased. On putting the 
 plate down on the cake there is only contact at very few 
 points, and everywhere else a thin plate of air between the 
 cake and cover. There will therefore be developed (Fig. 85, ii) 
 a charge of + E. on the under surface of the cover, while 
 there is an equal free charge of E. on the upper surface. 
 On touching the plate with the finger (Fig. 85, iii), the com- 
 plementary E. is driven to earth. The induction will now 
 be almost wholly between the cake and cover, owing to the 
 much greater nearness of the cover compared with the sole. 
 The + E. called up on the cover will now very nearly equal 
 the whole charge of E. on the cake. On lifting up the 
 cover it has a strong charge of + E., which can be used for 
 charging other conductors. The induction between the cake 
 and sole is again restored, the cake returning to the state 
 shown in Fig. 85 (i), and the charge is so well preserved that 
 in a dry atmosphere the electrophorus may be used with only 
 one charging for an hour or more together. 
 
 91. The Voss Machine. A great variety of machines 
 have been invented, in which the induction of a small initial 
 
 i 
 
Electricity. 
 
 [Book II. 
 
 charge is employed for raising continually the initial charge 
 in compound interest ratio, and also for giving the discharge 
 whose power increases as the machine is worked to a degree 
 only limited by the size of the machine and the perfection of 
 insulation attainable. Of these we have only room to refer 
 to two of the most modern. 
 
 FIG. 86. 
 
 We will take first the Voss machine (Fig. 86), because its 
 action is peculiarly simple when the difficulty of the initial 
 charging has been overcome. 
 
 The machine consists of one glass plate, which is fixed, and 
 of another glass plate parallel to the fixed plate, which is made 
 to rotate rapidly in front of it. In Fig. 86 the larger plate 
 
chap, iv.] Electrical Machines. \ 3 1 
 
 is fixed, and the smaller rotates in front of it, admitting of our 
 seeing the arrangement of the fixed plate through it. The 
 fixed plate has two sheets of paper (A A}, with tinfoil under- 
 neath it, pasted on to the glass, and called the armatures. 
 From each of these proceeds a metal arm (BB) bent three 
 times at right angles, and carrying on its end a metal 
 brush, which sweeps over certain metal buttons as they pass 
 by it. 
 
 The moveable plate has cemented to its front eight of these 
 metal buttons (a a . . .), which come in contact with the suc- 
 cessive brushes. 
 
 FIG. 87. 
 
 In front of the moveable plate, and facing it, are two brass 
 combs (CO) which face the plate, and are cut away opposite 
 to the buttons (Fig. 87), allowing them to pass without con- 
 tact. These are connected by metal rods with the moveable 
 conductors (DJD), between which the spark passes. 
 
 FIG. 88. 
 
 In addition there is a diagonal conductor (E) furnished at 
 each end with a brass comb, of which the central tooth is 
 replaced by a brush of metal wires which sweeps over the 
 buttons as they pass under it (Fig. 88). The combs all extend 
 the full width of the paper armature. 
 
1 3 2 Electricity. [Book n. 
 
 The knobs (DD) are in connection with the inner coats of 
 two Leyden jars (FF) whose outer coats are to earth. 
 
 The peculiarity of this apparatus is that no special priming 
 (that is, initial charging of the armatures) is required. It 
 appears that from accidental surface inequalities a slight 
 difference of potential is established by friction between the 
 brushes and buttons, and the construction of the machine is 
 such as to accumulate the initial charge, however small, on 
 compound interest principle. In working the machine the plate 
 is rotated in the direction of the arrows shown in Fig. 86. 
 We assume initially a small potential difference between the 
 armatures A, A, and will show how this difference is in- 
 creased. Omitting the conductor (7(7, which takes no part 
 in the initial stages of charging, each button passes during 
 a revolution four brushes two belonging to the armatures, 
 and two to the diagonal conductor. Fig. 89 either shows one 
 button in four consecutive positions, or four buttons simul- 
 taneously, remembering that pairs of buttons always occur at 
 ends of a diameter. 
 
 Consider first the pair of buttons in position (i) and (iii) 
 in Fig. 89, in which (i) represents a portion of the positive 
 armature, and (iii) a portion of the negative armature. At (i) 
 the positive armature induces a charge of E. on the button, 
 while at (iii), which is connected with (i) by the diagonal 
 conductor, the negative armature induces a charge of + E. 
 The button therefore leaves (i) with a negative charge bound 
 across the air space, and leaves (iii) with a positive charge. 
 The button, on passing from (i) to (ii), will give up its strong 
 bound negative charge to the negative armature, retaining only 
 a small free charge. Similarly, the button on passing from (iii) 
 to (iv) will give up its bound positive charge, retaining only a 
 
Chap. IV.] 
 
 Electrical Machines. 
 
 133 
 
 very small free charge. We see therefore that each button 
 which passes from (i) to (ii), or from (iii) to (iv), will 
 enforce the charge of these respective 
 armatures; and since at each point 
 there is actual metallic contact, the 
 electricity not having to break across 
 an air space, the action will go on, 
 however small the initial difference. 
 
 When the charges are high enough 
 to act inductively across the air spaces 
 between the plate and the combs (CC), 
 the neutralisation which usually takes 
 place in E will take place across the 
 air space (DD), giving rise to the spark. 
 As soon as this is the case, not only 
 the metal buttons, but the whole glass 
 surface between the combs and the 
 armature, help to enforce the action. 
 
 After turning for a very short time, 
 if the atmosphere be moderately dry 
 and the machine warm, sparks four or 
 five inches long may be easily obtained 
 from a comparatively small machine 
 (16-inch plates). 
 
 The use of the Leyden jars (FF) is to concentrate the 
 spark. If they be removed, the discharge takes place by what 
 is called the brush discharge, consisting of very fine branches, 
 giving a slight pricking sensation if received on the hand, and 
 making but very slight noise. If the Leyden jars be present, 
 the first effect of the electricity developed in the conductors 
 Z>, Z>, is to charge these jars, one with its inner coat positive, 
 
 FIG. 89. 
 
134 
 
 Electricity. 
 
 [Book H. 
 
 and the other negative, and these are discharged with their 
 characteristic sharp report as each spark passes. 
 
 It may be noticed in illustration of the action explained, 
 that when the machine is in action the diagonal conductor E 
 may be removed without stopping the action of the machine 
 until a discharge of the armatures takes place with one of the 
 sparks, an accident to which all these machines are liable. 
 
 The machines known as the Wimshurst is similar in construc- 
 tion, and its mode of action identical with that of the Voss. 
 
 *Q2. The Holtz Machine. This machine (Fig. 90), 
 which was of earlier date than the Voss, depends on the 
 same general principles. 
 
 Fio. 20. 
 
 In it we have two plates, one fixed and the other revolving 
 rapidly in front of and at a small distance from it, by means 
 of a spindle through its centre. 
 
 The fixed plate (Fig. 91) has, at opposite ends of a diameter, 
 
Chap. IV.] 
 
 Electrical Machines. 
 
 '35 
 
 two apertures or windows cut in the form of truncated sectors 
 of a circle. Below one and above the other are two sheets 
 of paper (BB), the armatures, glued to the glass, with two 
 tongues or pointed strips, also of paper, projecting from them 
 into their respective windows. In the centre is a circular 
 hole through which passes the spindle of the moving plate. 
 
 FIG. 91. 
 
 The moving plate is an entire circle with a hole in the 
 centre for fixing the spindle, and, for mechanical reasons, 
 having a diameter slightly less than that of the fixed plate. 
 
 The plate is fixed with the two armatures at opposite ex- 
 tremities of a horizontal diameter. Opposite to them, but on 
 the remote side of the moving plate, are two brass combs 
 (Fig. 90), as near as possible to the moving plate without actual 
 contact with it. These combs are well insulated, and connected 
 with two brass knobs (EE\ whose distance apart may be 
 adjusted by the insulating handles. These knobs are the 
 positive and negative conductors. The relative position of 
 
136 
 
 Electricity. 
 
 [Book II. 
 
 the parts near one end of a horizontal diameter is seen in 
 section in Fig. 92. In the section, A is the window, B the 
 armature, the tongue, and D one tooth of the brass comb. 
 
 Before working the machine, it must be primed. The brass 
 knobs are brought into contact, and a piece of ebonite rubbed 
 with flannel is held between the plates in contact with one 
 armature, by which this armature receives a weak charge of 
 negative electricity. Sometimes a small ebonite machine is 
 fixed to the base in such a position that the electrified ebonite 
 plate acts inductively on one tongue. 
 
 
 FIG. 92. FIG. 93 (i). 
 
 The further action can best be understood if we consider 
 the electrical actions which occur in six successive positions 
 of a portion of the revolving plate in the course of a single 
 revolution, just as we did in the Yoss machine. The plate 
 revolves in such a direction as to meet the tongues of the 
 armature, as shown by the arrows in Fig. 90. 
 
 1st Position. Opposite the window of the fixed plate which 
 contains the tongue of the negative armature, Fig. 93 (i). 
 
Chap. IV.] 
 
 Electrical Machines. 
 
 The tongue, being pointed, reduces the inner surface of the 
 glass plate to its own potential, giving it a negative charge. 
 This charge acts inductively through the glass, binding on the 
 opposite surface a positive charge, and leaving a negative 
 charge free. This action through a dielectric, though an 
 obvious consequence of Faraday's law of induction, was first 
 pointed out by Eeiss, and is often called Reiss's action. 
 
 2d Position. Between the negative armature and the brass 
 comb, as in Fig. 93 (ii). 
 
 H-* - 
 
 H- 
 
 t-f 
 
 FIG. 93 (ii). 
 
 FIG. 93 (iii). 
 
 The brass points of the comb neutralise the free negative 
 charge on the outer surface of the glass, and a redistribution 
 of the induced charges takes place. The negative charge on 
 the armature acts by induction both across the air and the 
 glass, calling up a positive charge across the air space, leaving 
 the negative charge bound to the positive charge on the 
 outside surface of the glass. 
 
 3d Position. After passing the armature, as in Fig. 93 (iii). 
 
 In this position the induction of the negative charge of the 
 armature is removed, and in consequence a positive charge is 
 set free on both sides of the moving plate. These charges of 
 course act inductively on the glass of the fixed plate, as shown 
 in the diagram. 
 
138 
 
 Electricity. 
 
 [Book II 
 
 4:th Position. Opposite the second window, which contains 
 the tongue of the positive armature, as in Fig. 93 (iv). 
 
 This tongue will here take up the free positive charge from 
 the inner surface of the glass plate, thus either charging or 
 increasing the charge of the positive armature. 
 
 5th Position. Between the positive armature and the brass 
 comb, as in Fig. 93 (v). 
 
 / 
 
 FIG. 93 (iv). 
 
 Fro. 93 (v). 
 
 FIG. 93 (vi). 
 
 The brass comb neutralises the positive charge on the outer 
 face, and a new inductive distribution occurs : the armature 
 acts inductively across both air space and glass, setting free an 
 increased negative charge on the inner surface of the moving 
 plate, leaving a positive charge bound to the negative charge 
 on the outer surface. 
 
 6th Position. After leaving the positive armature, as in 
 Fig. 93 (vi). 
 
 The removal of the charge on the armature sets free a 
 negative charge on both surfaces of the moving plate, leaving, 
 however, a bound charge, positive on the inner, and negative 
 on the outer, face. The reaction by induction on the fixed 
 plate will occur again as in the third position. In this con- 
 dition it comes round again to the negative armature, carrying 
 
chap, iv.] Electrical Machines. 139 
 
 a charge which will reinforce its electrification, after which 
 the whole process goes on over again. 
 
 The action of the machine may be briefly described thus, 
 each portion of the moving plate as it passes from the induc- 
 tion of the negative armature has a positive charge on both 
 faces, that on the inner face after half a revolution enforces 
 the charge on the positive armature, and that on the outer 
 face is taken up by the comb, and makes the spark. The 
 same will be the case, changing signs with each portion of the 
 plate as it leaves the positive armature. 
 
 For the neutralisation of the opposite electricities de- 
 veloped by the action of the machine on the combs and con- 
 ductors, the knobs should be kept together till the charging 
 has risen sufficiently for sparks to strike across, by which the 
 neutralisation (only partial, of course) takes place during the 
 whole time the machine is at work. 
 
 As in the Voss machine, two Leyden jars (not shown in 
 the figure), having their outer coats connected by a brass band, 
 are usually hung from the brass rods in connection with the 
 conductors E, E. They are, of course charged, one positively 
 and the other negatively, and their function is to store up 
 the electricity developed, allowing, when they are charged, 
 one strong spark to pass in place of a large number of sparks 
 of much smaller quantity, which form a brush discharge. 
 Occasionally the power of the machine is increased by having 
 four plates instead of two, in which case the fixed plates are 
 back to back, and the revolving plates outside ; the brass comb 
 being on the inside of a U-shaped rod to collect the electricity 
 from both plates at once. 
 
 From a Holtz machine, with plates 2 feet in diameter, a bril- 
 liant discharge of sparks 6 to 8 inches long can be obtained. 
 
1 4 Electricity. [Book H. 
 
 93. Experiments with the Electrical Machine. 
 
 Almost an infinite variety of experiments, both instructive 
 and amusing, can be exhibited by means of the electrical 
 machine. We briefly indicate a few under general head- 
 ings : 
 
 1. Subdivision of the Spark. This is done by means of 
 small discs of tinfoil pasted on the surface of glass, leaving 
 a very small interval between each two successive discs. In 
 this way any pattern that can be traced by one continuous line 
 can be formed, and when placed in the line of discharge of a 
 machine, each interval is lighted up by a spark. The pattern 
 traced by bright sparks can be seen in a darkened room. 
 
 2. Attractions and Repulsions. A head is cut in wood, with 
 long hair fastened on by a metal screw, which is in connection 
 with a metal rod, by which the head is supported on the prime 
 conductor: when the machine is worked, the hairs stand 
 out, owing to mutual repulsion, and can be swayed about 
 inductively in various directions by presenting the hand or 
 any flat conductor near them. 
 
 The Electrical Chimes consist of bells, of which alternate 
 ones are connected with the prime conductor and the earth. 
 Between them hang by silk threads small masses of metal, 
 which are attracted and repelled by the electrified bells in 
 succession, keeping up a ringing while the machine is worked. 
 
 Electrical Hail consists of a number of pith balls placed in a 
 glass cylinder, in the upper part of which is a moveable brass 
 plate connected with the prime conductor, and the base is 
 coated with tinfoil connected with the earth. On turning the 
 machine, the pith balls fly about between the plate and base. 
 
 The same thing can be shown by figures cut in pith 
 and placed between two brass plates, one of which hangs 
 
Chap, iv.] Electrical Machines. 141 
 
 from the prime conductor, and the other is to earth. On 
 working the machine, the figures continue dancing between 
 the two plates. 
 
 3. Conduction of the Human Body. By standing on an in- 
 sulating stool, and holding the prime conductor of an 
 electrical machine in the hand, a considerable charge may 
 be imparted, of which the recipient is quite unconscious, 
 unless it be by the standing out of the hair or of loose parts 
 of the clothing by electrical repulsion. A spark can be taken 
 from any part of the body of the person charged, just as 
 from any other conductor, when a pricking sensation is felt 
 just where the spark is drawn. Sparks drawn in this way 
 are harmless, and almost painless. 
 
 With this experiment should be compared one in which the 
 human body is in the line of discharge, and offers resistance to 
 the passage of electricity. This may be done in a perfectly 
 harmless manner by charging a Leyden jar with two or three 
 turns of an electrical machine. A large class, on joining hands 
 all round, the first holding the outer coat and the last touching 
 the knob, will receive the discharge through the muscles of 
 the arms and chest, and will receive a shock, most felt in 
 the elbow joints, where the muscle is discontinuous. The 
 arms and chest here act as a bad conductor, the right and 
 left hands being brought to a slight difference of potential 
 before the discharge takes place. 
 
 We have already noticed that conductors and non-con- 
 ductors are only relative terms, and we have here two 
 experiments in which the same body acts first as a con- 
 ductor, and next as a dielectric. 
 
 5. The Disruptive Discharge in Air. There are three ways 
 in which an electrical discharge may be shown to take place. 
 
142 Electricity. [Bookii. 
 
 The first is by the ordinary disruptive discharge. This 
 occurs when the air becomes strongly strained by the 
 potential difference, and, suddenly yielding, allows the dis- 
 charge to pass, not freely as through a conductor, but by a 
 violent disturbance of the molecules of air along the path, 
 which become strongly heated, and make the visible spark. 
 This spark is often spoken of very inaccurately as the electric 
 fluid. The spark will be observed to take a zigzag and 
 forked path. This seems due to the discharge passing along 
 the line of least resistance, which, owing to conducting 
 motes in the air, is not the straight line. The snap which 
 accompanies the discharge has never been fully explained, 
 but is no doubt due to the disturbance in the air caused by 
 the passage of the discharge. 
 
 6. The Glow Discharge. This takes place on sharp points, 
 either in connection with the machine or on pointed con- 
 ductors connected with the earth presented towards the 
 machine. It may be seen in the dark as a faint purplish 
 glow on the brass combs connected with the various forms of 
 machine. If a pointed rod be placed on the prime conductor, 
 the glow will immediately appear, and it will be found im- 
 possible to draw a spark from the machine, the electricity 
 being discharged silently from the point. If the hand be 
 placed near the point a strong current of air will be found 
 setting from the point. 
 
 A method of discharge, similar to that from points, is 
 afforded by a flame, which we have already noticed (see 
 Art. 78), and by any form of water-dripping apparatus, in 
 which the water dropping away from an insulated vessel 
 carries off a charge until it brings the nozzle from 
 which the water drips to the same potential as the air in 
 
chap, iv.] Electrical Machines. 143 
 
 contact with it. The electrical watering-pot depends on 
 this principle. A metal vessel, having a capillary outlet 
 by a syphon, is suspended from the prime conductor. 
 Before electrification the water drips only one drop at a 
 time, but on turning the machine the water flows out in 
 a continuous stream, owing to the repulsion between the 
 electrified vessel and the similarly electrified water which is 
 leaking away from it. 
 
 FIG. 94. 
 
 It appears from the current of air which proceeds from the 
 points, that the particles of the air themselves become charged 
 at the point, and are then repelled, carrying their charge with 
 them, and discharging as they come against the walls of the 
 room or other conductors. This current of air is accompanied 
 by a recoil if the pointed conductor is free to move. It is 
 employed as a source of motion in the electrical whirl 
 (Fig. 94) and electrical orrery, in both of which points are so 
 
1 44 Electricity. [Book n. 
 
 placed that the recoil sets the apparatus of which they are parts 
 spinning, the direction of rotation being against the points. 
 
 7. The Brush Discharge. This is best seen between the 
 conductors of a Voss or Holtz machine after the Leyden jars 
 in the interior have been removed. It seems intermediate in 
 character between the spark and glow discharges. It some- 
 times rises out from wooden knobs or conductors about the 
 machine like the stem of a tree, and spreads out in the air 
 like its branches. 
 
 The connection of these forms of discharge with the pheno- 
 mena of lightning cannot be overlooked. The spark discharge 
 is identical in character with the flash of forked lightning, 
 the forking and zigzag path being often seen in the spark from 
 the machine. 
 
 The glow discharge is known as St. Elmo's Fire, which is 
 frequently seen on the tops of the lightning-rods connected 
 with the masts of ships, and also upon other pointed objects 
 even on the tops of umbrellas or walking-sticks when the 
 atmosphere is much disturbed electrically. 
 
 The brush discharge may occur in some varieties of summer 
 lightning, though what is most commonly called so is only the 
 lighting up of the edges of cloud-masses by electric discharges 
 taking place behind them, or at points below the horizon of 
 the place of observation ; the discharge being too distant for 
 thunder to be audible. Thunder, for the volume of its sound, 
 is audible for an exceedingly short distance very much less 
 than the report of a cannon. 
 
 The only other form of discharge, that known as the fire-ball, 
 has not yet been explained or imitated experimentally. It 
 appears of the nature of a Leyden jar very powerfully charged, 
 which may move about through rooms, playing about the 
 
chap, iv.] Electrical Machines. 145 
 
 furniture, quite harmless till the instant of discharge, which 
 takes place with a terrible explosion and a deafening noise. 
 
 94. Experiments with a Leyden Jar Battery. 
 
 Many striking effects of electricity can only be shown by the 
 help of Leyden jars of large size, or batteries of several jars 
 charged powerfully by the machine. Batteries of several jars 
 
 FIG. 95. 
 
 are made by having all the knobs in metallic contact, and 
 the outer coats all to earth. Great care must be taken that 
 the discharge from such arrangements is not allowed to pass 
 through the body. For discharging them, either discharging 
 tongs (Fig. 95) must be employed, or, better, some form of 
 self -discharger like Lane's (Fig. 96), which only allows the 
 charge to pass when it has reached a certain degree. This 
 latter consists of two knobs (AB) placed one above the other; 
 
 K 
 
146 
 
 Electricity. 
 
 [Book ii. 
 
 the lower (B) is insulated, and connected with the knobs of 
 the Leyden jars. The upper (A), which is also insulated, 
 moves about a pivot within the hollow ball ((7). It is counter- 
 poised by a weight (D) on the opposite side of the pivot, so 
 as to be held up, away from the lower knob, in contact 
 with a fixed knob E, until the knob B reaches such a 
 charge that its pull on A draws A and B into contact, and 
 
 FIG. 96. 
 
 the discharge takes place between them. On the lever 
 between A and G is a small sliding weight (F), which can be 
 shifted along so as to alter the degree of charge necessary to 
 bring down the upper knob. The experiments here given 
 can easily be done by a Leyden battery of four quart jars 
 charged by a Holtz or good plate machine, and several of 
 them with a single jar. 
 
 The ignition of coal-gas is seen by simply bringing the 
 
chap, iv.] Electrical Machines. 147 
 
 knob of a single charged jar into contact with a gas burner 
 from which gas is issuing, the outer coat being connected 
 by a chain with the gas pipes. It may also be shown by 
 corking up in a metal tube a mixture of coal-gas and air. 
 The tube is furnished with an arrangement by which the 
 spark passes through the mixed gas within the tube. On 
 passing the spark an explosion takes place by which the 
 cork is driven out. 
 
 The explosion of gunpowder is not effected by passing the 
 spark in the ordinary way. It appears to be too rapid, and 
 in consequence the gunpowder is scattered about without 
 being ignited. On introducing a piece of wet string, which is 
 only a semi-conductor, in some part of the line of discharge, 
 the spark is retarded, and the powder then explodes. The 
 accompanying diagram (Fig. 97) shows an arrangement by 
 which this and several following experiments can be performed, 
 using Lane's discharger, already described, and Henley's dis- 
 charging table for supporting the apparatus through which 
 the discharge takes place. The Henley's table consists of a 
 table (A) supported on an adjustable stem, having a strip of 
 ivory or some bad conductor across its top. On opposite 
 sides are two insulated arms (BC), passing through a ball and 
 socket which has universal motion. These arms can be- 
 adjusted with their lower ends at any position on the table. 
 The Leyden battery (Z>) has its knob connected simply with 
 the lower knob of the Lane's discharger (E), and wires con- 
 nect the upper knob (F), through the Henley's discharger, 
 with the outer coat of the jars. For exploding gunpowder, 
 the gunpowder is laid on the discharging table, the points of 
 the arms being placed in it, and the wet string replaces part 
 of one of the wires. 
 
148 
 
 Electricity. 
 
 [Book II. 
 
chap, iv.] Electrical Machines. 149 
 
 The powder may be put in a small ivory mortar, with an 
 ivory bullet fitting into its mouth. If the discharge be made 
 across two wires which enter the mortar from opposite sides, 
 the bullet will be expelled with some force. 
 
 Ether may be ignited by simply putting it in a metal cup 
 connected with the earth. If the knob of the Leyden jar 
 whose outer coat is also to earth be approached towards the 
 ether the discharge passes and ignites the liquid. 
 
 If the charge from several jars be passed through gold leaf 
 or very fine wire, the metal offers resistance, and the charge 
 in passing may completely deflagrate the metal. This can 
 easily be shown with gold leaf. The gold leaf should be 
 gummed on a piece of cardboard, tinfoil being also gummed 
 on to the card in contact with the gold leaf, and projecting 
 from the ends. The card must then be put in a screw-press, 
 which replaces the top of the table on Henley's discharger, 
 and the arms must be brought into contact with the projecting 
 tinfoil. After the explosion has passed, the gold will, in part 
 or whole, be deflagrated, leaving a purplish stain on the card 
 where the discharge has passed. To show the mechanical 
 effects, such as splitting wood and puncturing glass, more 
 powerful Leyden batteries are required. An interesting ex- 
 periment, which can be shown with one or two jars, is that of 
 passing the discharge through a card held in the screw-press, 
 with the arms just on opposite sides. By the discharge a 
 hole is pierced through the card, and a burr is left round its 
 edges on the negative side, as if a material body, such as 
 a needle, had been pushed through from the positive to the 
 negative side. 
 
 An instructive experiment is that known as the Thunder 
 House, illustrating the effect of a discontinuous conducting 
 
Electricity. 
 
 [Book II. 
 
 line for a powerful discharge (Fig. 98). A conducting wire 
 passes down the end of a wooden model of a house gable, 
 except about half an inch where the discharge has to pass 
 across a piece of wood (A) fitted loosely into the wall. On 
 discharging a battery of Leyden jars through it, the loose piece 
 of wood, which occurs in the line of discharge, is frequently 
 projected several yards. If the wood be turned round, mak- 
 ing the conducting wire continuous, as at j#, the discharge 
 passes quietly through it without dis- 
 lodging the wood. In a similar way, a 
 pyramid built of loose bricks may be 
 thrown over by a discharge, if the con- 
 ducting line is broken near the base. 
 
 This illustrates the effect of lightning 
 when the conductor does not terminate 
 in "good earth" that is, earth con- 
 stantly damp, and continuous with the 
 conducting body of the earth. The light- 
 ning rod under these conditions becomes 
 itself a source of danger to the building 
 it is intended to protect, since the light- 
 ning no longer passes to earth by "the 
 rod, but flies from it across walls and 
 other bad conductors, rending them in pieces, in its passage 
 to the gas or water supply pipes of the house, which are 
 certain to be in " good earth." Similar accidents may happen 
 through not connecting by metal bands the lightning rod 
 with all external masses of metal, such as gutters, spouts, 
 and lead on the roof. 
 
 95. Chemical Decompositions by the Machine dis- 
 
chap, iv.] Electrical Machines. 1 5 1 
 
 charge. The power of the machine discharge to perform 
 chemical decompositions was originally shown by Faraday, 
 and can be repeated easily by the discharge of a Voss or 
 Holtz machine. In the case of iodide of potash it is only 
 necessary to place, on a piece of platinum foil, a few thick- 
 nesses of bibulous paper soaked in the solution. Then bring 
 a platinum wire from the positive terminal of the machine 
 on to the folds of moist paper, and connect the foil with the 
 opposite terminal. On turning the machine, a brown spot, 
 due to iodine, soon appears round the platinum point, proving 
 the decomposition of the salt. 
 
 For the decomposition of copper sulphate we have only to 
 bring two platinum wires, in connection with the terminals 
 of the machine, into a large drop of the solution on a plate of 
 glass. After turning the machine, the platinum wire in con- 
 nection with the negative conductor will be found coated with 
 copper. 
 
CHAPTER V. 
 ABSOLUTE MEASURE OF ELECTRICITY. 
 
 96. The Unit Jar, and Experiments with it. We 
 
 have in previous articles referred to changes and differences 
 of potential, and have explained how they theoretically 
 might be measured, but have not described any instru- 
 ments by means of which these measurements could be re- 
 duced to practice. The instruments we have used have been 
 essentially electroscopes means of detecting the presence 
 of a difference of potential; and not electrometers means 
 of actually measuring the difference. All instruments for 
 measuring differences of potential we owe to Sir William 
 Thomson, but, before referring to them, there is an earlier 
 instrument invented by Snow Harris, called the Unit Jar, by 
 means of which the quantity of electricity communicated to 
 a given conductor can be measured, and some of the laws of 
 electrification can be verified. 
 
 This (Fig. 99) consists of a small Leyden jar, placed on 
 an insulating stem, whose inner coat is connected with the 
 electrical machine, and outer coat with the body to be charged. 
 It is furnished with two balls, whose distance apart can be 
 adjusted, one connected with the inner, and the other with the 
 outer coat. When the jar reaches a certain definite charge, 
 a discharge takes place between the balls. The positive elec- 
 tricity from the outer coat, instead of going to earth, goes to 
 
 162 
 
Chap, v.] Absolute Measure of Electricity. 153 
 
 charge a conductor connected with it, and therefore at each 
 discharge of the unit jar a certain definite amount of electricity 
 has left the outer coat and gone to the conductor, this amount 
 being unaffected by the discharge of the bound charges of the 
 jar. We may take this amount as our provisional unit, and 
 so charge conductors with a certain number of units measured 
 by the number of sparks which pass between the coats of the 
 unit jar. As long as the conductor is the same, the rise in 
 charge is of course proportional to the rise in potential. 
 
 FIG. 99. 
 
 The inventor of the unit jar investigated several laws of 
 electrical action by its means, of which we will take two as 
 illustrations, the one referring to the striking distance, and 
 the other to the capacity of a Leyden battery or jar. 
 
 The striking distance really depends on the form and size 
 of the conductors between which the spark passes, but for two 
 nearly equal spheres it is approximately proportional to the 
 difference of potential. This may be shown by help of the 
 
154 
 
 Electricity. 
 
 [Book II. 
 
 unit jar. We must arrange on the knob of the jar to be ex- 
 perimented with a self-discharging arrangement, such as Fig. 
 100, where the distance between the knobs A and B connected 
 with the inner and outer coats can be varied and measured by 
 the sliding rod, which is graduated. If now, by the arrange- 
 ment of Fig. 99, we charge the Leyden jar, we can count how- 
 many units leave the unit jar by the number of sparks which 
 pass in it, before the Leyden jar has received a charge which 
 will strike across any given measured air space. If we double 
 
 FIG. 100. 
 
 the air space, we shall find that we have to double the num- 
 ber of units admitted before discharge takes place, and so on. 
 In making the experiment, the Leyden jar must be completely 
 discharged after each experiment, as the passage of a spark 
 across a considerable air space by fio means produces com- 
 plete discharge. 
 
 We may also easily show that the capacity of a battery is 
 proportional to the quantity of coated surface, assuming 
 that we have three or four jars of nearly -equal coated surface 
 and thickness of glass. Set the discharging electroscope at a 
 
chap, v.] Absolute Measure of Electricity. 155 
 
 certain distance on the knob of a single jar, and observe the 
 number of units required to produce discharge, that is, to 
 produce a certain definite potential difference between the 
 inner and outer coat. This number will be a measure of the 
 capacity. Connect another equal jar with the first mentioned 
 jar, in a battery of two jars. It will be found to require twice 
 as many units to produce a discharge. With a third jar it 
 will require three times as many, and so on. 
 
 *97. Theory of Thomson's Electrometers. It is 
 
 proved in works on the theory of electricity, that if we 
 have two plates parallel to each other, one insulated and 
 electrified and the other to earth, the lines of force proceed 
 from the plate at higher to that at lower potential in parallel 
 lines at right angles to either plate, if we exclude a portion 
 round the edge of each plate, which is subject to the induc- 
 tion of surrounding bodies. If, then, we take two spaces, 
 each of area S, opposite to each other and near the middle of 
 two parallel plates, it appears that the capacity of the system 
 
 Sf 
 
 formed by the two surfaces is -r. , where t is the distance 
 
 between the plates, and TT as before very nearly equal to -=-. 
 
 All the measures are of course referred to the absolute 
 system. 
 
 It also appears that the attractive force between the por- 
 
 tions indicated of the two plates is given by g-p, measured 
 
 in dynes or absolute units of force. 
 
 In applying this theory, Thomson has two parallel plates, 
 which are brought to the potentials whose difference is to be 
 measured. In one of these he makes an aperture, into which 
 
156 Electricity. [Booirn. 
 
 a moveable disc almost exactly fits, and he then measures the 
 force exerted on this disc alone ; taking care that when the 
 reading is taken, the disc is at the same potential and in the 
 same plane with the annulus or "guard ring" surrounding it. 
 This position is often called the "fiducial position." 
 
 *p8. The Absolute Electrometer. Sir William 
 Thomson divides his electrometers into two classes, Idiostatic, 
 in which the electrification to be measured is the only one 
 employed, and Heterostatic, in which the electrification is 
 measured by means of an independent electrification, made in 
 the electrometer. In one of his earliest forms of absolute 
 electrometer (Fig. 101), the moveable disc (A) was suspended 
 
 FIG. 101. 
 
 by three metal wires from one end of a long metallic lever, and 
 counterpoised by a weight (B) at the other end. The fulcrum 
 consists of a wire stretched between two metal supports ((7(7), 
 to which a certain amount of torsion is given, so as to keep 
 
chap, v.] Absolute Measure of Electricity. 157 
 
 the metal disc, when unelectrified, above its fiducial position. 
 Its register is made by the fine hair which joins the ends of 
 the arms (D) projecting from the lever, and moving with its 
 motion over the surface of an upright enamelled rod, on which 
 are two black dots separated by about a hair's-breadth. The 
 hair and dots are viewed simultaneously through a strong con- 
 vex lens, and the fiducial position is registered when the hair 
 bisects the distance between the centres of the two black dots. 
 
 All the parts of the instrument we have described, as 
 well as the guard ring, are in communication with the earth. 
 
 The lower disc, whose potential is required to be measured, 
 is insulated on a glass stem, and has its distance from the 
 first plate adjusted by a micrometer screw. 
 
 Before using the instrument the guard ring is placed in 
 metallic connection with the lower disc, so that there is no 
 electrical attraction. The disc or trap-door is above its fiducial 
 position, owing to the torsion of the wire. By means of 
 weights placed on the moveable disc, and a light wire rider 
 on the arm, the disc can be brought to its fiducial mark. The 
 force acting on the disc when in fiducial position will then 
 always equal the weights which had been used in this experi- 
 ment. In making a measure of potential the lower disc is 
 connected with the body whose potential is required, and 
 by turning the micrometer screw the distance between 
 the discs is adjusted till the register is brought to its 
 fiducial mark. Then, knowing the attraction F by the 
 weights previously used, 1 the distance t by the micrometer 
 screw, and the area S of the moveable disc, the difference of 
 
 1 F, the weight in grams, must be multiplied by the absolute 
 measure of gravity to reduce it to absolute units of force. Tins 
 may be assumed 981. 
 
158 
 
 Electricity. 
 
 [Book II. 
 
 potential becomes known in absolute measure by the formula 
 
 'tfrF 
 
 In the drawing we have omitted the external case, the 
 mechanical arrangement of the micrometer screw below, and 
 he vessel containing pumice-stone moistened with sulphuric 
 acid for securing dryness. 
 
 *pp. The Portable Electrometer. Where small 
 potential differences have to be measured, the absolute 
 
 FIG. 102. 
 
 electrometer is not sensitive enough. In these cases 
 heterostatic instruments have to be employed. Fig. 102 
 
chap, v.] Absohcte Measure of Electricity. 159 
 
 represents the Portable Electrometer, constructed specially 
 for observations on atmospheric electricity. The attracted 
 disc (A) consists of a very thin sheet of aluminium held below 
 its fiducial position by the torsion of a wire which supports 
 it. The movements of the disc are registered by a long arm 
 (AA\ also of aluminium, whose end is divided into two arms 
 crossed by a hair, which moves over an enamel plate, as in 
 the absolute electrometer. The case containing the instru- 
 ment is a Leyden jar, and all the parts we have named are in 
 connection with its inner coat (C). This is charged inde- 
 pendently by an electrophorus. The plate (D) is supported on 
 a glass stem, and its movements registered by a micrometer 
 screw (E). It is connected by a spiral wire with a terminal 
 which passes through the case, but is insulated from it (Fig. 
 103). This terminal is connected with the body of which the 
 potential is to be measured, ^represents pumice-stone mois- 
 tened with sulphuric acid to secure dryness in the instrument. 
 
 Fig. 103 gives a sketch of the brass umbrella, which, by 
 sliding on the terminal in connection with D, either, when 
 raised, insulates it from the earth, or, when lowered, puts it 
 in connection with the earth. The importance of this will be 
 seen in taking an observation. 
 
 Supposing the Leyden jar charged, we first determine the 
 earth reading. This is done by depressing the brass umbrella, 
 thus bringing the plate D to earth. On turning the micro- 
 meter screw we can bring the disc to its fiducial mark, and 
 read off its exact position by means of the micrometer screw. 
 Now raise the umbrella, and put D in connection with the 
 body whose potential is to be found. Turn round the 
 micrometer screw until the disc is in fiducial position, and 
 again read the micrometer screw, 
 
i6o 
 
 Electricity. 
 
 [Book II 
 
 The difference between the two readings is a measure 
 of the potential difference between the body and the earth, 
 independent of the charge given to the Leyden jar. 
 
 To prove this, let U be the unknown potential of the 
 charge in the Leyden jar. Connect the moveable plate with 
 
 FIG. 103. 
 
 the earth, and suppose that the observed distance between 
 the plates is t^ Then we have (Art. 97) 
 
 S 
 
 (1). 
 
 Next let V be the potential required to be found, and let t be 
 the second reading of the micrometer. Then 
 
 87T^ 
 
 S 
 
 (2V 
 
chap, v.] Absolute Meas^lre of Electricity. 161 
 showing that the measure obtained is altogether independent 
 
 /o ZT 
 
 of the charge in the jar. The constant multiplier v/ can 
 
 be found once for all by comparison with an absolute electro- 
 meter, and the readings reduced to absolute measure ever 
 afterwards. 
 
 This instrument is most frequently used for finding the 
 difference of potential at a point in the air and at the earth's 
 surface. For this purpose a wire is attached to the terminal 
 which carries on its further end a burning slow match, the 
 effect of which is to reduce the conductor (D) to the potential 
 at the point in the air at which the products of combustion 
 are escaping. 
 
 ioo. The Quadrant Electrometer. To the same 
 class belongs Sir William Thomson's earliest electrometer, 
 the Quadrant Electrometer, which is adapted to detect 
 and measure very minute potential differences. The prin- 
 ciple of the instrument is, that when one conductor is under 
 the cover of another, so that the induction on external 
 bodies may be neglected, the force between them, what- 
 ever their forms, is proportional to the square of their 
 potential difference. Thus if U be the potential of the 
 internal body, which we will suppose at the higher potential, 
 and V the potential of the external body, the force between 
 them is C(U- V) 2 , where C depends only on the geometry of 
 the two bodies. Next let the body of potential U be placed 
 symmetrically between two bodies alike in all respects whose 
 potentials are V and V. It will be urged in opposite direc- 
 tions by the forces C(U- V? and C(U- V'}\ and therefore 
 will be urged towards the body of lower potential by the force 
 
 L 
 
1 62 Electricity. [Bookii. 
 
 If Z7be very large compared with both F"and V,' then the force 
 
 This theory is carried into practice by making the external 
 conductors in form of four quadrants cut from a shallow 
 circular closed box of brass (Fig. 104), the opposite pairs 
 
 FIG. 104. 
 
 being joined by wires. These are separately insulated, and 
 within them hangs horizontally a light needle made of 
 aluminium, maintained at a high potential by being con- 
 nected with the inner coating of a Leyden jar. When 
 the four quadrants are at the same potential, the needle 
 is kept either by a magnet attached to it or by a bifilar 
 suspension symmetrically over one of the planes of division. 
 If the pairs of quadrants A A are at different potentials 
 from BB, the needle will be urged at both ends in the same 
 direction of rotation, with a force proportional to the 
 product of the potential of the needle and the difference of 
 
chap, v.] Absolute Meas^lre of Electricity. 163 
 
 potentials of A and B. It will, acting against the torsion or 
 magnetic force, be slightly deflected towards the quadrants at 
 lower potential, and in this case the amount of deflection is 
 also proportional to the disturbing force. In the form of the 
 instrument (Fig. 105) now commonly used, the quadrants (A A, 
 
 FIG. 105. 
 
 BB) are supported on the base by four glass stems; the 
 opposite pairs are connected by wires, and each pair is con- 
 nected with a terminal passing through the base, but insulated 
 from it. Under the quadrants is a glass vessel, coated 
 on the outside with tinfoil, and containing sulphuric acid, 
 which forms the inner coating of the Leyden jar, and also 
 keeps the instrument dry. The aluminium needle has a 
 platinum wire passing vertically through its centre, whose 
 
164 
 
 Electricity. 
 
 [Book II. 
 
 lower end dips in the sulphuric acid, and whose upper end is 
 formed in a T, to the top of which the bifilar suspension (D) 
 is attached. To register the movements of the needle a light 
 concave mirror (E} is cemented to the wire immediately 
 under the head of the T. The whole is enclosed under a 
 bell-glass, and supported on levelling screws. By means of 
 a lens (F) the light from a narrow slit in front of the flame 
 of an oil lamp (G) is thrown on the mirror, reflected from 
 it, and focussed on a graduated screen (H) placed above 
 the slit. As the distance between the slit and the mirror is 
 about 18 inches, the smallest movement of the mirror causes 
 a considerable movement in the image of the slit on the 
 graduated screen. 
 
 *IOI. The Gauge. In Sir William Thomson's original 
 form the bell-glass itself formed the Leyden jar. and the parts 
 
 PIG, 106. 
 
 Sulphuric Acid 
 
 of the apparatus were suspended from a metal plate which 
 closed it at the top. This form is still adopted where there 
 
chap, v.] Absolute Measure of Electricity. 165 
 
 is an arrangement for maintaining the charge of the jar con- 
 stant, without which the observations made at considerable 
 intervals of time are not comparable, owing to the unavoid- 
 able leakage of the Leyden jar. This consists of a gauge for 
 showing when the acid of the jar is at its normal potential, 
 and a replenisher to bring it back to its normal charge when 
 it has fallen below it. 
 
 The gauge consists simply of an attracted disc electrometer, 
 of which the attracted disc is in the cover plate, and the 
 attracting disc is placed below and parallel with it, insulated, 
 but in connection by a wire with the sulphuric acid in the 
 jar. The diagram (Fig. 106) gives a section. 
 
 *I02. The Replenisher. The replenisher (Figs. 107 and 
 108) is a small inductive electrical machine. It consists of 
 
 two inductors (AB) in the form of half-cylinders separated 
 by a small air space, and two insulated rnetal carriers (CD) 
 
1 66 Electricity. [Book n. 
 
 attached to an ebonite spindle, by which they can be rapidly 
 rotated between the inductors. 
 
 FIG. 108. 
 
 One inductor is insulated, but connected by a wire with the 
 acid in the jar, and the other is to earth. By means of two 
 springs (E and F) which pass without contact through slits 
 cut in the faces of the inductors, the two carriers come for a 
 moment into contact with each other when under full induc- 
 tion of the two inductors. These springs are connected by a 
 metal band under the instrument, but insulated from the 
 earth. 
 
 Assuming A connected with the inner coat of the Leyden 
 jar, charged positively, the carrier under the inductor A re- 
 ceives a minus charge, and D similarly a plus charge. The 
 carrier (D) which has the + charge comes by rotation under 
 cover of the + inductor (A\ from which a spring (6r) projects 
 internally, just touching the carrier before it comes in contact 
 with the spring (F). This carrier gives up its charge to the 
 inductor, and thus strengthens the charge of the jar. The 
 
chap, v.] Absolute Measiire of Electricity. 167 
 
 opposite carrier at the same time gives up its charge by a 
 spring to the opposite inductor, by which it passes to earth. 
 A few turns of the milled head at the top of the ebonite 
 spindle will then bring up the charge if it be too low ; and it 
 can easily be seen that turning the head in the opposite 
 direction will bring down the charge should it be too high. 
 
 *i02a. Arrangements of the Electrometer. Various 
 attempts have been made to make a reliable instrument of 
 the Quadrant Electrometer, while saving the expense of the 
 gauge and* replenisher. 
 
 One is that known as Mascart's arrangement. In this the 
 quadrants are permanently electrified to a constant potential, 
 one + and the other by a battery (see Art. 119) of 50 to 
 100 cells whose terminals are kept in contact with the 
 quadrants. The body whose potential is to be measured is 
 connected with the Leyden jar. In Art. 100, for the force 
 
 deflecting the needle we have 20(7' F)fl7- ^ 
 
 this case F= P", and the expression reduces to 4CF'U, 
 showing that when V is constant the force and therefore the 
 deflection of the needle is proportional to U. 
 
 Another method of keeping the potential of the Leyden jar 
 constant is to connect it permanently with a terminal of a 
 dry-pile (Art. 122). The potential is in this case low, and 
 the deflections obtained in use low in proportion. 
 
 *I03. Experiments with the Quadrant Electro- 
 meter. The following are interesting experiments with the 
 electrometer, omitting those in relation to Voltaic electricity, 
 which form the subject of succeeding chapters. 
 
1 6 8 Electricity. [Boot n 
 
 Pyro-electricity. We have already referred to this subject 
 (Art. 59), but the experiment can be performed by help of 
 this instrument on small broken crystals, half an inch long, 
 which would give no indications by the previous method. 
 Bind closely round each end of the crystal a platinum wire 
 and hang it by the wires over a metal plate under which is a 
 lamp or Bunsen burner. The wires are connected with the 
 terminals of the electrometer. On heating the plate the 
 needle is found to deflect, showing the presence of pyro- 
 electricity. On removing the plate and passing the flame 
 over the crystal the electrification disappears, but reappears 
 in the opposite direction as the crystal cools. 
 
 Electrical Density. Measures can be obtained of the density 
 at various points on a charged conductor by connecting one 
 terminal of a charged electrometer to earth, and bringing up 
 charges by a proof plane from successive points on the con- 
 ductor to the other electrometer terminal. The deflections 
 will be proportional to the quantities on the proof plane, and 
 therefore to the density at the point from which it is brought. 
 We lose in each experiment the charge on the proof plane, 
 but this may be avoided by connecting the terminal at first 
 with a small metal vessel open at the top (see Art. 75), and 
 merely lowering the charge into it each time without contact. 
 
 Contact Electricity. This name was given by Yolta to the 
 electrification obtained when two metals are simply placed in 
 contact with each other. The simplest way of showing it is 
 to have two plates, one of zinc and one of copper, ground 
 together so as to fit very closely when placed in contact. 
 Each must be furnished with an insulating handle. The two 
 plates are then connected by wires with the terminals of a 
 quadrant electrometer- Placing the plates in contact and then 
 
Questions on Book //. 169 
 
 separating them by help of the insulating handles, there is 
 a large deflection in the electrometer needle, showing that 
 the zinc is positively and the copper negatively electrified. 
 The mere contact of the metals in this experiment never 
 gives any sign of electrification, because in a circuit of metals 
 the successive potential differences just neutralise each other, 
 and the effect is only obtained when at some point a large 
 accumulation is allowed to occur on the condenser principle, 
 and is then set free by a separation of the condenser plates. 
 
 QUESTIONS ON BOOK II. 
 
 1. A sheet of paper well dried and rubbed with a brush will adhere 
 to the wall of a room, but it will remain longer adherent the drier the 
 air of the room. Explain this. 
 
 2. Two gold-leaf electroscopes, charged with opposite electricities, 
 are approached towards each other till the caps nearly touch. Explain 
 the effect observed on the leaves. 
 
 3. A gold-leaf electroscope is taken from a colder room and at once 
 placed on the table of a warmer room ; a charged body is brought in 
 contact with the cap. Describe the effect on the electroscope. 
 
 4. A crystal of tourmaline is suspended by a silk fibre between two 
 bodies, one positively and the other negatively electrified ; the whole 
 system is enclosed in an oven, which is gradually heated from outside. 
 Describe the behaviour of the tourmaline crystal during heating, and 
 also during cooling. 
 
 5. Explain why, after heating a tourmaline crystal, it is usual to/'-^ 
 draw the flame of a lamp across it before observing the phenomena on .. 
 cooling. Explain the effect on the observed phenomena, consequent * 
 on neglect of this precaution. 
 
 6. A piece of glass rubbed with cat's fur is pivoted freely, and 
 approached by another piece of glass rubbed with silk. Describe the 
 action between them. 
 
T 70 Questions on Book II. 
 
 7. A silk glove is drawn off the hand. What will be the electrical 
 condition of the glove ? 
 
 8. A gold-leaf electroscope is charged by napping it with a silk 
 handkerchief, and a piece of roll-sulphur, rubbed with cork, is ap- 
 proached towards its cap. Describe the observed effect. 
 
 9. In Coulomb's Balance, when the carrier ball is introduced, the 
 needle ball, after contact, shows a deflection of 30. Explain how the 
 torsion circle must be treated to bring the balls 15 apart, and also to 
 bring them 60 apart. 
 
 ANS. 105 in the negative direction, i.e. opposite to the deflection ; 
 52 30' in the positive direction. 
 
 10. If the balls in the balance had been at first 30 apart, and 260 
 of torsion had been put on in a negative direction (i.e. opposite to the 
 deflection of the needle), find the position of the needle. 
 
 ANS. At 10. 
 
 11. If the balls in the balance show at first charging a deflection of 
 a, and torsion /3 in the negative direction is applied, write down an 
 equation for finding the position of the needle. <- * A 4x ^ -"^ .' ^ 
 
 ANS. If x be the position required, a?+!3x 2 =a?. 
 
 12. A fixed charge is given to the needle ball, and the carrier ball 
 introduced without contact, carrying charges from successive con- 
 ductors, show that the charges can be compared by turning the torsion 
 circle till the balls are at a constant distance apart, and observing the 
 torsion on the wire. These charges will then be simply proportional 
 to the torsion in each case. 
 
 13. If the balance be discharged completely before each observation, 
 and the carrier ball introduced several times successively with different 
 charges, show that the charge in each case will be proportional to the 
 square root of the cube of the observed deflections. 
 
 14. The charge on the carrier ball of the balance, which at first 
 shows a deflection of 36, is halved, and the ball introduced again 
 without contact with the needle ball. Find the reading of the torsion 
 circle when the balls again diverge 36. 
 
 15. The needle ball of a balance is electrified, and charges are 
 carried from three selected points on a conductor by the carrier ball, 
 which is introduced each time into the balance without contact. The 
 readings of the torsion circle corresponding to the three charges are 
 respectively 35, + 3, and + 20, the deflection of the needle being 
 in all cases 45. Compare the electrical density at the three points. 
 
Questions on Book II. 171 
 
 16. A sheet of tinfoil, of which two opposite edges are held by in- 
 sulating handles, is charged, and has a gold-leaf electroscope connected 
 with its surface. What change in the indication of the electroscope 
 would be noticed, supposing the sheet rolled up like a wall map ? 
 
 17. A gold-leaf electroscope has its base to earth, and an electrified 
 wire cage is lowered over its cap, just avoiding contact with the base. 
 Describe the changes in the electroscope as it is lowered. 
 
 18. A gold-leaf electroscope has a sharp point attached to its cap, 
 and a glass rod, charged by friction with silk, is held over the point 
 for a short time, and then removed. Describe all the indications of 
 the electroscope. 
 
 19. A person on an insulating stool draws a silk glove off his hand, 
 and, holding the glove in the opposite hand, presents the ungloved 
 hand to the cap of an uncharged electroscope. What indications will 
 be obtained ? If he now drop the glove on the floor, what change will 
 there be ? 
 
 20. A glass funnel with a narrow tube is filled with copper filings, 
 which gradually flow out on to the cap of a gold-leaf electroscope ; 
 a rod of sealing-wax rubbed with flannel is held over the funnel as the 
 copper filings are discharged. Show that the electroscope acquires a 
 permanent charge. 
 
 21. A platinum dish is placed on the cap, and over it a glass 
 funnel with a capillary tube, filled with acidulated water. Show that 
 on holding an excited sealing-wax rod over the funnel the liquid will 
 flow through the capillary tube into the platinum dish, and will com- 
 municate a permanent charge to the electroscope. What is its sign ? 
 
 22. A sphere whose radius is 5 cm. has a charge of 10 absolute 
 units communicated to it. Find its potential and the density of its 
 electrification in absolute measure. 
 
 23. A sphere whose radius is 10 cm. is brought to potential 5 in 
 absolute measure. Find its charge. 
 
 24. Spheres whose radii are 5 and 6 cm. are connected by a long 
 wire (whose capacity is nil). Find how a charge communicated to the 
 system is divided between them. 
 
 25. Spheres whose radii are 1, 2, and 3 cm., are charged to poten- 
 tials 1,2, 3 in absolute measure, and are then suddenly connected by 
 a long wire. Find the potential of them all after contact. 
 
 ANS. $. 
 
6U / 
 172 Questions on Book II. ^^ ' 
 
 26. The radii of two spheres are as 2:3, and the density of their 
 electrification as 9 : 8. Compare their potentials. 
 
 ANS. 3:4. 
 
 27. An electrophorus cake excited by friction is dropped face 
 downwards on a metal plate connected with the earth. What is the 
 electrical condition of the sole? 
 
 28. One of two insulated hollow vessels has a weak charge of elec- 
 tricity. A carrier ball, supported on a silk fibre, is brought near the 
 outside of the charged vessel, touched by the finger, and then dropped 
 into the second vessel. It is lifted out, approached to the outside of 
 this vessel, when near it touched by the finger, and then dropped into 
 the first vessel. The whole process is repeated over and over again. 
 Show that the potential difference of the two vessels rises in compound 
 interest ratio. 
 
 29. If one thousand spherical mist particles, all at the same elec- 
 trical potential, fall together into a single rain-drop, the potential of 
 the rain -drop is one hundred times that of each mist particle. 
 
 30. Compare potential in a battery of 6 jars charged by 12 turns of 
 a machine, with that of a battery of 12 jars of equal area charged with 
 36 turns of the same machine working at the same power. 
 
 ANS. As 2 to 3. 
 
 31. Compare the quantity in a fully-charged battery of 8 jars with 
 that in another battery of 12 jars, the quantity of coated surface in 
 each jar of the latter being double that in each of the former, and the 
 thickness of the glass one-half. 
 
 ANS. As 1 to 6. 
 
 32. In a certain trap-door electrometer the trap-door was brought 
 to its fiducial position by a weight of '0133 grams, the whole being 
 unelectrified. The disc is a square whose side is '8 cm., and in a 
 certain experiment the trap-door was brought to its fiducial mark 
 when the moveable disc was distant *5 cm. Find the potential differ- 
 ence in absolute measure. 
 
 ANS. 11 *3 nearly. 
 
 33. The replenisher in a quadrant electrometer is a modified Voss 
 machine. Trace out the corresponding parts of the apparatus in the 
 two instruments. 
 
 34. Point out the exact source of danger in holding a piece of metal 
 in the hand during a thunderstorm. 
 
Questions on Book II. 173 
 
 35. Show, on the general principles of induction, that a person may 
 be killed at the instant of a lightning discharge without the discharge 
 passing through his body (the return shock). 
 
 36. When the electrification of the earth is resinous, what would be 
 the electrical condition of rain falling to the earth, and of sinoke rising 
 from the earth ? 
 
 37. Show that a knight of the middle ages in a coat of mail could 
 not be injured by lightning. 
 
 38. Why should you not in a thunderstorm take refuge under a 
 
 tree ? 
 
 39. Would you in a thunderstorm feel yourself secure in a house 
 built of sheet iron ? 
 
 40. Show why a house in which a gas or water supply exists is more 
 liable to damage from lightning than one without them. , 
 
BOOK III. 
 VOLTAIC ELECTRICITY. 
 
 CHAPTER L 
 THE BATTERY. 
 
 104. Electrical Conditions of a Zinc-Copper Couple. 
 
 Voltaic Electricity may be defined as the electrical condi- 
 tions developed in metals and liquids when in contact. As an 
 illustration (Fig. 109) we take a strip 
 of pure zinc and a strip of copper of 
 the same size. Dip them, without 
 contact between them, in a vessel of 
 water, acidulated with sulphuric acid. 
 If we now connect the plates with 
 the terminals of a quadrant electro- 
 meter, or with the plates of a con- 
 densing electroscope, it will be found 
 that the copper is positive to the 
 zinc. It can be shown that in this, 
 as in other cases, there is not a 
 development of one kind of electricity 
 only, for on insulating the vessel it 
 will be found that the copper is posi- 
 tive to the earth, and the zinc negative to the earth. 
 
 If we now connect the copper and zinc by a thick wire, all 
 
 176 
 
 
 FIG. 109. 
 
1 76 Electricity. [Book in. 
 
 trace of electrification disappears, but on separating them 
 again the difference of potential instantaneously reappears. 
 On substituting a very thin wire for the thick wire, we find 
 that the difference of potential is diminished but does not 
 disappear, and can be made less and less by shortening or 
 thickening the conducting wire. This shows that there is in 
 this case not a single discharge of electricity, as in a Leyden 
 jar, but a continuous discharge depending in some way on the 
 connecting arc. 
 
 105. Chemical Conditions of the Cell. If we next 
 examine the fluid in the vessel, we shall notice that while 
 the zinc and copper are in contact, bubbles of gas stream up 
 from the copper plate. This gas can be collected and proved 
 to be hydrogen. After the contact has lasted for some time, 
 we shall find that the liquid contains sulphate of zinc, and on 
 removing the zinc plate, washing, and drying it, we shall find 
 that it has lost in weight. 
 
 If we separate the zinc and copper plates, we shall see that 
 the stream of hydrogen bubbles from the copper-plate at once 
 ceases. 
 
 We have thus shown that when zinc and copper are dipped 
 in acidulated water they assume different potentials, without 
 any sensible chemical action taking place ; but as soon as 
 they are in contact with each other, the potential difference 
 is diminished, and as long as contact continues, chemical 
 action takes place in the liquid ; zinc, being dissolved, forming 
 zinc sulphate in the liquid, and hydrogen being evolved at 
 the copper plate. 
 
 If weighed amalgamated zinc and copper plates be placed 
 under an inverted glass jar in a pneumatic trough, and 
 
chap, i.] The Battery. 177 
 
 there brought into contact, the hydrogen can be collected and 
 its weight computed. If the loss in the weight of zinc be 
 also determined, these two weights will have a constant ratio 
 hydrogen to zinc of 2 to 65, which is the ratio of their 
 chemical equivalents. We see, therefore, that the action in 
 the cell is purely the chemical action of the fluid on the 
 metallic zinc, although the action on the zinc takes place at 
 the zinc plate, and the hydrogen is given off at the copper plate. 
 
 106. Thermal Condition of the Cell. While the 
 zinc and copper are in contact, we shall find that the 
 temperature both of the liquid and the solid conductors 
 has risen, and by performing the experiment in a calorimeter 
 it can be shown that the total heat evolved is exactly equal 
 to that which would be evolved on dissolving the same weight 
 of ordinary granulated zinc in dilute acid. This further con- 
 firms the conclusion that the action in the cell is a purely 
 chemical one. 
 
 107. Source of Energy of the Current. From the 
 experiments on the simple zinc-copper cell, we see that, 
 although we may have difference of potential, we cannot 
 have a flow of electricity maintained in the conductor, with- 
 out a sensible amount of chemical action in the cell. This 
 might have been in a measure anticipated, by considering 
 that the current in the conductor is a form of energy 
 (developing heat, and capable of doing work in a variety of 
 ways), and can therefore only be maintained by an expendi- 
 ture of energy. This source of energy is found in the energy 
 of chemical combination in the battery. For the maintenance 
 of the current it therefore appears necessary that we should 
 have at least one fluid capable of decomposition, and of form- 
 
 M 
 
1 78 Electricity. [Book in. 
 
 ing compounds with some other body with which it is in con- 
 tact. Thus we might in the cell have substituted, for sulphuric 
 acid, hydrochloric or nitric acid, or even pure water, and the 
 action would, initially at least, have been much the same. 
 We might also have varied the metals, provided we still had 
 one of them capable of being dissolved by the liquid. Thus, 
 if we had used copper and platinum, we should have had the 
 copper attacked by the acid, taking the place of the zinc in 
 the typical cell ; but if we had used gold and platinum, neither 
 of which is acted upon by sulphuric acid, we should have had 
 no current. We should also find, in all changes of the metals, 
 that that which is acted on by the acid is always at the lower 
 potential. 
 
 For convenience of reference, the plates in the liquid are 
 called electrodes, that which is consumed by the acid being 
 called the zincode, and the opposite plate the platinode, from 
 their analogy to the zinc and platinum in a typical zinc 
 platinum cell. 
 
 I08. Local Action. When only commercial zinc is 
 used in making the cells in place of pure zinc, a rapid 
 evolution of gas takes place from the zinc plate, accompanied 
 by the corrosion of this plate when the zinc and copper are 
 not in contact, thus causing a waste of zinc, a weakening of 
 the current, and obliging the use of a very weak acid solution 
 in the cells. This is called local action, and can be avoided 
 to a considerable extent by rubbing the zinc plate first 
 dipped in dilute acid, to remove oxide with liquid mer- 
 cury. In this way an amalgam of zinc and mercury is 
 formed on the suriace of the zinc. The cause of this 
 local action, as it is called, seems to be the existence of other 
 
c&ap. L] The Battery. 179 
 
 metals as impurities in the zinc. These with the zinc and 
 the acid set up small voltaic couples, by which the zinc is 
 consumed and hydrogen evolved. The presence of the mer- 
 cury seems to keep a uniform amalgam of zinc and mercury 
 always in contact with the acid, and prevents these local 
 circuits. When the battery is in action the zinc alone is 
 consumed, the mercury amalgam being constantly replenished 
 from the solid zinc behind. 
 
 109. Action of Evolved Hydrogen. In every battery 
 in which there is employed one fluid and two metals, a 
 further defect consists in the deposit of the hydrogen gas on 
 the platinode, forming a layer of hydrogen instead of metal. 
 This, in the first place, acts as a non-conductor to the elec- 
 tricity, so weakening the current; in the second place, its 
 contact with the copper plate lessens its potential, so that, 
 after the battery has been working for a short time, the 
 potential difference between the ter- 
 minals is much lessened. It also de- 
 composes the zinc sulphate in the liquid, 
 causing a deposit of zinc on the copper 
 
 HO. Smee's Cell. These effects 
 are somewhat obviated by Smee's 
 battery, in which the platinode con- 
 sists of thin sheets of silver or plat- 
 inum, in either case covered over with 
 finely divided platinum. This rough- 
 ened surface discharges the hydrogen FlG - 110 
 in a very remarkable degree, so that this form of cell is far 
 more constant than any other one fluid arrangement. In 
 
i8o 
 
 Electricity. 
 
 [Book in. 
 
 this cell there are generally two amalgamated zinc plates 
 on opposite sides of the platinised plate, all bound together 
 by a metal clip (A, Fig. 110). The platinised silver plate is 
 very thin, and supported on a wooden frame (B) placed be- 
 tween the opposite zinc plates. 
 
 III. The Bichromate Cell. The only other one-fluid 
 cell now commonly used is the bichromate cell, which is 
 useful for ringing a bell, or other purposes where the current 
 is intermittent. 
 
 In this, as in other cells described later, the platinode is of 
 ^as___coke, a substance obtained from 
 the inside of gas retorts, very hard, 
 not attacked by any acids, and a 
 good conductor. The other plate is of 
 zinc, and the exciting liquid is a solu- 
 tion of bichromate of potash, acidu- 
 lated with sulphuric acid. The zinc 
 is often attached to a sliding rod (A, 
 Fig. Ill), by which it can be lowered 
 into the acid when wanted to be used. 
 This is necessary, because the solution 
 acts on the zinc even when there is no 
 contact. There is often a single zinc 
 opposed to two carbon plates in the 
 cell. 
 
 The chemical action in this cell is 
 somewhat complicated. In addition 
 to the corrosion of the zinc by the acid 
 FIG. 111. with the evolution of hydrogen, the 
 
 potassium bichromate (K 2 Cr 2 T ) parts with some of its oxygen 
 
chap, i.] The Battery. 181 
 
 to the zinc, forming zinc oxide 3(ZnO), three atoms of zinc 
 entering into the action, and the salt, in doing so, is decom- 
 posed into potassium oxide (K a O) and chromium sesquioxide 
 (Cr 2 3 ). Each of these oxides, in the presence of free sulphuric 
 acid, forms a sulphate, the ultimate products being zinc sul- 
 phate and a compound sulphate of potassium and chromium 
 (KCr2S0 4 ) called chrome alum, which gives a green colour 
 to the liquid after the cell has been in action for some time. 
 
 Chromic acid, or rather chrome-trioxide (Cr0 3 ), is now 
 commonly used in place of bichromate of potash. The ulti- 
 mate products here are zinc sulphate (ZnS0 4 ) and chromium 
 sulphate (Cr 2 3S0 4 ). The liquid for this battery may be 
 made by slowly adding, with stirring, to four litres of water, 
 363 c. cm. of sulphuric acid (density 1-8) and 100 gms. of 
 chromi um- trioxide. 
 
 112. Daniell's Cell. In two fluid and two metal batteries 
 the hydrogen evolved acts chemically on some other sub- 
 stance, and causes a solid or liquid to be formed at the 
 platinode which has no injurious effect. 
 
 A great variety of such cells are in existence for various 
 purposes, of which we shall describe those most commonly used. 
 
 Daniell's Cell is constructed in a great variety of forms, 
 but consists essentially of a zinc rod immersed in dilute 
 acid, separated by porous earthenware, or some material 
 gradually permeable by liquids, from sulphate of copper in 
 which a copper rod is immersed. In this case the hydrogen 
 set free by the action of the acid on the zinc attacks the 
 copper sulphate, forming sulphuric acid, and causing a 
 deposit of metallic copper on the copper plate. 
 
 This cell continues working apparently at the expense only 
 
T 8 2 Electricity. [Book HI. 
 
 of the zinc and the copper sulphate, the latter of which can 
 be replaced by packing crystals of copper sulphate round the 
 copper plate, and in this case the working of the cell continues 
 till the zinc is consumed. The formation of zinc sulphate in 
 the zinc cell appears not to be injurious till a deposit of 
 crystals occurs, as the cell is found to work equally well 
 when the zinc cell is filled with a concentrated solution of 
 zinc sulphate instead of acid. In this latter case the zinc 
 sulphate has no direct action on the metallic zinc, except when 
 the terminals are joined. The chemical action originating the 
 current in this case is the tendency, in the presence of free 
 zinc, to replace copper sulphate by the more stable compound 
 zinc sulphate, an action which can only take place in the 
 pores of the material separating the zinc sulphate from the 
 copper sulphate. 
 
 The form given to this cell may be an outer glazed porce- 
 lain cell containing the zinc plate and acid, with an inner 
 vessel of porous porcelain filled with copper sulphate with the 
 copper rod immersed, shown in section in Fig. 112. Another 
 form is to have the outer vessel entirely copper, containing the 
 copper sulphate, and an inner porous vessel with the zinc rod 
 immersed in acid (Fig. 113). 
 
 On the same principle are constructed specific-gravity 
 batteries, of which one form is shown in section in Fig. 114. 
 It depends on the difference in specific gravity of zinc sulphate 
 and copper sulphate. At the bottom of the vessel lies a copper 
 plate embedded in crystals of copper sulphate, and a saturated 
 solution of the salt is poured over it to about half fill the 
 vessel. A copper wire is fastened to the plate, and, passing 
 through the liquid (insulated by a coating of gutta-percha), is 
 connected with a terminal outside. On the top of the copper 
 
Chap. I.] 
 
 The Battery. 
 
 '83 
 
 FIG. 112. 
 
 Fio 113 
 
 FIQ. 11&. 
 
1 84 
 
 Electricity. 
 
 [Book III. 
 
 sulphate is carefully poured a solution of zinc sulphate or 
 dilute acid, which, being specifically lighter, rests upon it 
 without mixing. In contact with this is suspended a zinc 
 plate. Menotti's battery differs from this only in placing a 
 layer of sawdust or sand over the copper sulphate crystals, 
 which takes the place of the porous cell. 
 
 113. Grove's and Bunsen's Cells. In Grove's Cell 
 (Fig. 115) the outer porcelain or glass vessel contains the 
 
 Zn 
 
 FIG. 115. 
 
 zinc plate immersed in dilute acid, and the porous vessel con- 
 tains a sheet of platinum immersed in strong nitric acid. 
 In this the hydrogen set free by the corrosion of the zinc 
 attacks the nitric acid, reducing it to water and one or 
 more compounds of nitrogen and oxygen, which are soluble 
 m the water and nitric acid to a large extent; but the 
 
Chap. L] 
 
 The Battery. 
 
 continued working of the battery causes them to be evolved 
 in the form of red fumes. 
 
 The evolution of gas may be avoided by substituting 
 chromic acid for nitric acid in the cell. The hydrogen then 
 acts on the chromic acid, forming chromic oxide and water, 
 the oxide being insoluble. 
 
 FIG. 116. 
 
 FIG. 117. 
 
 Bunsen's Cell differs from Grove's only in the substitution 
 of gas graphite for platinum in the porous vessel. This 
 diminishes the cost of the cell, but makes it less compact, 
 and, on account of the porous texture of the carbon, less 
 cleanly to work with (Fig. 116). 
 
 . ' 114. Leclanche's Cell. In this cell (Fig. 117) the porous 
 pot contains a rod of gas carbon, tightly packed round with 
 fragments of the same gas carbon and manganese binoxide, this 
 packing being covered over by a layer of pitch. The gas carbon 
 which projects has a lead socket cast on to it, to which a bind- 
 
i86 
 
 Electricity. 
 
 [Book III. 
 
 ing screw is attached. The outer cell contains a zinc rod 
 immersed in a solution of sal-ammoniac. The sal-ammoniac or 
 ammonium chloride (H 3 NHC1) attacks the zinc, forming zinc 
 chloride (ZnCl 2 )j which combines with the ammonia (H 8 N) to 
 form a compound (2H 3 NZnCl a ), and liberating hydrogen. The 
 hydrogen reduces the manganese binoxide (Mn0 2 ) in the 
 porous vessel to a lower oxide (Mn 2 3 ) and water. This cell 
 continues working till the whole of the manganese binoxide 
 has been reduced, if occasionally filled up with the sal- 
 ammoniac solution. 
 
 115. Latimer Clark's Cell. This is a cell not intended 
 to be used for ordinary work, but is very valuable as a 
 standard, in which respect we shall have occasion to refer to 
 it again presently. The form known as the H form is shown 
 
 in section in Fig. 117A. 
 It consists of a glass 
 vessel of the shape 
 shown, with platinum 
 wires fused through the 
 bottoms of the glass 
 tubes as electrodes. In 
 the right-hand side A 
 represents an amalgam 
 of pure zinc and pure 
 mercury covered by a 
 paste of mercurous sul- 
 FIO. ii7A. phate. In the other 
 
 tube is placed pure 
 
 mercury. The whole of the space above is filled up with 
 solution of pure saturated zinc sulphate, to which a few 
 
 ft 
 
Chap I.] 
 
 The Battery. 
 
 i8 7 
 
 crystals of zinc sulphate are added. Evaporation is pre- 
 vented by two paraffined corks which are inserted in the 
 mouths of the tubes. In this arrangement the amalgam is 
 the zincode, and the pure mercury the platinode of the cell," 
 denoted by the signs + and . 
 
 116. Becquerel's Cell. This, called by its inventor the 
 
 Ft 
 
 PIG. 118. 
 
 "oxygen battery," is of rather theoretical than practical im- 
 portance, being constructed without the use of two metals. 
 It consists (Fig. 118) of an outer vessel containing nitric acid, 
 and a porous vessel containing caustic potash, platinum plates 
 dipping into each vessel to form the terminals. On joining 
 the terminals a current flows from the platinum in the acid 
 to that in the alkali, nitrate of potash being formed in the 
 pores of the diaphragm. 
 
 117. Electromotive Force. In dealing with voltaic 
 cells, a very important element in their working is the differ- 
 ence of potential of their terminals when separate. This is 
 commonly called the Electromotive Force (written E.M.F.) 
 though of course not a Mechanical Force. 
 
 The unit used for E.M.F. is not the ordinary unit of 
 
1 8 8 Electricity. [Book HI. 
 
 potential which we used in Electrostatics, but a unit obtained 
 in a theoretical manner, and called a Volt. For the present 
 there will be no appreciable error if we take it as the E.M.F. 
 of a Daniell's cell formed of an amalgamated zinc rod in 
 saturated zinc sulphate, and a copper rod in semi-saturated 
 copper sulphate. The actual value of this E.M.F. is found to 
 be 1-07 Volt. 
 
 A better standard for reference, on account of its superior 
 constancy, is found to be the Latimer Clark cell, which, when 
 carefully made, and its terminals never joined so as to yield 
 an appreciable current, is found to retain an extremely con- 
 stant potential for any particular temperature, its value in 
 volts being 1-438 at 15 C. 
 
 In terms of this unit we can express the E.M.F. of different 
 cells by simply connecting their terminals with those of 
 a quadrant electrometer and observing the deflections, which 
 are directly proportional to the E.M.F.s of the different cells 
 experimented with. 1 By this means the following values may 
 be approximately verified (slight differences being unavoidable 
 owing to variation in the metal and fluids): 
 
 Volta (zinc, acid, copper), . . . about 1 
 
 Smee (zinc, acid, platinised silver), . 1 
 Bichromate (zinc, potas. bichromate, carbon 
 
 when freshly prepared), . . . 2 
 
 Daniell (zinc, acid, copper sulphate, copper), . 1 to 1*14 
 
 Grove (zinc, acid, nitric acid, platinum), . ,, 1'94 to 1'97 
 
 Bunsen (zinc, acid, nitric acid, carbon), . 1*75 to 1'96 
 Leclanche (zinc, sal-ammoniac, manganese 
 
 dioxide, carbon), . . . 1*41 
 Latimer Clark (zinc, mercurous sulphate, zinc 
 
 sulphate, mercury, . . . 1'438 
 
 1 It is preferable to reverse the terminals in each experiment, the 
 difference of the readings being then proportional to double the E.M.F. 
 
chap, i.] The Battery. 1 89 
 
 118. Battery arranged in Simple Circuit According 
 to the purpose for which a battery is to be used, the cells are 
 grouped either in simple or compound circuit, or in a manner 
 compounded of the two. 
 
 PIG. 119. 
 
 In a simple circuit arrangement, called also multiple arc, 
 all the cells have their zincs connected to a common terminal, 
 and all the coppers connected to another (Fig. 119). Since 
 the zincs are all connected together, as also the coppers, they 
 are respectively at the same potentials, and the battery is 
 equivalent to a single cell with the size of the plates in- 
 creased in proportion to the number of cells. The E.M.F. 
 of the battery will be found to be the same as for a single 
 cell, since it is independent of the size of the plates. 
 
 119. Battery arranged in Compound Circuit. In 
 
 this arrangement (Fig. 120) the copper of the first cell is 
 connected to the zinc of the next, the copper of that to the 
 zinc of the third, and so on. The cells arranged in this 
 manner are often said to be in series. 
 
 In this case the E.M.F. rises in proportion to the number 
 of cells, for there is a certain potential difference between the 
 zinc and copper of the first, and the same between the zinc 
 and copper of the second ; but the copper of the first and zinc 
 of the second are in contact, and therefore at the same 
 
1 90 Electricity. [Book in. 
 
 potential ; hence the whole potential difference will be double 
 that of one cell. The same reasoning applies, however many 
 cells there may be in the battery. 
 
 Pio. 120. 
 
 This arrangement was used by Volta, and termed by him 
 "a crown of cups." He also constructed on this principle 
 what is known as Volta's pile. This consists of a series of zinc 
 and copper discs soldered together by their backs, and piled 
 up with thicknesses of flannel between them, always retaining 
 the same order, flannel, zinc, copper, flannel, and so on, the 
 first and last plates being copper and zinc respectively. On 
 fitting the pile into a wooden framework, by which the 
 elements are pressed together, and dipping the whole into 
 brine or dilute acid, the flannels become saturated, and act 
 as liquid in the successive cells. Electrical indications were 
 easily obtained from the terminals of a pile consisting of fifty 
 or sixty couples. 
 
 Since Volta's time various modifications of this arrange- 
 ment have been made. In the trough battery the compound 
 zinc copper plates are let into grooves cut in the sides of a 
 wooden trough, covered internally with pitch, to secure in- 
 sulation, the space between the plates making a series of cells 
 into which the liquid is poured. In this arrangement there 
 is no means of removing the zinc plates for amalgamation, 
 great local action being the consequence, necessitating the use 
 of very weak acid. 
 
 Batteries of five or six cells, either of Smee's or the 
 bichromate type (sufficient for most experimental purposes), 
 
Chap. I.] 
 
 The Battery. 
 
 191 
 
 are now constructed with the plates all attached to a wooden 
 framework. This, by a rack-and-pinion motion, can be lifted 
 wholly out of the acid, which is contained in ebonite or 
 stoneware cells. Such a battery is figured in Fig. 121. 
 
 FIG. 121. 
 
 For post-office and other work, it is found more convenient 
 to use series of Daniell's cells, which, when the plates are 
 well amalgamated at first, remain in action without further 
 attention for several weeks. The same is true of series of 
 Leclanch6 cells, provided continuous currents are not required. 
 They are excellent for bell-ringing and other purposes, and 
 require less attention even than Daniell's. 
 
 120. Frictional Electricity obtained from a Battery. 
 
 M. Gassiot, and since him other experimenters, have con- 
 structed many thousand cells, carefully insulated and arranged 
 in compound circuit. By this means the E.M.F. is vastly 
 
192 Electricity. [Boo*m. 
 
 increased, so much that sparks can be obtained, electro- 
 scopes and Leyden jars charged, and all the phenomena 
 characteristic of frictional electricity demonstrated. 
 
 To compare the effects of frictional with those of voltaic 
 electricity, it may be instructive to give the results obtained 
 by Messrs. De La Eue and Miiller, working with silver 
 chloride cells, whose potential difference is about the same as 
 that of the zinc-copper cell we are using. They found that 
 
 1,000 cells in series give a striking distance of '0205 cm. 
 
 5,000 "1176 
 
 10,000 "2863 
 
 15,000 -4882 
 
 These confirm what was said above, that the striking distance 
 is not strictly proportional to the potential difference when 
 that difference is very small. 
 
 121. Comparison of Frictional with Voltaic Elec- 
 tricity. Faraday has, on the other hand, compared the 
 quantities derived from frictional and voltaic electricity both 
 by their magnetic and chemical effects. He found that "two 
 wires, one of platina 1 and one of zinc, each one-eighteenth of 
 an inch in diameter, placed five-sixteenths of an inch apart, 
 and immersed to the depth of five-eighths of an inch in acid 
 consisting of one drop of oil of vitriol and four ounces of 
 distilled water at a temperature of about 60 (Fah.), and 
 connected at the other extremities by a copper wire eighteen 
 feet long and one-eighteenth of an inch thick . . . yield as 
 much electricity in ... -j-f-^ths of a second as ... thirty 
 turns of the large electrical machine in excellent order." 
 "The electrical machine," he says, "is fifty inches in 
 diameter ; it has two sets of rubbers ; its prime conductor 
 1 Called by modern chemists Platinum. 
 
chap, i.] The Battery. 193 
 
 consists of two brass cylinders connected by a third, the 
 whole length being twelve feet, and the surface in contact 
 with air about 1422 square inches. When in good excitation 
 one revolution of the plate will give ten or twelve sparks, each 
 an inch in length. Sparks or flashes from ten to fourteen 
 inches in length may easily be drawn from the conductors." 1 
 From these two results we learn that in frictional elec- 
 tricity the potential differences are very high, but the 
 quantity of electricity concerned is very minute, while in 
 voltaic electricity the differences of potential are very small, 
 but the quantity enormously great. Returning to our hydro- 
 static analogy, we may say that the machine discharge is as 
 the tiniest rill falling down a very steep hill; the voltaic 
 current is like a vast river flowing through a nearly level 
 valley. 
 
 122. Dry Piles. On the principle of the compound 
 series are constructed certain modifications of Volta's pile, 
 called Dry Piles. In these the liquid is replaced by paper, 
 which, unless specially dried, contains a large quantity of 
 water. The only one now used is Zamboni's. This consists 
 of paper coated on one side with tinfoil and rubbed over on 
 the opposite side with manganese dioxide slightly moistened. 
 The sheets are then cut out with a punch and piled together 
 in the order tinfoil, paper, binoxide of manganese. With 
 several thousand sheets a high electromotive force is obtained, 
 though the current is insignificant. The most remarkable 
 thing about them is their permanence of action. By affixing 
 suitable terminals the pile can be discharged by alternate con- 
 tacts, giving motion to a light pendulum or see-saw, which 
 1 Faraday, Experimental Researches, Series in., Jan. 1833. 
 N 
 
1 94 Electricity. [Book m. 
 
 under suitable conditions has been known to keep up its 
 motion for several years. This pile is also used in Bohnen- 
 berger's electroscope, in which a single gold leaf is suspended 
 between two parallel plates near together, which are connected 
 with the terminals of a dry pile. The gold leaf then shows 
 electrification by diverging to one side or the other. 
 
 This, however, as well as every other form of electroscope, 
 is superseded by Thomson's Quadrant Electrometer, which 
 can be made to measure the hundredth part of the E.M.F. 
 of a single Darnell's cell. 
 
CHAPTER II. 
 ELECTROLYSIS. 
 
 123. Phenomena of the Current. We now proceed to 
 consider some of the actions belonging to the electricity in 
 motion as they are presented in the wire joining the termi- 
 nals of a battery. These are the peculiar phenomena which 
 form the subject of voltaic electricity. The properties of 
 the current may be classed as Chemical, Magnetic, and 
 Thermal. In the present chapter we consider the Chemical 
 phenomena. 
 
 124. Direction of the Current. As the phenomena 
 of the current all depend on certain directions, it is con- 
 venient to have conventional rules by which these directions 
 can be remembered. We have seen that in a zinc-copper cell 
 the copper is at a higher potential than the zinc, and conse- 
 quently when they are joined by a conductor, a neutralisation 
 of electricity takes place along the conductor. This can best 
 be represented by a movement of + E. from the copper to 
 the zinc, and an equal movement of E. from the zinc 
 to the copper. The motion of the + E. may be called 
 the positive current, and we fix our attention on this, and 
 speak of it as the direction of the current. This is only a 
 convention or memoria technica to represent to our mind the 
 neutralisation of unequal potential, and does not imply any 
 theory as to the nature of the current. 
 
 195 
 
196 
 
 Electricity. 
 
 [Book HI. 
 
 FIG. 122. 
 
 If we always had a flow of + E. to the zinc plate, and 
 E. to the copper, without any compensating flow in the 
 opposite direction, the potential of the zinc 
 would constantly rise, and that of the 
 copper constantly sink. Hence we infer 
 that there is a flow of electricity through 
 the liquid of the cell equal in amount and 
 opposite in direction to that in the conduc- 
 tor. That is to say, the current will flow 
 in the liquid from zinc to copper, and in 
 the external conductor from copper to zinc, 
 making a complete circuit (Fig. 122). This 
 assumption of the current in the liquid 
 will be confirmed through all our experiments, since we 
 shall find that the liquid obeys exactly the same laws as 
 the solid conductor while the current is passing. 
 
 In every battery, then, we shall assume that the current in 
 the liquid is from the zincode to the platinode, and in the 
 external conductor from the platinode to the zincode. 
 
 125. Electrolysis of Potassium Iodide. Let us now 
 
 place the terminals of a zinc-copper or other cell on opposite 
 sides of a piece of blotting or other kind of bibulous paper 
 moistened with potassium iodide. Near the end of the wire in 
 connection with the copper will appear a brown discoloration 
 owing to the liberation of iodine. If the bibulous paper be 
 first soaked in a solution of starch, the discoloration becomes 
 blue owing to the action of the liberated iodine on the starch. 
 To actions of which this is the type Faraday gave the general 
 name of Electrolysis, and to him we owe the very full in- 
 vestigation of the general laws on which the action depends. 
 
Chap. II] 
 
 Electrolysis. 
 
 197 
 
 126. Electrolysis of Water. Although the decompo- 
 sition of potassium iodide can be shown by a very weak cell, 
 many substances can only be decomposed by very powerful 
 batteries. The decomposition of water is easily shown with 
 a battery of four or five Grove cells. 
 
 Fio. 123. 
 
 For exhibiting the decomposition, some kind of voltameter 
 must be used. This, in the form shown (Fig. 123), consists 
 of two glass tubes, calibrated to measure the volumes of the 
 gases given off. In each tube is a platinum plate half an 
 inch wide and four or five inches long, with a platinum wire 
 
1 9 8 Electricity. [Book m. 
 
 welded to it, which is fused through the glass tube, and enables 
 communication to be made with the battery. These tubes 
 communicate either by being parts of the same U-shaped 
 tube (Fig. 123), or by being inverted over water in an inde- 
 pendent vessel. The apparatus must be at first filled with 
 water, slightly acidulated with sulphuric acid, for which the 
 third upright tube is provided. On passing the current, the 
 gases are rapidly evolved, hydrogen bubbling up from the 
 platinum plate connected with the zincode of the battery, 
 and oxygen from the plate connected with the platinode. 
 If we measure the volumes of the hydrogen and oxygen 
 evolved, after reducing them to the same pressure, we shall 
 find that the hydrogen occupies exactly double the volume 
 of the oxygen, and if we compute their weight, we shall find 
 the weight of the oxygen to be exactly eight times that of 
 the hydrogen. In practice it will be impossible to collect the 
 whole of the gases, since the oxygen is to some extent soluble 
 in the water. 
 
 127. Electrolysis of Hydrogen Chloride. Hydrogen 
 chloride or hydrochloric acid may be decomposed by a similar 
 arrangement, but the terminals must be made of carbon, since 
 platinum is attacked by the "nascent" chlorine (i.e. chlorine 
 at the instant of its separation from hydrogen). Moreover, 
 the chlorine is soluble in water, but its solubility is diminished 
 by saturating the water with common salt. After allowing 
 the current to pass for several hours, to saturate the liquid 
 with chlorine, it will be found that very nearly equal volumes 
 of hydrogen and chlorine are given off", the hydrogen as be- 
 fore collecting on the terminal connected with the zincode, and 
 chlorine on that connected with the platinode of the battery. 
 
chap. IL] Electrolysis. 199 
 
 In both these cases we see that the substance is decomposed 
 into its elements in exactly the proportions in which chemistry 
 teaches they enter into the substances, and which are indi- 
 cated by the form of their chemical formulae, H 2 for water, 
 and HC1 for hydrogen chloride. 
 
 128. Secondary action in the Decomposition of 
 Sulphates, etc. In many cases the electrical decomposition 
 is accompanied by a secondary action which may be purely 
 chemical. Thus if by means of two platinum plates we pass 
 the current through copper sulphate (CuS0 4 ), we shall find 
 pure copper deposited on the plate next to the zincode, and 
 oxygen only given off from the plate next to the platinode. 
 In this case the copper sulphate appears to be electrically 
 decomposed into copper, and the radical S0 4 , which is un- 
 stable, and cannot exist alone. It consequently attacks the 
 water of the solution, taking up hydrogen from it, and 
 forming H 2 S0 4 , liberating only the oxygen. The presence of 
 the free sulphuric acid around the plate can easily be shown 
 by performing the decomposition in a V-tube. In the case 
 of the sulphates of the metals, potassium and sodium, which 
 cannot exist as metals in the presence of either water or air, 
 we have a double decomposition. If, for instance, sulphate 
 of sodium (Na 2 S0 4 ) solution be decomposed, only oxygen 
 and hydrogen will make their appearance at the plates. In 
 this case it appears that sodium is set free by electrolysis at 
 the plate next the platinode, but immediately attacks the 
 water, forming soda (NaHO) and liberating hydrogen. At 
 the same time S0 4 is set free at the opposite plate ; it, too, 
 cannot remain free, but attacks the water, forming with it 
 sulphuric acid (H 2 S0 4 ) and liberating oxygen. We thus 
 
2OO Electricity. [Book IIL 
 
 have exact equivalents of hydrogen and oxygen set free, as 
 though water had alone been the electrolyte. The presence of 
 the acid and alkali are shown by performing the decomposi- 
 tion in a V-tube (Fig. 124), and colouring the sodium sulphate 
 solution with litmus, which when neutral (i.e. neither acid 
 nor alkaline) exhibits a violet tint. On passing the current 
 the liquid on one side becomes blue, proving the presence of 
 an alkali, and on the other side becomes red, proving the 
 presence of free acid. 
 
 FIG. 124. 
 
 129. Potassium set free by Electrolysis. Under 
 
 proper conditions, potassium has been obtained in a pure state 
 as a product of electrolysis. Its existence was thus demon- 
 strated by Davy. He applied to the surface of a fragment of 
 caustic potash, slightly moistened by exposure for a few 
 minutes to the air, the terminals of a battery of about 200 
 zinc-copper cells, when globules of the metal appeared at 
 the terminal of the wire connected with the zincode of the 
 
Chap, a] Electrolysis. 201 
 
 battery. These were preserved by performing the decom- 
 position under naphtha. 
 
 The experiment may be repeated with a battery of five 
 or six Grove cells, by making a hollow in the surface of a 
 block of caustic potash, and putting in it a globule of mercury. 
 If the block be rested on a platinum plate, and the current 
 passed from the platinum plate to a wire dipping in the 
 mercury, the potassium is liberated and forms an amalgam 
 with the mercury, from which it can be separated by distilling 
 away the mercury in the absence of air. 
 
 130. Faraday's Terminology for Electrolysis. In 
 
 all the foregoing experiments it can hardly have escaped 
 notice that hydrogen and the metals have appeared uniformly 
 at the terminal connected with the zincode of the battery, 
 while oxygen, chlorine, iodine, and acids have appeared at 
 the opposite terminal, and this will be found the case in 
 almost every decomposition into which these substances enter. 
 To avoid confusion, Faraday, with the help of the late Dr. 
 Whewell of Cambridge, invented certain terms for ex- 
 pressing the observed facts of electrolysis apart from any 
 theory as to their cause. The process of separating by voltaic 
 action chemical compounds into their constituents he termed 
 electrolysis, 1 and any substance which could be thus decom- 
 posed he called an electrolyte. We have already employed 
 the term electrode, 12 by which he means " that substance, or 
 rather surface, whether of air, water, metal, or any other 
 body, which bounds the extent of the decomposing matter in 
 the direction of the electric current." It will be noticed that 
 our use of the term for the plates of the battery is strictly in 
 1 fj\fKTpov and Xvo>, to set free. - rjKfKrpov and odos, a way. 
 
2O2 
 
 Electricity. 
 
 [Book lit 
 
 accordance with this use. " The surface at which the cur- 
 rent," according to our present notion, enters " the electrolyte 
 is called the anode 1 : " it is the negative extremity of the decom- 
 posing body, is where oxygen, chlorine, acids, etc., are 
 evolved, and is against or opposite the positive electrode 
 (platinode)." "The cathode 2 is that surface at which the 
 current leaves the decomposing body, and is its positive 
 extremity; the combustible bodies, metals, alkalies, and 
 bases, are evolved there, and it is in contact with the negative 
 electrode" (zincode). 
 
 l 
 
 FIG. 125. 
 
 For the purpose of distinguishing the substances which are 
 set free at the electrodes, Faraday continues, " I propose to 
 distinguish such bodies by calling those anions 3 which go to 
 the anode of the decomposing body, and those passing to the 
 cathode, cations, 41 and when I have occasion to speak of these 
 together I shall call them ions." * 
 
 Thus in the decomposition of water hydrogen and oxygen 
 
 1 avo), upwards, and 686s. 2 Kara, downwards, and 686s. 
 
 3 dvio>v, that which goes up. * Kariotv, that which goes down. 
 
 5 Faraday, Experimental Researches, Series vn., vol. i. p. 195. 
 
Chap. II.] 
 
 Electrolysis. 
 
 203 
 
 are the ions, oxygen being an anion, which is set free at the 
 anode, and hydrogen the cation, which is set free at the 
 cathode. 
 
 131. Quantity of Ions separated by the same 
 current. As to the quantity of the ions separated at each 
 electrode, we may notice first that if any number of volta- 
 meters be placed in different points in the same circuit, the 
 amount of decomposition is the same in all. This will be true 
 even though some of the voltameters have large plates and 
 others small ; or some have their plates near together, and 
 others far apart. The amount of electrolytic decomposition 
 
 FIG. 126. 
 
 is also the same in all, even when secondary and local actions 
 are taking place in some or all the voltameters. Faraday 
 showed this by including in the same circuit three decomposi- 
 tion vessels filled with the same dilute sulphuric acid. The 
 anodes in the three were of zinc, copper, and platinum 
 respectively. But the cathodes were all of platinum, and 
 were fixed in glass vessels, closed above, and filled with the 
 liquid, so that the amount of hydrogen given off" could be 
 measured. At the zinc anode there was violent local action, 
 while both the zinc-platinum and copper-platinum cells formed 
 
2O4 Electricity. [Book in. 
 
 voltaic couples, zinc sulphate forming at the zinc, and copper 
 sulphate at the copper anode. In the cell with both anode 
 and cathode of platinum there was of course no chemical 
 action beyond the direct decomposition of the liquid. After 
 passing the current through this compound arrangement till 
 a measureable amount of gas was collected at the three 
 cathodes, it was found that the amount of hydrogen in all 
 three was absolutely the same. 
 
 From these and numerous experiments, on nearly all the 
 electrolytes with which he was acquainted, and including 
 experiments both with frictional and voltaic electricity, 
 Faraday was enabled to lay down the principle that the 
 quantity of any given element separated in a given time by 
 electrolytic decomposition is simply proportional to the 
 strength of the current. Having established this, he used a 
 voltameter in the circuit as the measure of current strength 
 in many experiments with strong currents. 
 
 Further than this, if the current were passed through a 
 series of cells, some of which contained acidulated water, and 
 others contained hydrochloric acid, the quantity of hydrogen 
 collected at the cathodes of all the cells was found to be the 
 same. 
 
 Or again, if we take a series of cells containing different 
 electrolytes, e.g. (1) acidulated water, (2) copper sulphate, 
 (3) fused chloride of tin, (4) hydrochloric acid, when proper 
 precautions are taken for collecting the whole of the products 
 of decomposition, it will be found that the hydrogen collected 
 at the cathodes of (1) and (4), the chlorine at the anodes of 
 (3) and (4), the copper at the cathode of (2), and the tin at 
 the cathode of (3), will have certain definite ratios to each 
 other which will be absolutely invariable wherever any of 
 
chap. IL] Electrolysis. 205 
 
 these substances form the ions in any electrolytic decom- 
 position. 
 
 132. Electro - Chemical Equivalents. Having seen, 
 then, that (1) the quantity of any given electrolyte decqm- 
 posed in different cells in the same circuit is always the same, 
 (2) that the amount of any ion set free from different com- 
 pounds is the same for the same current, (3) that the 
 different ions are set free in quantities which bear a certain 
 definite relation to each other in respect of quantity when 
 liberated by the same current, we conclude that passing 
 unit current for unit time causes the separation of a certain 
 definite amount of each elementary substance which forms an 
 ion. This amount may be expressed in grains or grams, and 
 is independent of everything but the kind of ion and the 
 arbitrary unit of current we choose to adopt. This amount 
 of each ion is called its electro-chemical equivalent. 
 
 We have assumed in the above statement, as Faraday did, 
 that only one compound of each pair of ions is an electrolyte, 
 being generally that in which, according to the chemical 
 notation of his time, one atom of each ion entered. Later 
 researches have shown that in many cases two compounds of 
 the same ions (e.g. cupric and cuprous chloride) are both 
 electrolytes, thus giving rise to two or more electro-chemical 
 equivalents. 
 
 When these electro-chemical equivalents are calculated, 
 they are found to have the same ratio as the ordinary 
 chemical equivalents ; but while these latter are only the 
 ratios in which certain substances enter into chemical com- 
 binations, the former are perfectly definite masses of the sub- 
 stances. Thus it is found that for every 65 grams of zinc con- 
 
206 Electricity. [Bookin. 
 
 sumed in each cell of the battery, there will be set free in a 
 voltameter 2 grams of hydrogen, and 1 6 grams of oxygen, and 
 in a series of decomposition cells included in the circuit, and 
 containing solutions of metallic salts such as Faraday contem- 
 plated, there will be set free 254 grams of iodine, 71 of 
 chlorine, 63'3 of copper, 207 of lead, 200 of mercury, 78 of 
 potassium, 216 of silver, 118 of tin, etc. The equivalents 
 obtained from other salts will be simple multiples or sub- 
 multiples of these numbers, generally either double or one 
 half. 
 
 133. The Battery obeys the Laws of Electrolysis. 
 
 The same laws which hold in the decomposition cell also 
 hold in each cell of the battery. Thus for each electro- 
 chemical equivalent of zinc consumed in each cell of the 
 battery, without local action, there will be an equivalent of 
 each ion separated in every cell through which the battery 
 current passes. This can easily be demonstrated by allowing 
 a Daniell cell to decompose copper sulphate, making both elec- 
 trodes in the decomposition cell of copper. Taking the^ pre- 
 caution that all the copper plates, both of the battery and the 
 decomposition cell, are cleaned and weighed before the action 
 begins, it will be found, after the current has passed for any 
 length of time, that the increase of weight of the battery plate 
 and of the plate forming the cathode are exactly the same. 
 
 134. E.M.F. necessary for Electrolysis. It is now 
 
 easy to understand, on the ordinary principles of energy, why 
 we require a high E.M.F. to decompose certain compounds in 
 which chemical affinity is strong. If the decomposition, say 
 in a water voltameter, is effected at all, we must have an 
 equivalent of water separated for each equivalent of zinc 
 
chap, ii.] Electrolysis. 207 
 
 consumed in the battery cell. If the cell be a simple zinc- 
 copper couple, the total thermal energy due to the consump- 
 tion of an equivalent of zinc in the battery is simply the 
 number of thermal units evolved during the conversion of 
 that weight of zinc into zinc sulphate. This is a superior 
 limit to the amount of energy available in the circuit, since in 
 every circuit some energy is expended in heat developed in 
 its solid and liquid parts. 
 
 Again, the combustion of an equivalent of hydrogen in 
 an equivalent of oxygen evolves a certain definite amount of 
 heat which may be measured in thermal units, and this 
 number of thermal units must be expended in decomposing 
 the equivalent of water into its elements. If then the energy 
 (measured thermally) required for the decomposition of an 
 equivalent of any substance be greater than the thermal 
 energy developed per equivalent of zinc in the battery, that 
 decomposition cannot take place. 
 
 *I35. E.M.F. measured thermally. Again, the 
 E.M.F. of the battery cell may be measured by the thermal 
 energy developed by the decomposition of an equivalent of 
 zinc in each cell. For the E.M.F. is by definition measured 
 by the work done in bringing a unit of electricity from the 
 negative to the positive pole, and is therefore measured by 
 the energy developed in the passage of the same quantity of 
 electricity from the positive to the negative pole. If the 
 unit of electricity be that which . passes in our arbitrary unit 
 current in .unit time, the thermal energy developed by the 
 passage of unit current for unit time through the battery will 
 be a measure of the E.M.F. of the battery. 
 
 Hence, if we are able to express in thermal units the 
 
208 Electricity. [Book m. 
 
 amount of all the chemical actions which takes place in 
 any battery cell, we have a thermal measure of its E.M.F. 
 This Sir William Thomson has done for a Daniel cell (Phil 
 Mag., May 1851). In this cell there is (Art. 11 2) a zinc plate 
 in zinc sulphate, and a copper plate in copper sulphate. The 
 chemical actions may be represented thus 
 
 (1) Zinc decomposes the water, and forms zinc oxide. -^w ( 
 
 (2) Zinc oxide combines with sulphuric acid, and forms zinc 
 
 sulphate. 
 
 (3) Copper oxide is separated from the copper sulphate. 
 
 (4) Copper is separated from the copper oxide, the oxygen 
 
 recombining with the hydrogen liberated in (1). 
 
 In (1) water is decomposed, and in (4) the elements of water 
 recombine. These may be neglected, since they are equal 
 and opposite in their thermal relations, the same amount of 
 heat being evolved when the elements recombine, as was 
 absorbed in their separation. Again, the action in (1) and 
 (2) is of the nature of a running down of energy, and there- 
 fore accompanied by an evolution of heat ; while (3) and (4) 
 are of the nature of a building up of (potential) energy, and 
 therefore are accompanied by an absorption of heat. 
 The following data are supplied by experiment : 
 
 (1) The heat evolved in the combustion of one gram of 
 
 zinc in oxygen to produce 1-246 grams, of oxide 
 = 1301 thermal units. 
 
 (2) The heat evolved by 1'246 grms. of zinc oxide in 
 
 combining with sulphuric acid =369 units. 
 
 (3) Heat evolved by combustion of an equivalent of copper 
 
 (=9727 grin.) in oxygen to form 1-221 grms. of 
 copper oxide = 588 -6 units. 
 
chap, ii.] Electrolysis. 209 
 
 (4) Heat evolved by the combination of 1'221 grms. of 
 copper oxide with dilute sulphuric acid=293 units. 
 
 Therefore, for each gram of zinc consumed in a cell we 
 have 1301 + 369-(588-6 + 293) = 788-4 thermal units avail- 
 able for external work. OtffLI A l~ 
 
 < b \ (UkM^VA^* l<r-f I 
 
 The decomposition of an equivalent weight /pf water 
 1(*2^7 grm.) will require about 1060 thermal units for its 
 decomposition. Hence a Daniell cell cannot decompose 
 water; but a Grove cell, whose E.M.F. is about 1*9 of a 
 Daniell, can perform the decomposition of water, as also can 
 a battery of two Daniell's cells in series. 
 
 136. Hypothesis of Molecular Electrification. 
 
 Seeing that in every electrolytic decomposition we have two 
 ions, and for every electro-chemical equivalent of one ion which 
 collects at the cathode a certain definite quantity of positive 
 electricity has passed to the cathode, and for every equivalent 
 of the other ion the same definite amount of negative electricity 
 has passed to the anode, it is impossible not to think of the 
 charges of electricity as bound up in the molecules of the two 
 ions, and bound up with them in definite proportions, so that 
 the same absolute quantity of electricity is associated with the 
 electro-chemical equivalent of every ion, this charge being 
 positive for a cation and negative for an anion. In this 
 way electrolysis may be compared to an electrical convection 
 in which each molecule of each ion with its own specific charge 
 of electricity is constantly being transferred from and towards 
 the opposite electrodes. 
 
 That this hypothesis is not an ultimate molecular law may 
 be seen by noticing numerous exceptions to the rules cited 
 above. Thus iodine in some compounds is an anion and in 
 
 o 
 
21O 
 
 Electricity. 
 
 [Book in. 
 
 others a cation, and, as we have noticed, two chlorides of 
 copper (Cu 2 Cl 2 and CuCl 2 ) may be decomposed by electro- 
 lysis, the same amount of chlorine being yielded by both, 
 but twice as much copper by the former as by the latter. 
 
 137. Grotthiis' Hypothesis. The appearance of the 
 separate ions at the electrodes without their appearance in a 
 free state in the intervening liquid is generally explained by 
 Grotthiis' hypothesis. 
 
 This assumes that throughout the liquid there is a series of 
 decompositions, and recompositions in the direction determined 
 by the E.M.F. active at the electrodes. 
 
 Thus in the decomposition of water each element (hydrogen 
 and oxygen) in the compound molecule retains its electrical 
 affinity. The hydrogen being + is turned in each molecule 
 towards the cathode, and the oxygen towards the anode. 
 The series of polarised molecules may be represented thus 
 (a, Fig. 127) :- 
 
 ....& 
 
 The discharge consists in the neutralisation of the electricity 
 in each H 2 with the of the next molecule at the same instant 
 that these two elements unite to make a new water molecule. 
 Thus, after discharge, the arrangement is represented by 5. 
 
Chap. II.] 
 
 Electrolysis. 
 
 21 I 
 
 After discharge the polarised state is instantly restored, and 
 the series of polarisations and discharges succeed each other 
 so rapidly that they present to our means of observation the 
 appearance of a continuous current. 
 
 Exactly the same series of decompositions and recomposi- 
 tions takes place in the battery itself, the only difference 
 being that the oxygen set free attacks the zinc, forming with 
 it zinc oxide. We assume here that in the typical cell water 
 is the electrolyte ; but since sulphuric acid is always present, 
 there is some doubt whether this is not really the electrolyte, 
 the oxygen being a product of secondary action, as in every 
 sulphate. It is at least remarkable that the quantity of acid 
 present does not affect the E.M.F. of the cell. 
 
 ...J 
 
 FIG. 128. 
 
 In the case of the two fluid cells it will easily be understood 
 that a similar series of decompositions and recompositions 
 takes place. Thus, in a Daniell cell, we should have the 
 series of polarised molecules shown in Fig. 128 (a), and, after 
 discharge, the series of Fig. 128 (b). 
 
212 
 
 Electricity. 
 
 [Book III 
 
 138. Polarisation of Electrodes. After passing a 
 current between electrodes, we find a backward E.M.F. which 
 is called Polarisation. To exhibit it, arrange (Fig. 1 29) a battery 
 (A) and a voltameter (B) in one branch of a contact breaker (C), 
 and the same voltameter with a galvanometer (G) in the other 
 branch. This can be arranged as shown (Fig. 129), where, 
 when the moveable tongue is to the left, the battery is in cir- 
 cuit, but the galvanometer out ; and when to the right, the 
 
 Kio. 129. 
 
 battery is excluded, and the galvanometer included. A 
 mercury cup may be substituted for the contact breaker, 
 putting in the battery and galvanometer wires alternately. 
 
 After passing the current for a short time with evolution 
 of gas in the voltameter, turn the contact breaker ; a current 
 will pass through the galvanometer showing a current in the 
 voltameter opposite in direction to the battery current. 
 
 139. Grove's Gas Battery, and Ritter's Secondary 
 Pile. This principle is used both in Grove's Gas Battery 
 
Chap. II.] 
 
 Electrolysis. 
 
 213 
 
 and Bitter's Secondary Pile. In Grove's Gas Battery (Fig. 
 130) the cell consists of two tubes, each containing a plati- 
 num plate, to which platinum wires are attached, which are 
 fused through the glass tube, and terminate in binding screws 
 or mercury cups. On passing the battery current, oxygen 
 and hydrogen are liberated and collected. If the process be 
 
 Fio. 130. 
 
 stopped, a current will be found to flow from the plate in the 
 hydrogen to that in the oxygen, decomposing water, and 
 setting free oxygen against the hydrogen plate, and hydrogen 
 against the oxygen plate ; these combine with the occluded 
 hydrogen and oxygen to form water again. The E.M.F. of this 
 battery is low, four cells being required to decompose water. 
 
214 Electricity. [Book in 
 
 In Bitter's Secondary Pile, the plates of platinum are large, 
 and it has been used as a condenser for storing large quantities 
 of electricity. 
 
 140. Polarisation the test of an Electrolyte. Clerk- 
 Maxwell has pointed out that the existence of the polarisation 
 current is the best test whether a given substance is an 
 electrolyte, and may be applied where the quantities of the 
 products of decomposition are too small to be detected by 
 chemical means. Faraday has laid down the general law that 
 no solid is ever an electrolyte, but it can be easily proved 
 that glass, even at a temperature below 100 C., and while 
 perfectly hard, is an electrolyte. Put mercury in a test-tube, 
 and sink the test-tube in another vessel (a larger test-tube will 
 do) containing mercury, and surrounded by a steam bath. 
 Dip two wires in the mercury, one inside and the other 
 outside the inner tube, and connect with a battery and gal- 
 vanometer. As the temperature rises, a current begins to 
 pass before the mercury is at 100 C., and on detaching 
 the battery, and leaving the galvanometer alone in circuit, a 
 polarisation current is seen to pass in the opposite direction, 
 proving that the glass has been decomposed by the current. 
 
 141. Planters and Faure's Cells. In the practical use 
 of electricity, it is probable that storage batteries on the 
 principle of the Secondary Pile will play an important part. 
 The form to which attention has most been directed was in- 
 vented by Plante" , and improved by Faure and others. Planters 
 idea was to immerse two lead plates in dilute sulphuric acid, 
 and by a series of actions, partly electrolytic and partly 
 chemical, to obtain a deposit of lead peroxide (PbO 2 ) on the 
 anode, and pure lead in a spongy condition on the cathode. N 
 
 \L 
 
chap, ii.] Electrolysis. 2 1 5 
 
 In the cell, while discharge is taking place, the spongy lead 
 acts as the zincode, and the lead coated with lead peroxide 
 as the platinode. The preparation of Planters plates requires 
 a long time, as the current has to be sent through the cell 
 several times with long periods of rest between. These in- 
 tervals of rest are necessary, as during them both chemical 
 and local actions take place between the lead and the products 
 of electrolytic decomposition. When the plates are once 
 brought to a proper condition, a single passage of the current 
 for a few hours is sufficient to restore the cell after each dis- 
 charge. The ultimate product of the discharge seems to be 
 a deposit of sulphate of lead on both plates, and this is re- 
 moved by electrolysis on repassing the current, that on the 
 zincode (which in electrolysis is the cathode) being con- 
 verted into spongy lead, and that on the platinode (or anode) 
 into lead peroxide. The improvement introduced by Faure 
 was designed to hasten the preparation of the lead plates. 
 He coats both the plates at first with minium or red-lead 
 i), which, after chemical and electrolytic action, in a 
 relatively short time gives the plates the same condition as 
 in Planters cell. The E.M.F. of the cell, when in good con- 
 dition, is about two volts. 
 
 ! 
 
 142. Electro-metallurgy. A very important application 
 of electrolysis in the arts is the deposit of metals (especially 
 copper, gold, and silver) from the solution of their salts, called 
 electrotyping or electroplating. 
 
 The deposit of copper is very easily accomplished by using 
 a cell containing a concentrated solution of copper sulphate, 
 a strip of copper being suspended in it as the anode, and the 
 body to be coated with copper as the cathode, with a single 
 
2i6 Electricity. [Bookin. 
 
 Daniell's cell, or, for large plates, three or four Daniell's cells, 
 as battery. The body to be coated with copper is often an im- 
 press or cast taken from a seal, coin, or other object, in wax, 
 plaster, or gutta-percha. These moulds are non-conductors, 
 but on being evenly coated with plumbago or black-leacLjhey^ 
 become conductors. The prepared mould is suspended by a^ 
 copper wire in the electrolytic cell. An even coat of copper 
 is thus deposited upon it, and after it has acquired a suitable 
 thickness it can be removed from the wax mould, and will be 
 found to give an exact copy of the engraved marks or stamp 
 on the original seal or medal. 
 
 In some arrangements the conducting mould is made to 
 take the place of the copper plate in the Daniell's cell 
 itself. 
 
 Flowers and leaves can be coated with copper and after- 
 wards silver-plated by making their surfaces conducting. The 
 best method of accomplishing this is by immersing the object 
 in a weak solution of phosphorus in carbon disulphide, and 
 then allowing the solvent to evaporate, leaving a thin deposit 
 of phosphorus. On immersing the object in a bath of silver 
 nitrate, the silver becomes reduced as a thin superficial film. 
 This is sufficient to make the surface conducting, and it can 
 be coated with copper in the manner described above. 
 
 Copies of engraved copper plates can be made by immersing 
 the original in the copper sulphate bath (having first rubbed 
 its back over with a varnish, to prevent a deposit taking place 
 on it). The deposit of copper will adhere to the surface, but 
 after a sufficiently thick deposit has been made, it can be easily 
 separated and will give a reverse of the engraving. On 
 repeating this process with the reverse any number of copies 
 of the original engraving can be obtained. It is now more 
 
chap, ii.] Electrolysis. 2 1 7 
 
 usual to coat the original engraving with a very thin coat of 
 steel in a specially prepared bath, which, after half an hour's 
 immersion, gives a surface of extreme hardness, exhibiting 
 every mark on the original plate. From this a great number 
 of copies can be taken, and, if necessary, the steel coating can 
 be removed by dilute nitric acid, and a fresh deposit made 
 without injury to the original engraved plate. 
 
 The deposit of silver can best be made on a previously 
 prepared surface of copper, nickel, brass, or gilding metal, 
 which is a variety of brass rich in copper. Articles to be 
 plated are first cleansed from grease by boiling in a weak 
 solution of soda or potash, and then dipped into diluted 
 nitric acicl to remove any film of oxide. They are then 
 brushed with a hard brush and sand, rinsed from any adher- 
 ing impurities, and separately attached to clean copper wires. 
 After this they are once more dipped in dilute nitric acid, 
 washed, and while wet immersed in the silvering bath. 
 
 FIG. 131. 
 
 The silvering bath consists of a solution of silver cyanide, 
 
 
 4 
 L in potassium cyanide and water (one part of silver cyanide 
 
 and one part of potassium cyanide in 125 parts of water), 
 which should be gently warmed while the deposit is 
 taking place. The objects to be silvered are suspended in 
 
2 1 8 Electricity. [Book in. 
 
 the bath from copper rods and form the cathode of the 
 cell, the anode being formed by a strip of silver also sus- 
 pended in the liquid to prevent the solution from becoming 
 weakened. The battery may be either Daniell's, Bunsen's, or 
 Smee's ; the number of cells employed depending on the 
 size and number of objects to be plated. The diagram 
 (Fig. 131) shows the arrangement for silvering with one 
 Bunsen's cell. 
 
 The process of electro-gilding is very similar, except that 
 the objects are first " pickled " in a bath of mixed dilute nitric 
 and sulphuric acids. The gilding bath is usually a solution of 
 potassio-gold cyanide, but many other baths can be employed 
 with success. 
 
 143. Nobili's Rings. These are obtained very easily by 
 placing a drop of copper sulphate on a silver or platinum 
 plate, and touching the plate with one end of a bent strip of 
 zinc, whose other end dips into the copper sulphate. These 
 form together a minute voltaic cell, and copper is deposited 
 from the solution on to the platinum plate. The film of copper 
 is thickest immediately under the zinc point, and diminishes 
 pretty regularly, giving rings of varied colours. By using 
 a solution of lead oxide in potash, and connecting the sup- 
 porting plate with the platinode of a battery of several Grove 
 cells, while the zincode is connected with a platinum wire 
 which dips in the liquid, a deposit of lead peroxide is made, 
 
 /^ f\ 
 
 which exhibits very bright iridescent colours. 
 
 144. The Lead Tree. To Electrolysis (partially, at 
 any rate) we may refer the formation of the lead and silver 
 trees. If we place a zinc and a copper rod in contact with 
 
chap, ii.] Electrolysis. 219 
 
 Co, \+$ Ov * &-<->'& 
 each other in a flask which contains a solution of lead 
 
 acetate, the zinc replaces the lead in the salt, forming zinc 
 acetate, and the lead becomes deposited on the copper. Under 
 these conditions the lead appears in bright branching crystals 
 growing out from the copper, to which the name Lead Tree, 
 or Arbor Saturni, has been given. The replacement of the 
 lead by the more oxidisable zinc is a chemical action, but the 
 peculiar form which the ramifications of the lead take is due 
 to the electrolytic deposit. 
 
 
CHAPTER III. 
 OHM'S LAW. 
 
 145. Ohm's Law. This most important law, discovered 
 by Ohm, states that with any given conductor, of which 
 two parts are kept at different potentials, there is a con- 
 stant ratio between the numerical measure of the poten- 
 tial difference, and of the strength of the current which 
 traverses the conductor. This constant ratio depends only 
 on the form, material, and temperature of the conductor, and 
 is usually called its Resistance., Different conductors may 
 be compared numerically, in respect of resistance, just as 
 in respect of mass, capacity for heat, or any other physical 
 property. By choosing suitable units of potential difference, 
 current strength, and resistance, we may express Ohm's 
 law numerically thus : Let V be the potential difference, / 
 the current strength, and R the resistance of the conductor, 
 
 all measured in these units, then -=-=J?, or V=.IE. 
 
 In the case of a battery cell, V will denote the difference of 
 potential between the terminals when open, and R will be 
 the total resistance made up of the internal resistance of 
 the liquid part of the cell, and the external resistance of 
 conductors, solid or liquid, outside the cell. If we denote 
 the former of these by r and the latter by 7?, and if E denote 
 the E.M.F. of the cell, we shall have E=I (R + r), 
 
 or !=-/ 
 220 R + r 
 
CHap. III.] 
 
 Ohms Law. 
 
 221 
 
 146. Measurement of Resistance. To measure a re- 
 sistance we have to compare it with a certain standard resist- 
 ance, which we will assume to be that of a certain measured 
 length of standard wire at a certain temperature. This resist- 
 ance is called the Ohm, and is universally used as the standard 
 to which resistances are referred. We will assume at present 
 that we have a series of these resistances made by taking 
 
 PIG. 132. 
 
 multiples of the length of the standard wire which gives one 
 ohm resistance. These are issued in boxes of what are called 
 Resistance Coils. Each coil is made of carefully insulated wire, 
 folded in the middle and coiled round double, as shown in A 
 and B, Fig. 132. The terminals of each wire are soldered to the 
 stout brass rods A to C and D, B to D and E, which are sepa- 
 rated by small air spaces, the air space being formed of a conical 
 
222 Electricity. [Book IIL 
 
 hole, into which brass plugs (F, G) fit. When the plugs are in 
 position, the current passes across the plug; but when the 
 plug is withdrawn, the current goes through the correspond- 
 ing wire. The coils are fitted up in boxes (Fig. 133), the 
 numbers of ohms in successive coils being 1, 2, 3, 4, from 
 which, by means of addition, all numbers up to 10 can be 
 obtained. Then follow 10, 20, 30, 40, taking us up to 100; 
 and then 100, 200, 300, 400, taking us up to 1000, and so 
 on to any required extent. 
 
 FIG. 133. 
 
 We may observe that the ohm is about equal to the resist- 
 ance of a yard of fine galvanometer copper wire (B. W. G-. 
 
 No. 40). 
 
 *I47. Potential Gradient. Our first illustration of 
 Ohm's law consists of the construction of potential 
 gradients. Take a battery of three or four Daniell's cells 
 (A, Fig. 134), and introduce a set of resistances, of 100, 
 200, 300, 400 ohms respectively between the terminals 
 BF. Also connect B with one terminal of a quadrant 
 electrometer, the other terminal being connected with a 
 
Chap. III.] 
 
 Ohm's Law. 
 
 22 
 
 loose wire, which can be applied to either of the brass pieces 
 C, D, E, F. 
 
 The deflection of the electrometer shows the difference of 
 potential between B and C, B and J9, B and E, and B and F 
 respectively. 
 
 FIG. 134. 
 
 Taking a particular experiment, the number of scale 
 degrees read off from the screen were 
 
 For B and 
 Btm&D 
 
 9 scale divisions. 
 28 
 52 
 
 87 
 
 The numbers 9, 28, 52, 87 are sufficiently nearly in the 
 ratios of 100, 300, 600, 1000 to suggest to us the rule that 
 the fall in potential is simply proportional to the resistance. 
 
 If now we set off on a horizontal line distances propor- 
 tional to the resistance, so that (Fig. 135) BC, CD, DE, EF 
 
224 Electricity. [Bookin. 
 
 represent on any scale the resistance in the previous figure 
 (Fig. 134), and setup at (7, D, E, F, ordinates or perpendiculars 
 
 BCD E F 
 
 PIG. 135. 
 
 proportional to the observed potential differences, the extremi- 
 ties of these ordinates will be in a straight line, and that 
 straight line may be taken as giving graphically the potential 
 gradient in the conductor. The potential at any point may be 
 found by simply drawing a perpendicular to meet the gradient 
 line from the corresponding part of the line of resistances. 
 
 We may notice that this, in connection with the law of 
 Ohm, gives us an independent proof of the constancy of the 
 current in all parts of a circuit; the ratio between the 
 potential difference and the resistance being the measure of 
 the current strength. This measure is, in fact, the tangent 
 of the angle at J5, or of the inclination of the potential 
 gradient. 
 
 When any amount of resistance is introduced between the 
 terminals of the cell, the difference of potential becomes less 
 than the total E.M.F. observed when the circuit is open. 
 Assuming the current to consist of a series of polarisations 
 and discharges, the chemical affinities or contacts must call up 
 the difference of potential representing the whole E.M.F. 
 after each discharge. The remaining part of the E.M.F. is 
 really present in the liquid of the cell, which offers resistance 
 to the current, and in it the potential follows exactly the same 
 laws as in the solid part of the circuit. To illustrate this, let 
 
Chap. III.] 
 
 Ohms Law. 
 
 225 
 
 us take a single cell, and complete the diagram by setting off 
 a horizontal line ABC, in which AE represents the resistance of 
 the cell, BC the resistance of the connecting arc, and AD a 
 vertical line representing the E.M.F. Then the line DC will 
 give us the potential at every point in the circuit. 
 D 
 
 B 
 
 PIG. 136. 
 
 If there are several cells in compound circuit, AB represents 
 the total resistance, and AD the total E.M.F. of the battery. 
 The line of potential will not then be DC, but a broken line 
 which rises at each cell. Thus, supposing we have three 
 cells, the line of potential will be given by E, F, G, H, K, G. 
 
 D 
 
 K 
 
 A 
 
 B 
 
 FIG. 137. 
 
 The potential gradient gives us only potential differences, 
 and not the absolute potential at any point, If the cell and 
 circuit be all insulated, the potential at some parts will be + , 
 and at other parts , depending on the capacity of the 
 various parts of the circuit. If we connect the circuit with 
 
 p 
 
226 Electricity. [Book m. 
 
 earth at any one point, we have only to draw a line parallel to 
 the base line through the corresponding point on the gradient, 
 and perpendiculars to this line will then give the absolute 
 potential, positive when above and negative when below this 
 line. The figures drawn would represent the potential, sup- 
 posing the zinc plate brought to earth. 
 
 148. Oersted's Experiment Galvanometers. 
 
 Oersted, a Danish philosopher, was the first who discovered 
 the action of a conductor carrying a current on a magnet 
 placed near to it. It can be shown by a stout wire bent in 
 the form of Fig. 138, with a freely-pivoted magnet needle 
 
 B C 
 
 FIG. 138. 
 
 within the circuit. AEG are three mercury cups for the 
 purpose of introducing the battery wires. After placing the 
 coil in the magnetic meridian, so that the wires are parallel to 
 the magnet when no current is passing, and the north pole 
 suppose towards jB, place the battery terminals in A and B, so 
 that the current passes under the magnet from A to 7?, and the 
 
Chap. IIL] 
 
 Ohm's Law. 
 
 22 
 
 north pole will be seen to deflect towards the east on passing 
 it from B to A it will deflect in the opposite direction ; hence 
 the direction in which the magnet deflects is reversed with the 
 current. Next place the original ^-terminal in (7, so that the 
 current passes above the magnet from A to C ; the deflection 
 will be to the west, or opposite to that which was seen when 
 the current passed under the magnet from A to B. Hence we 
 see that the deflection is in contrary directions, according as 
 the current passes above or below the magnet. Lastly, put 
 one terminal in B and the other in (7, so that the current 
 passes from B to A under the magnet, and from A to B above 
 the magnet; these two parts of the current 
 will conspire to deflect the north pole west- 
 wards. 
 
 The following rule for the direction of motion 
 of the magnet given by Ampere was : If a little 
 figure swim in the current (which enters by his 
 heels and leaves by his head), and look towards the 
 magnet, the north pole will be driven to his left. 
 A rule identical with Ampere's, which will be 
 greatly used afterwards, is : The direction of 
 motion of the north pole is related to the 
 direction of the current, as the direction o* 
 propulsion of any right-handed screw is re- 
 lated to the direction of the twist in the 
 muscles of the wrist in driving it in. These 
 two directions are said to be related in right- 
 
 Fio. 139. 
 
 handed cyclical order. In Fig. 139 they are 
 shown, the direction of the straight arrow being that in 
 which a corkscrew is pushed in, and the arrows on the spiral 
 being the direction of motion of the spiral or of the twist in 
 
228 Electricity. [Book in. 
 
 the muscles of the wrist when driving it in. The central 
 arrow then shows the direction in which a free north pole 
 would be urged by a current in the direction of the arrow 
 circulating in the screw. Otherwise, if the current circulate 
 with the hands of a watch, a north magnetic pole will be 
 driven from the front towards the back of the watch. 
 
 A variety of instruments have been constructed on the 
 principle of Oersted's phenomenon for detecting and measur- 
 ing currents. To detect very weak currents, the effect on 
 the magnet may be increased to a great extent by simply 
 increasing the number of circuits round the magnet by 
 winding the wire in a continuous coil, each coil producing 
 its own effect on the magnet, and the sum of the effects of 
 all the coils being added together Such an arrangement is 
 often called a current multiplier 
 
 149. The Tangent Galvanometer. Where currents 
 of considerable strength have to be measured, the most con- 
 venient instrument is that known as the Tangent Galvanometer 
 (Fig. 140). It consists of one or several coils of stout wire 
 on the edge of a narrow circular hoop (A\ whose terminals are 
 attached to the base. In the centre is pivoted a very short 
 magnet (B) furnished with a pointer of aluminium, glass, or 
 any non-magnetic substance. Under the needle is a graduated 
 card for observing the deflection of the needle. The zero of 
 the graduations is in the plane of the wire coil, and the in- 
 strument is capable of being turned on its base about a central 
 axis to allow of the zero of graduation, and therefore the 
 plane of the coils, being brought into the magnetic meridian 
 before taking an observation. 
 
 Since a conductor carrying a current exerts force on a magnet 
 
chap. IIL] Ohms Law. 229 
 
 pole near it, the current causes in the air around it a field of 
 magnetic force, of which we may estimate the direction and 
 intensity on the principles of Bk. I. We shall at present 
 assume that the lines of magnetic force due to a plane circuit 
 cut the plane at right angles, and that the strength of the field 
 
 A 
 
 Fio. 140. 
 
 at each point is proportional to the current strength, but not 
 the same for different points in the field. The movement of 
 the needle will therefore generally bring its poles into parts of 
 the field at which the strength is different. By making the 
 needle very short compared with the diameter of the coils, 
 the force urging each pole of the needle may be assumed in 
 all positions sensibly the same as at its centre. This force 
 is perpendicular to the plane of the coils, which we have made 
 
230 
 
 Electricity. 
 
 [Book III. 
 
 the plane of the meridian, and is proportional to the current 
 
 strength. The method and construction of Art. 1 5 shows that 
 
 the needle will rest at an inclination to the meridian, and that 
 
 the force at right angles to the meridian is proportional to the 
 
 tangent of the deflection. Thus, with 
 
 the same instrument, the strength of 
 
 the current traversing the coils will 
 
 always be proportional to the tangent 
 
 of the angle of deflection of the needle, 
 
 and when we do not require currents 
 
 in absolute measure it is sufficient to 
 
 use the tangent of the angle as the 
 
 measure of the current. A table of 
 
 tangents for this purpose is given in 
 
 Appendix II. 
 
 It is an improvement in con- 
 struction to have two parallel coils 
 (Fig. 141), with the current traversing them in the same 
 direction, the magnet being suspended in the centre of the 
 line joining their centres. By this arrangement, due to Helm- 
 holtz, the field round the magnet becomes much more nearly 
 of uniform strength. 
 
 150. Sine Galvanometer. In this galvanometer the 
 reading is taken with the magnet poles always in the same 
 position relatively to the coils, and the strength of the field 
 therefore is strictly proportional to the current strength. 
 
 The tangent galvanometer can be used as a sine galvano- 
 meter by having a graduated circle attached to its base, and 
 a pointer to the moveable framework which carries the coils. 
 First bring the coils into the magnetic meridian, and observe 
 
 FIG. 141. 
 
Chap. III.] 
 
 Ohrns Law. 
 
 231 
 
 the reading of the pointer on the fixed scale. On passing the 
 current the magnet will deflect, but the coils can now be 
 turned round so as to follow its deflection until (supposing 
 the current not too strong) the magnet remains at rest in the 
 plane of the coils. The fixed circle is again read, and the 
 difference of the readings gives the angle through which the 
 coils have been turned from the magnetic meridian. In this 
 case the current strength is proportional to the sine of the 
 angle of deflection, and for use with this form of galvanometer 
 a table of sines is given in Appendix II. 
 
 The sine galvanometer can be made without any loss of 
 accuracy in a portable form by making the coil long and flat, 
 with a long needle suspended in its centre. 
 
 151. Astatic Galvanometer. When we have to detect 
 or to measure very weak currents, either the astatic galvano- 
 
 s 
 
 PIG. 142. 
 
 meter or Sir W. Thomson's mirror galvanometer may be used. 
 The astatic galvanometer is named from the employment 
 of an astatic needle. This consists of two exactly equal 
 
232 
 
 Electricity. 
 
 [Book m. 
 
 magnetic needles attached to a common axis, with their poles 
 in opposite directions. Such a system will set equally in all 
 directions under the action of the earth's magnetism that 
 is, it will be astatic. The magnets are very light, and the 
 whole system is suspended by a single fibre of unspun silk. 
 If a coil of wire carrying a current pass between the two 
 magnets, and entirely surround the lower one, as in Fig. 142, 
 Ampere's principle shows that the parts of the coil above and 
 below the lower magnet conspire to deflect this magnet in the 
 same direction; also that the part of the coil between the 
 magnets, by its action on the upper magnet, tends to turn 
 the magnetic system still in the same direction; while the 
 lower part of the coil, by its action on the upper magnet 
 alone, tends in the contrary direction. This effect will be 
 much smaller than either of the 
 other actions, owing to the greater 
 distance between the magnet and 
 the current. If the magnetic sys- 
 tem were absolutely astatic, any 
 current, however weak, would be 
 shown by the magnets at once 
 setting at right angles to the 
 coils. In practice there is never 
 an absolutely astatic system, but 
 the earth's power is so much 
 weakened that the very weak cur- 
 rent becomes sensible by a deflec- 
 tion of the needle. In the best 
 
 instruments the set of the magnets is at right angles to the 
 meridian. The general arrangement of the instrument is 
 shown in Fig. 143. The upper needle moves over a gradu- 
 
 FIG. 143. 
 
Chap, in.] 
 
 Ohm s Law. 
 
 233 
 
 ated card to show the deflections, while the lower needle 
 swings within the long flat coils shown below. The coils are 
 capable of rotation so as to bring the needle to the zero of 
 graduation, which is also in the plane of the coils, and the 
 levelling screws on the base bring the suspension of the 
 needle to the centre of the card. 
 Since the magnets are long, 
 and near to the coils, this instru- 
 ment is only adapted to detect, 
 and not to measure currents ; 
 it is rather a galvanoscope than 
 a galvanometer. 
 
 152. The Mirror Galvano- 
 meter. In the reflecting or 
 mirror galvanometer (Fig. 144), 
 the magnet is very short and 
 light, and attached to the back 
 of a concave mirror (A) made of 
 very thin glass, the mirror and 
 needle not weighing more than a 
 grain. This is suspended by a 
 single fibre of silk in a cylinder 
 of small diameter, round which is 
 coiled the wire in a solid cylinder. 
 The length of the wire depends on the purpose for which the 
 galvanometer is used, in some consisting of a few yards of 
 stout wire, and in others of several miles of the very finest 
 wire. The wire is carefully insulated by silk covering, and 
 afterwards soaked in melted paraffin, which, on hardening, 
 forms an excellent insulator. The reading of the instrument 
 
 FIG. 144. 
 
234 
 
 Electricity. 
 
 [Book III. 
 
 is accomplished by means of the lamp and screen, just as 
 shown in the quadrant electrometer (Fig. 105). On the top 
 of the coils is placed a permanent magnet, which controls the 
 magnet in the galvanometer, bringing the spot of light initially 
 to the zero on the screen. By proper adjustment it may be 
 made to neutralise the earth's action on the needle, so that 
 the magnet is almost astatic. This is really a tangent galvano- 
 meter, but as the deflections are always small, and the magnet 
 is very short, the current is simply proportional to the deflec- 
 tion, the tangent being proportional to the angle, if the angle 
 is small. (See table in Appendix II.) 
 
 153. Magnetic action of a Current in a Liquid. 
 
 That Oersted's principle applies to currents in liquids, accom- 
 
 Fio. 145. 
 
 panied by electrolysis, as well as to currents in solids, can 
 be shown by the arrangement represented in Fig. 145. The 
 
chap, in.] Ohms Law. 235 
 
 magnet (A) is suspended at right angles to the parallel zinc 
 and copper plates of a simple unclosed zinc-copper couple, and 
 immediately over the liquid. It is supported by a wire fixed 
 to it, on which is cemented a mirror, and the whole is sus- 
 pended by a single fibre of unspun silk. The movements of 
 the needle are registered by the lamp and screen, as in a 
 mirror galvanometer. On closing the circuit by means of 
 the mercury-cup (C) the spot of light moves so as to indicate 
 a current in the liquid from the zinc to the copper. 
 
 The deflection is much greater if, for the zinc and copper 
 plates, we substitute two platinum plates, and send a current 
 through the liquid (supposed to be acidulated water) from a 
 battery of four or five Grove cells. 
 
 154. Units employed in Voltaic Electricity. In 
 
 every voltaic circuit there are three physical quantities con- 
 cerned, E.M.F., Eesistance, and Current Strength, connected 
 together by Ohm's law. We have now described instruments 
 by help of which these may be measured: E.M.F. by the 
 Quadrant Electrometer, Eesistance by a box of resistance coils, 
 and Current Strength by a Voltameter or Galvanometer. 
 
 Before illustrating their use, it may be convenient to notice 
 the units actually employed in practice, as they are different 
 from those referred to in Frictional Electricity. These, called 
 absolute Electrostatic units, are : 
 
 For E.M.F., the theoretical unit of potential, which is the 
 potential of a sphere of unit radius charged with unit 
 quantity (Art. 80). 
 
 For Current Strength, a current in which a unit of elec- 
 tricity passes per second. 
 
 For Eesistance (by Ohm's law), the resistance of a con- 
 
236 Electricity. [Book ra. 
 
 ductor in which unit of potential difference would cause 
 a unit of electricity to pass per second. 
 For capacity, the capacity of a conductor in which unit 
 quantity produces unit potential. This will be (by Art. 
 80) a sphere of 1 cm. radius when freely electrified. 
 In Voltaic Electricity it has already been pointed out that 
 these units are very inconvenient, since every E.M.F. would 
 be represented by a very small fraction, and every current 
 strength by a very large number. We consequently adopt a 
 new and more convenient system, which will be fully explained 
 later. For the present our units will be : 
 
 For E.M.F., the E.M.F. of a Darnell's cell of given con- 
 struction (see Art. 124). This is called a Volt. 
 For Eesistance, the resistance of a certain length of a cer- 
 tain wire at a given temperature. This is called an Ohm. 
 For Current Strength, that in a circuit in which the 
 E.M.F. is one volt and the resistance is one ohm. 
 This current strength is called an Ampere. 
 The quantity of electricity which flows per second in a 
 current of one Ampere is called a Coulomb. It is 
 our new unit of Electrical Quantity. 
 The condenser in which a charge of one Coulomb causes 
 a potential of one Volt is said to have unit capacity, 
 and its capacity is called a Farad. The more usual 
 unit in practice is one-millionth of this unit, and is 
 called the Microfarad. 
 
 To connect these units with our units in electro-chemistry, 
 the most natural assumption seems to be that the electro- 
 chemical equivalents shall be the masses of the respective 
 ions which appear to be associated with one coulomb of 
 electricity. The results obtained by various experimenters 
 seem to show that one coulomb of electricity sets free nearly 
 
chap, in.] Ohm s Laiv. 237 
 
 0000105 gm. of hydrogen. (Numerical Tables and Constants, 
 by S. Lupton.) 
 
 155. Illustrations of Ohm's Law. The law as 
 
 stated by Ohm can be illustrated by showing that in a 
 battery (1) the E.M.F. is proportional to the current when 
 the resistance is constant ; (2) the E.M.F. is proportional to 
 the resistance when the current is constant. It then follows 
 on ordinary algebraical principles that the E.M.F. is pro- 
 portional to the product of current strength and resistance 
 where both vary. 
 
 (1) To prove that the E.M.F. is proportional to current 
 strength with a constant resistance, use a series of Daniell's 
 cells, all of equal E.M.F. If we interpose a very large resist- 
 ance (5000 ohms say), the difference of potential at the ter- 
 minals will be practically the whole E.M.F., the resistance of 
 the battery being insensible compared with this large resist- 
 ance. The current will then be so small that we must 
 employ a Thomson's mirror galvanometer to detect it. 
 
 Fitting up the galvanometer and resistance with one cell, 
 we get a certain deflection, 12-5 scale-degrees, suppose; with 
 two cells the deflection becomes 24'6 divisions; with three 
 cells, 37 divisions, and so on ; hence proving the constancy 
 of the ratio between the difference of potential and the 
 current strength. 
 
 (2) To prove that the E.M.F. is proportional to the resist- 
 ance when the current is constant. 
 
 Although we do not know the internal resistance of a cell 
 of the battery, we may assume that when the battery is in 
 compound circuit and the current passes through all the cells 
 in succession, the total resistance is the sum of the resistances 
 of each cell. 
 
238 Electricity. [Bookin. 
 
 Fit up the battery and a set of resistance coils with a 
 tangent galvanometer of no sensible resistance (or, at any 
 rate, very low resistance compared to one cell). If we use 
 one cell only, and introduce 10 ohms' additional resistance, the 
 galvanometer will give a certain reading, say 20. Next, use 
 two cells and introduce 20 ohms' resistance, and the galvano- 
 meter reading is sensibly the same. And this reading will 
 not alter if we introduce 3 cells and 30 ohms, or 4 cells and 
 40 ohms, and so on. Now in these cases the KM.F.s have 
 been in proportion of the numbers 1, 2, 3, 4, and so have the 
 resistances, for if r be the resistance of one battery cell, the 
 resistances have actually been r+10, 2r+20, 3?'+ 30, 4r-f 40. 
 
 Of course these two illustrations can only be taken as 
 suggesting the soundness of the law. Like every great 
 induction of science, its proof rests on an infinite series of 
 observations which are constantly in progress. We can only 
 add here that Ohm's law has borne the most rigorous tests 
 of absolute accuracy that have been applied to it. 
 
 156. Experimental Determination of Battery Re- 
 sistance. On account of the importance of Ohm's law we 
 shall now, with a set of resistance coils, use it to determine 
 certain resistances. These determinations are not susceptible 
 of very great accuracy, and are not such as would be employed 
 in practice. More accurate practical methods will form the 
 subject of the next chapter. 
 
 To find the resistance of a cell or battery, fit it up with 
 resistance coils (R) and a galvanometer (G-) of small resistance 
 (Fig. 146). Observe the deflection, and take the measure of 
 the current from the table of tangents. Halve this measure 
 and find the deflection which corresponds to half current. 
 By introducing resistance, the current can be brought down 
 
Chap. III.] 
 
 Ohm s Law. 
 
 239 
 
 to this reading. The resistance introduced will now be equal 
 to the internal resistance. For if we halve the current, we 
 double the resistance in the circuit, and since at first the only 
 resistance was internal, the external resistance introduced 
 must be equal to it. As an example, take the battery of four 
 Daniell's cells used before, which, when fitted up with a 
 galvanometer of small resistance, gives 73 deflection. Now 
 tan 73 = 3-270, therefore \ tan 73 = 1 -635= tan 58 30' 
 nearly. On introducing 24 ohms' resistance, the deflection 
 of the galvanometer falls to 58 J. We infer that the resist- 
 ance of the four cells and of the galvanometer equals 24 ohms, 
 or that the resistance of each cell is 6 ohms, neglecting the 
 galvanometer resistance. 
 
 - f 
 
 1 f 
 
 1 t 
 
 1 [- 
 
 FIG. 146. 
 
 157. Resistance of the Galvanometer Fit up the 
 
 galvanometer, whose resistance is supposed to be consider- 
 able, with resistance coils in the circuit of a battery or cell 
 of known resistance, as in Fig. 146. Observe the reading 
 with only the resistance of the battery and galvanometer 
 (r-j-6r say). As before, introduce resistance till the current 
 is halved, and then the introduced resistance will also equal 
 r-f Q\ whence r being known, G, the galvanometer resist- 
 
240 
 
 Electricity. 
 
 [Book III. 
 
 ance, becomes known. If necessary, resistance may be intro- 
 duced at first to bring the galvanometer reading down if too 
 high, since the reading should not be taken with a deflection 
 above 75, the change in the tangent becoming very large for 
 each degree at higher angles. 
 
 158. To find the Resistance of a given Wire Coil. 
 
 This can be done either by balancing the unknown against 
 a known resistance, or by calculation. 
 
 (1) By balancing. Fit up as in Fig 147 a circuit consisting 
 of a battery (A), a galvanometer (6r), a box of resistance coils 
 (E), and the unknown resistance (X), whose terminals are 
 connected with the mercury cups (B, C). When the battery 
 wire (P) dips into B, and the coil (X) is included, read the 
 galvanometer. Next lift the wire (P) from B into (7, thus 
 excluding the coil. Introduce resistance in E till the galvano- 
 meter regains its former reading. The resistance introduced 
 will then equal that of X, the unknown resistance. 
 
 Fio. 147. 
 
 (2) By calculation. Let E be the E.M.F., and r the internal 
 resistance of the battery, g the galvanometer resistance, and 
 the unknown resistance. 
 
chap. in.] Ohms Law. 241 
 
 Take out all resistance except that of the battery and 
 galvanometer (when the battery is said to be short-circuited), 
 and let the observed current be I lt Then by Ohm's law 
 
 Introduce the unknown resistance x, and let the current be 
 
 /a 
 
 Introduce a known resistance n ohms, and let the current 
 be/a 
 
 Dividing equations (2) and (1) 
 
 Dividing equations (3) and (1) 
 
 1=1+-! 
 
 Hence we have, by eliminating r+g, 
 
 n I, /!-/,' 
 
 Since in this result only ratios of current strengths enter, 
 we may for the current strengths I lt J 2 , / write the tangents 
 of the observed deflections of the galvanometer, assuming it 
 to be of the tangent form. 
 
 As a particular example, using the same battery of four 
 Darnell's cells, and the galvanometer of small resistance, we 
 find on short-circuiting the battery a deflection of 73 ; on 
 introducing the coil, whose resistance is unknown, the deflec- 
 
 Q 
 
242 Electricity. [Book in. 
 
 tion sinks to 37, and on introducing 20 ohms, external re- 
 sistance, the deflection is 61. 
 
 We have from the tables (Appendix II.) 
 
 tan 73 = 3-271, tan 37=-756, and tan 61 = l-784. 
 Hence 3-271= : -756= 
 
 r+g r+g+x 
 
 E 
 
 2-515 
 
 3-271_, 20 
 
 and 1-784" 1+ f+^ '' 7+g"l'7S4: 
 
 = x x 20 = 80 ohms nearly. 
 
 *70O ' 
 
 The same equations give r + g, which, on working out, is 
 found to be 24 ohms nearly. 
 
 159. Relation of Resistance to Dimension of a 
 Conductor: Specific Resistance. We have seen that 
 the resistance of a wire or of the liquid of a battery is pro- 
 portional to the length which the current has to traverse ; we 
 may next inquire how it is related to the sectional area of the 
 wire. The easiest way to do this is to take two equal lengths, 
 cut from the same wire, and place them breast to breast 
 (Fig. 148) as a single conductor, when we find the resistance 
 to be exactly half that of either wire taken separately. 
 Since the two wires are equal in all respects, they will 
 behave exactly as if they were lying side by side, or in 
 
chap, in.] Ohms Law. 243 
 
 fact formed parts of a wire of twice the sectional area. 
 
 Hence we infer that the resistance of a wire is inversely 
 
 as its sectional area. 
 
 We may prove it roughly for the liquid in a battery by 
 taking two equal cells, and after 
 determining their resistances care- 
 fully (to see that they are nearly 
 equal), fit them up in simple circuit, 
 and it will be found that the resist- 
 ance of the battery so formed will 
 be half that of a single cell. 
 
 We learn that the resistances of 
 wires of the same material are pro- 
 portional to their length directly, and 
 
 Fio. 148. _ . . , 
 
 to their sectional area inversely. As 
 
 the resistance also depends on the material, we may generally 
 say that for any wire or liquid in a battery it 
 
 _ length 
 
 sectional area 
 
 where p depends only on the material, and is called its specific 
 resistance. If we make the length and sectional area each 
 unity, the resistance will then be simply />, the specific re- 
 sistance. We may therefore define the specific resistance of 
 any material as the resistance of a cube of that material whose 
 edge is 1 cm. the current being supposed to pass directly 
 between two opposite faces. 
 
 The following are the specific resistances of the commonest metals 
 at C. 1 The unit is the millionth part of an ohm (or 10 ~ 6 ohm), 
 called the microhm. 
 
 1 See Lupton's Numerical Tables and Constants. 
 
244 Electricity. [Book in. 
 
 Silver, annealed, 1*521 
 
 Copper, hard drawn, 1*642 
 
 Platinum, annealed, 9158 
 
 Iron, soft, 9*827 
 
 Mercury, 96*146 
 
 Bismuth, 132*65 
 
 German Silver, 21 '17 
 
 Brass, 5*8 
 
 The specific resistances of liquids most commonly used are, accord- 
 ing to the best determinations, in ohms, 
 
 Water at 4 C., 9*1 x 10 6 
 
 at 11 C., 3*4 xlO 5 
 
 Dilute hydrogen sulphate (5% acid) at 18 C., 4*88 
 
 (20% acid) 1*562 
 
 n (30% acid) 1*38 
 
 (40% acid) 1*5 
 
 Hydrogen nitrate, at 18 C.,. . . 1'61 
 
 Copper sulphate sat. solution at 10 C., . 29*3 
 
 Zinc sulphate sat. solution at 14 C., . 21*5 
 
 Sodium chloride sat. solution at 13 C., . 5*3 
 
 In all cases the resistance diminishes rapidly as temperature rises. 
 The specific resistances of the commonest insulators measured in 
 megohms or 10 6 ohms. 
 
 Glass (crystal) below 40 C., infinite. 
 
 at46C., . . 6*182 x 10 9 
 
 at 105 C., . . 1*16 xlO 7 
 
 Paraffin, at 46 C., . . . . 3*4 x 10 10 
 
 Ebonite, at 46 C., . . { . 2'8 x 10 10 
 
 160. Application of Ohm's Law to a Simple Circuit. 
 We can now compute the current obtained from a battery 
 in simple circuit. The E.M.F. we have seen to be the same 
 
chap, m.] Ohm's Law. 245 
 
 as for a single cell, and if we have n cells, each of resistance 
 
 T 
 
 r, the total internal resistance becomes , and hence Ohm's 
 formula becomes 
 
 E nE 
 
 /= 
 
 r + nR 
 
 When .72=0, or the external resistance vanishes, the current 
 = , or n times the current from one cell. If the external 
 resistance becomes large, so that r vanishes in comparison 
 
 with nE, the current becomes ~~ = 15> or the same as for a 
 single cell. This can be proved experimentally by introducing 
 a resistance of say 10,000 ohms, and showing that the current 
 is the same as for a single cell. 
 
 161. Application of Ohm's Law to a Compound 
 Circuit. In the compound series of n cells, the E.M.F. be- 
 comes nE and the internal resistance of the battery nr. Hence 
 
 nE 
 
 
 
 ? 
 
 When R is very large compared to nr, the current is -^-, 
 and therefore proportional simply to the number of cells. 
 If R, on the other hand, be very small compared to r, the 
 
 nE E 
 current becomes = , or the same as from a single cell. 
 
 162. Application of Ohm's Law to a Mixed Circuit. 
 
 We have seen that with a simple circuit, and small external 
 resistance, the current is directly proportional to the number 
 
246 
 
 Electricity. 
 
 [Book III. 
 
 of cells, while with a compound circuit and small resistance 
 it is the same as for one cell. When the resistance is moder- 
 
 Fio. 149. 
 
 ately large, a better arrangement of the battery can be 
 obtained by what is termed Mixed Circuit. In this a number 
 of cells are compound-circuited, and placed in a row with 
 other equal rows also compound-circuited abreast of them. 
 Each row of q cells (each having E.M.F. = E, and resistance 
 = r) will be equivalent to a single cell whose E.M.F. is qE, 
 and resistance qr. 
 
 If we have p rows then we have p such cells in simple 
 circuit, and we have for the current strength 
 
 /= 1 E = P9 E 
 qr+pE 
 
 If we have n cells, then pq = n, and 
 
 ~qr+pR 
 
 *i6s. Arrangement of a Battery for the greatest 
 Current. This is to find the values of p and q which make 
 / the greatest possible. In the last expression we may write 
 
 nE 
 
chap, in.] Ofaris Law. 247 
 
 This will be the greatest possible when the denominator is 
 the least possible, and that is when the square it contains 
 vanishes. 
 
 which gives the condition that the external and internal 
 resistances shall be equal. 
 
 If the cells are in simple circuit the external resistance is 
 
 , and for this, or for any less external resistance, the simple 
 
 circuit is the best. If the cells are in compound circuit, the in- 
 ternal resistance is nr, and for this, or any greater external re- 
 sistance, the compound circuit is best. For intermediate values 
 of R the best arrangement is found by solving the equations 
 for p and q. For example, to find the best arrangement of 48 
 cells, each of resistance *5 ohms to be used with an external 
 resistance of 6 ohms. Here 
 
 pq=iS, and 6= x -5 
 or --12 
 
 q =24 
 . . best arrangement is 2 rows each of 24 cells. 
 
 If the external resistance had been 1 ohm, we should have 
 had |-=2 and #2=48, 
 
 .*. q is between 9 and 10. 
 Neither 9 nor 10 is a submultiple of 48; we must therefore 
 
248 
 
 Electricity. 
 
 [Book in. 
 
 give to q either the value 8 or 12, and find which will give 
 the greater current. 
 
 A Q V A Q 
 
 Substituting #= 8, gives /= - = ^ ( Artt 
 
 and = 
 
 4SE 
 
 48 
 
 or the currents are equal, and the best arrangement is either 
 six rows each of eight cells, or four rows of twelve cells. 
 
 164. Method of changing rapidly the Battery 
 arrangement. For verifying these deductions from Ohm's 
 law, it will be found useful to fit up a battery of six Daniell's 
 cells, so that they can easily be changed from one arrange- 
 ment to another. This can be done by placing the battery on 
 a frame, one wire from each plate passing to a binding-screw or 
 mercury cup on the framework all the zincodes being in one 
 straight line and all the platinodes in another, so placed that the 
 
 x^ J=2 ^ _ 
 
 Zn ZT* 
 
 ZTL 
 
 <SfflS3 
 
 2ZOT 
 
 (( 
 
 
 
 
 2ZOIOIO 
 
 lOZH 
 
 ' 
 
 / y/ /# Pt 
 
 Pt 
 
 FIG. 150. 
 
 terminals form a series of equilateral triangles. By brass or 
 copper strips placed across the terminals, either screwed down 
 by tightening the binding-screws or dipping in the mercury 
 
Chap, in.] Ohms Law. 249 
 
 cups, we can put the battery in simple circuit (a, Fig. 150), or 
 in compound circuit (b, Fig. 150), or in any mixed circuit. 
 Also, by a binding-screw which can be attached to any one 
 brass strip, we can include as many cells as we please. 
 
 A caution must be here given against the use of the ordi- 
 nary resistance coils with batteries of several cells, unless the 
 resistance introduced be great, since strong currents are apt 
 to heat and injure the resistance coils. 
 
 165. Measurement of E.M.F. by Galvanometer. 
 
 p 
 
 Ohm's law gives us /= ^ ~ > in which if r, the internal resist- 
 ance, be made small compared with R (which can be made a 
 large constant resistance), the current strength with different 
 cells is in each simply proportional to its E.M.F. By using 
 a sensitive mirror galvanometer and a very large external 
 resistance (5000 ohms suppose), we may treat the total resist- 
 ance as a constant with any battery we employ. The in- 
 dications given by different cells or batteries are therefore 
 proportional to their respective E.M.F. 
 
 Results obtained by this means may be compared with 
 those obtained (Art. 117) by the quadrant electrometer, and 
 will accord well for constant batteries, being smaller for all 
 one-fluid cells owing to polarisation. 
 
 Instruments depending on this principle are called Potentio- 
 meters. 
 
 166. Laws of Divided Currents. We may here in- 
 vestigate experimentally some of the laws of divided currents. 
 Suppose there are two conductors joining two points, the 
 conductors being of different resistance, we shall find that the 
 current in either branch is inversely as the resistance of that 
 branch. 
 
250 
 
 Electricity. 
 
 [Book III. 
 
 To show this we require two sets of resistance coils (A and 
 B in Fig. 151) put breast to breast, in connection with mercury 
 cups (C, D), into which the battery wires dip, and a galvano- 
 meter of small resistance compared to the resistances in A and 
 B. In this case there will be no sensible alteration of the cur- 
 rent in either branch by introducing the galvanometer. In- 
 troduce resistances in A 20 and in B 30 ohms, the galvano- 
 meter resistance being a fraction of an ohm. 
 
 FIG. 151. 
 
 First include the galvanometer in the branch SO, the de- 
 flection is seen to be 30. Next remove the galvanometer 
 from the branch JBC, and include it in AC; the reading then 
 becomes 41. 
 
 Eeferring to the table of tangents, we see that tan 30 
 = 577, and tan 41 = -865, 
 
 , 865 30 i 
 
 and ^~ = M as nearly as may be. 
 D7 7 <uO 
 
chap, in.] Ohm's Law. 251 
 
 Next, with the same arrangement, it is easy to prove 
 that the total resistance of two branches of the divided 
 
 circuit is given by the formula ~p = oQ"*~3o := T2> anc ^ ^ nere ~ 
 fore the resistance is 12 ohms. 
 
 The galvanometer must be placed in the battery branch, 
 and its deflection observed when the coils are abreast. Re- 
 move the branch CAD, and introduce in B 12 ohms' resistance, 
 and it will be found that the galvanometer is at its former 
 reading, showing that the 12 ohms' resistance just balances 
 the two resistances, 20 and 30 ohms, when placed abreast. 
 
 167. Galvanometer Shunts. For measuring strong 
 currents a delicate galvanometer can be used by means of a 
 shunt circuit. This generally consists of a short thick wire 
 joining the galvanometer terminals, and having a resistance 
 
 equal to -g > 99 > or 999 of the galvanometer. The current 
 
 is therefore divided between the galvanometer and the shunt 
 in the proportion of 1 to 9, 1 to 99, or 1 to 999. With the 
 
 respective shunts y^ > y^ > or TTTTTQ of the current passes 
 
 through the galvanometer. This method can only be applied 
 when the total resistance in the circuit is large compared with 
 the galvanometer resistance; otherwise, the introduction of 
 the shunt of small resistance, by diminishing the total resist- 
 ance, increases the total current in nearly the same proportion 
 that the shunt diminishes the galvanometer current. 
 
 i67a. Condensers. These are constructed of sheets of 
 tinfoil separated by sheets of thin paper dipped in melted 
 
252 
 
 Electricity. 
 
 [Book III. 
 
 paraffin, the successive tinfoil sheets having lugs at opposite 
 sides which project beyond the paper and form the terminals. 
 A pile of several hundred is placed while still hot in a press, 
 by which superfluous paraffin is rejected. The sheets of 
 paraffined paper between the conducting tinfoil sheets form the 
 
 dielectric, and a condenser 
 of high capacity is made, 
 suitable, of course, only for 
 electricity of low potential. 
 These are adjusted to any 
 required capacity (the one. 
 third Microfarad being 
 most common) and supplied 
 in boxes like resistance 
 coils. 
 
 The experiment shown 
 (Fig. 152) illustrates their 
 use. B is a cell or a battery, 
 C a condenser, and G- a 
 very sensitive mirror gal- 
 vanometer. The key K, 
 FIG. 152. when in its normal posi- 
 
 tion, presses up against a 
 
 bridge piece D, and makes contact in a circuit consisting of 
 the condenser and galvanometer, the terminal of the battery 
 being insulated, until the knob A is depressed. On pressing 
 down A a circuit is formed, including B, 0, and G. An 
 instantaneous deflection of the galvanometer is observed, due 
 to the displacement of electricity through the galvanometer 
 for charging the condenser. The needle will merely deflect, 
 showing a certain throw, and come to rest. On breaking 
 
chap, in.] O&m's Law. 253 
 
 contact, and making again contact in the C-G- circuit, there is 
 observed an equal throw in the opposite direction, due to the 
 discharge of the condenser. Under these conditions the 
 throw is simply proportional to the quantity of electricity 
 which passes, or to the charge in the condenser ; and this for 
 a given condenser is proportional to the potential difference 
 of its terminals. This affords one of the best practical 
 methods of comparing potential differences. 
 
 In these experiments galvanometer shunts (Art. 167) can 
 
 be most usefully employed, since on introducing the shunt 
 
 y y 
 
 J-QQ of the discharge passes through the galvanometer, and 
 
 the rest through the shunt the question of resistance (which 
 is practically infinite) not coming in. 
 
 168. Thermal Effects of a Current in the Con- 
 ductor. The heating effect of a current in the conductor can 
 be shown by connecting the terminals of a battery of five or 
 six Grove cells with platinum wires of various sections. The 
 thicker the wire the smaller will be the rise in temperature ; 
 but with a very thin wire, such as is used for blowpipe experi- 
 ments, 4 or 5 inches may be kept glowing at red heat. The 
 shorter the wire, the more intensely it will glow, owing to the 
 decrease in resistance, and therefore increase of current where 
 the wire is shortened. It has been shown by experiment that 
 the current which will keep an inch of wire at a given tempera- 
 ture would maintain a mile of the same wire at an equal 
 temperature, but practically increasing the length of a con- 
 ductor of considerable resistance diminishes the current, and 
 fresh battery power must be supplied to maintain the same 
 current. 
 
2 54 Electricity. [Book in. 
 
 The heating effect is closely analogous to the heating caused 
 by passing a current of liquid through narrow tubes. The 
 more rapidly the liquid flows, and the narrower the tube, 
 the greater will be the frictional resistance. 
 
 The heating effect also depends on the nature of the 
 material, being greater the greater its specific resistance. 
 This is shown by having a chain, whose alternate links are of 
 platinum and silver wires of about the same gauge. If the 
 chain be placed between the terminals of the battery, the 
 platinum will be found to glow with a red heat, while the 
 silver remains dark and cold, though of course the current is 
 the same in both. This is owing to the specific resistance of 
 the platinum being about six times that of the silver. 
 
 *i69. Measure of Heating Effect. If we have a con- 
 ductor whose extremities are at potential difference F, and a 
 current / passes through it, that current represents a loss of 
 energy represented by VI units of energy per second (Art. 143). 
 Unless work is being done externally, that energy must be 
 converted into heat in the conductor itself. Hence the heat 
 given out per second will be the thermal equivalent of VI 
 units of energy. If H be the number of thermal units given 
 out, and / be Joule's mechanical equivalent of heat, we have 
 
 JH= VI=PR, where R is the resistance, since V=IR 
 by Ohm's law. 
 
 Let now m be the mass, c the specific heat, and 6 the rise in 
 temperature, then H=mc6. Also let I be the length, a the 
 sectional area, p the specific resistance, and D the density ; 
 
 then m=laD and R=^. Substituting, we have 
 
 a 
 
chap, in.] Ohms Law. 255 
 
 JDc a 2 ' 
 
 This will represent the rise in temperature per second, sup- 
 posing no heat lost by radiation or otherwise. 
 
 This confirms our rule that the rise in temperature is 
 independent of the length when the current is constant, and 
 shows that the heating is inversely as the square of the 
 section, or as the fourth power of the diameter when the 
 section varies. This explains the enormous heat developed 
 in a thin wire forming part of a circuit, as in the incandescent 
 lamp or fuse in mining. 
 
 The same general laws apply to the heating of the liquid 
 parts of a circuit, the heat being simply proportional to the 
 resistance in each section of the circuit. Thus on short-cir- 
 cuiting a battery, the cells are rapidly heated, and the stout 
 wire remains cool. Here the energy of the current is wholly 
 converted into heat in the battery itself. When a large 
 resistance is interposed, the current is smaller, and only a 
 small fraction of that heats the battery, the greater part 
 heating the larger external resistance. 
 
 The formula JHPEi for the amount of heat given out 
 in t seconds gives the result in gram-degrees, if we give J 
 the value 4'2 x 10 7 ergs, and measure / and R in absolute 
 units of either the electrostatic or electromagnetic system. 
 It can be proved (Art. 184) that if /be measured in amperes 
 and R in ohms, the right-hand side must be multiplied by 
 10 7 , which reduces the formula for the number of gram- 
 degrees given off to 
 
 n=m 
 
 IT 
 
256 Electricity. [Bookm. 
 
 i6oa. The Watt and Joule. We noticed in the last 
 article that El was a measure of the energy per second due to 
 a current of strength /, passing through a conductor whose 
 terminals have a potential difference E. This will represent 
 the power transmitted per second by such a current. If / be 
 measured in amperes and E in volts, the power is measured 
 in Watts. Thus one Watt is the power transmitted per second 
 by a current of one ampere passing in a circuit whose poten- 
 tial difference is a volt, or, in other words, a current of one 
 ampere passing through a resistance of one ohm. 
 
 The total energy developed by a Watt in one second is 
 called a Joule (not of course the quantity denoted by J above) ; 
 
 and is equivalent to 10 7 ergs, which equals gm.-degrees, 
 or -238 gm.-degrees. 
 
 The Watt=10 7 ergs per second = of a horse-power 
 
 (Appendix L). 
 
 The Board of Trade have introduced as a commercial unit 
 in electric lighting the 1000 Watt-hour; that is to say, one 
 B.T. unit of power is the power transmitted by 10 amperes 
 
 at 100 volts in one hour. 
 
 ,s (T. y f .; " nr 
 
 \* *rJ*4 - /- * 
 
 
CHAPTER IV. 
 WHEATSTONE'S BRIDGE. 
 
 *I7O. Theory of the Bridge. The measurements de- 
 tailed in the last chapter depend on the use of a tangent 
 galvanometer, an instrument which gives a good rough 
 measure of a strong current, but is not very sensitive to small 
 changes in current, nor capable of being read to a very great 
 nicety. All the most accurate measurements are therefore 
 made by extremely sensitive galvanometers of the astatic or 
 mirror type, the adjustment of the apparatus requiring that 
 the current through the galvanometer shall vanish. 
 
 The chief instrument used for measuring all resistances 
 
 is Wheatstone's Bridge. The principle of this instrument 
 
 is a divided circuit whose terminals are by a battery kept 
 
 at a certain potential difference. Let the resistance be 
 
 G 
 
 represented by the lines AS, AC in one plane, and the 
 potential difference between A and B or C by a line AD 
 perpendicular to the plane. The lines DB and DC will 
 (Art. 147) give the potential-gradient. If two points E, .Fbe 
 taken in A B and AC respectively, so that AE : EB :: AF-.FC 
 
 R 257 
 
258 
 
 Electricity. 
 
 [Book III. 
 
 and EG, FH be drawn parallel to AD, then EG=FH for 
 OP 
 
 EG BE _ FH 
 :^and 
 
 which shows E and F to be at the 
 
 same potential. Hence a galvanometer placed in EF would be 
 unaffected. This was put in practice by Wheatstone, who 
 arranged a parallelogram into the sides of which resistances 
 could be introduced. Let AE BF be the parallelogram, the 
 
 " 
 
 Pro. 154 
 
 gaps in the sides being left for the resistances. In the diagonal 
 AB is placed a battery, and in the other diagonal EF the gal- 
 vanometer. Into one side he introduced the resistance to be 
 measured, and into the others he put known resistances, 
 which he varied till the galvanometer remained at zero. 
 The unknown resistance was then given by the formula 
 
 Resistance in AE _ Resistance in AF 
 Resistance in EB ~~ Resistance in FB 
 
 *i7i. Use of the Bridge to find the Resistance of a 
 Coil. In modern instruments the form is altered, the fixed 
 portions consisting of stout copper strips of no appreciable re- 
 sistance (Fig. 155), the gaps in AE and EB being for the in- 
 troduction of the unknown resistance, and a certain measured 
 resistance. The branches AF and BF are formed by a single 
 
chap, iv.] Wheatstones Bridge. 259 
 
 stout German silver wire, a metre in length, along which slides 
 a key (jP), by pressing down which contact can be made with 
 the wire at any point. The key runs along a raised wooden 
 
 FIG. 155. 
 
 rod, whose upper surface is graduated carefully in millimetres, 
 and read from both ends ; so that the length of the two parts 
 of the wire can be at once read off. This key is slid along the 
 wire till the galvanometer remains at rest, whether the key is 
 up or down, and in this position the reading is taken. If, 
 then, p be the unknown resistance in AE, and q the known 
 resistance in EB, and x, a the distances of F measured along the 
 
 wire from A and B respectively, we have = 5 or p=z 
 
 In performing experiments it is often convenient to have 
 two galvanometers one a rough one, for getting an approxi- 
 mate adjustment, and finally a very sensitive one for getting 
 an accurate adjustment. 
 
 Fig. 156 shows the arrangement actually made in finding 
 the resistance of a coil of wire. Its terminals are placed in 
 two mercury cups used for securing better contact, these 
 being connected with the binding-screws by wide copper 
 strips. The resistance-coils are connected with the other 
 corresponding terminals. The battery consisting of a single 
 
260 
 
 Electricity. 
 
 [Book III. 
 
 Daniell cell, and the galvanometer are in the two diagonal 
 branches. 
 
Chap. IV.] 
 
 Wheatstones Bridge. 
 
 261 
 
 1 71 a. A commercial form of Wheatstone's Bridge is now 
 used in the form of a box of resistance coils with four 
 
 CD 
 
 1000 100 10 
 
 + 
 
 1000 100 10^8 
 
 1 1 3. 
 
 $$\ ' 
 
 25 IO 10 
 
 1000 500-200 
 
 IOO lOD-,50 
 
 & 
 
 Fia 156A. 
 
 terminals. The arrangement of resistances is shown by the 
 diagram A BCD being binding-screws. 
 
 The unknown resistance x is inserted between C and D ; the 
 battery between A and C ; the galvanometer between B and D. 
 
 To bring the galvanometer to zero, we must arrange the 
 
 resistances so that 
 
 x Resistance in CB 
 
 Resistance in AD~ Resistance in BA' 
 Now, the resistance in CD can be adjusted to any number 
 of ohms from 1 to 2000. Hence, by making resistances in 
 AB, BC equal, any resistance within these limits can be 
 determined within 1 ohm. If CB to BA be made in ratio 
 10 : 100, -any resistance from 1 to 200 can be determined to 
 tenths of an ohm. Also if AB to BC be made in ratio 
 10 : 1000, any resistance from 1 to 20 ohms can be determined 
 to hundredths of an ohm. We can obviously approximately 
 determine still higher resistance by making CB to BA in 
 ratio 100 : 10 or 1000 : 10. 
 
 rv <: 
 
262 Electricity . [Book in . 
 
 *I72. Method of finding Galvanometer Resistance. 
 
 The bridge may be used for finding the resistance of the 
 galvanometer actually in use. The galvanometer is included 
 in the branch AE (Fig. 155). Now it is clear that if E and F 
 are at the same potential, the mere joining them by a wire will 
 not alter the current in any branch. Hence if we put a contact 
 breaker in the branch EF, and move the key till the galvano- 
 meter reading is not altered by depressing it, we may find the 
 galvanometer resistance exactly as in the preceding case. 
 
 With a very sensitive galvanometer the current is often so 
 strong as to deflect the needle through very nearly 90, in 
 which case the reading cannot be taken. To reduce the read- 
 ing we must either introduce a very large resistance into the 
 galvanometer branch EF, which can afterwards be subtracted 
 from the final result, or we can, better, introduce a large resist- 
 ance into the battery branch AB, so reducing the current in 
 all parts of the bridge. 
 
 This method is due to Sir W. Thomson, and was suggested 
 to him by Mance's method for finding internal resistance 
 which follows. 
 
 *I73- Method of finding Battery Resistance. To 
 
 understand Mance's method, we must notice a further exten- 
 sion of the principle of the bridge, which appears from theory, 
 
 T 1 W 
 
 namely, that so long as the relation =- holds between the 
 
 a Q 
 
 resistances, whatever electromotive forces be introduced in 
 the branches, the current in the branch circuit EF (Fig. 157) 
 is independent of any E.M.F. or resistance in the branch 
 circuit AB, while the current in AB is independent of E.M.F. 
 and resistance in EF Hence if we include the battery of 
 unknown resistance in the branch AE, a galvanometer in A /?, 
 
Cnap. IV.] 
 
 Wheats lone s Bridge. 
 
 263 
 
 and a contact breaker in EF, we must shift the key till rais- 
 ing or lowering its button makes no difference in the galvano- 
 meter reading. 
 
 FIG. 157 
 
 As in the last case if the current be too strong for the 
 galvanometer, we can increase the resistance in the galvano- 
 meter branch. 
 
 *174- Method of comparing the E.M.F. of Cells. 
 
 We conclude this chapter with a method of comparing the 
 E.M.F. of two constant cells by a method analogous to that 
 of the Wheatstone Bridge. 
 
 Place the cell, whose E.M.F. we will denote by E, and a set 
 of resistance-coils (A ) in an open circuit which terminates in 
 two mercury cups (CD). Also place the second cell, whose 
 E.M.F. is E\ with another set of resistance-coils (B) with its 
 terminals in the same mercury cups, so placing the cells that 
 they would send the current in opposite directions through 
 a branch joining CD (Fig. 158). The circuit of resistance 
 ACBDA is electrified from two independent sources E and E' t 
 
264 
 
 Electricity. 
 
 [Book III. 
 
 whose effects we may superimpose. First consider the 
 E M.F. : E. The circuit of resistances is made up of R the 
 
 FIG. 158. 
 
 resistance in A, r the internal resistance of E, r' the internal 
 resistance of E\ and R' the resistance of B. From the prin- 
 ciple of potential gradient, it appears that (7s potential will 
 
 be higher than Z>'s by 
 
 R+r' 
 
 E. (Art. 147.) 
 
 Similarly taking the cell E', it appears that D's potential is 
 higher than CM by 
 
 If these potential differences in opposite directions be equal, 
 (7, D will be at the same potential. The condition is that 
 
 (B'+r')E=(R+r)E' or * = T*-, . . . (I). 
 
 Under these conditions a galvanometer in CD shows no 
 deflection. 
 
 Let one of the coils AB contain resistances which can be 
 adjusted to small fractions (e.g. twentieths or hundreths of 
 an ohm) ; we can so arrange R, R' that the current in the 
 galvanometer vanishes. If r, / be known, this gives us the 
 ratio of E to E'. 
 
chap, iv.] Wheat stone's Bridge. 265 
 
 If r, r' be unknown, they may be eliminated by a second 
 adjustment, for if we alter the resistance in A, B till there is 
 again no current in the galvanometer, and if these resistances 
 be now X, X', we shall have 
 
 fe) \ 
 
 which combined with (1) gives 
 
 E E' 
 
 R-X~R'-X'' 
 in which the internal resistances do not appear. 
 
 As a particular example we give the numbers obtained on 
 comparing a Daniell and Leclanche" cell. On taking out 
 40 ohms resistance in the Leclanche" branch, and 31*5 in 
 the Daniell branch, the galvanometer was at zero. Secondly, 
 altering the resistance in the Leclanche branch to 70 ohms, 
 that in the Daniell had to be adjusted to 54. 
 This gives 
 
 Leclanch6 : Daniell : : 70-40 : 54-31-5 
 
 : : 30 : 22'5 
 Or Leclanche=l-3 Daniell in respect of E.M.F. 
 
CHAPTER V. 
 ELECTRO-MAGNETISM AND ELECTRO-DYNAMICS. 
 
 I75 Berlins' Commutator, In many of the experi- 
 ments which form the subject of this chapter we require a 
 convenient and rapid means of changing the direction of the 
 current. This is done by a commutator, of which there 
 
 FIG. 159. 
 
 are many forms. That known as Bertins' is perhaps the 
 simplest, as mere inspection of the instrument shows the 
 direction in which the current is passing. On a fixed ebonite 
 base (Fig. 159) are four binding-screws, two (AB) connected 
 
 266 
 
chap, v.] Electro- Magnetism and Dynamics. 267 
 
 with the battery terminals, and two (CD) with the apparatus in 
 use. On this base is a disc of ebonite carrying a brass horse- 
 shoe, and a brass tongue within the horse-shoe, but insulated 
 from it. These are separately connected with the battery 
 terminals by metal strips and sliding contacts underneath. 
 The other two binding-screws have metal springs attached to 
 them, so that either end of the horse-shoe and the tongue may 
 be simultaneously in contact with them. By turning the 
 ebonite through a small angle, the tongue and horse-shoe 
 come into contact with the springs in the reverse order, and 
 so reverse the direction of the current. The diagrams show 
 the commutator in the two positions, the direction of the 
 current being shown by arrows. 
 
 176. Magnetic Field of a Straight Current, 
 
 Oersted's experiment has taught us that a magnet pole 
 placed near a current experiences force. Since this is the 
 test of a magnetic field, it follows that a current of electricity 
 possesses the properties of a distribution of magnetism in that 
 it is surrounded by a magnetic field. To investigate this 
 magnetic field we will take a straight wire, and place it so 
 that it passes at right angles through a sheet of paper, on 
 which we can sprinkle iron filings. On passing the current 
 from five Grove cells in simple circuit, and tapping the paper, 
 it will be seen that the iron filings arrange themselves in con- 
 centric circles round the wire. These are therefore the lines 
 of force ; and from Oersted's experiment, or by the use of a 
 small magnet, we see that the direction of the lines of force is 
 related to the direction of the current in right-handed cyclical 
 order, as indicated by the arrows (Fig. 160). That is to say, if 
 the direction of the current be the direction in which a cork- 
 
268 
 
 Electricity. 
 
 [Book III. 
 
 screw, or other right-handed screw, is propelled through the 
 cork, the direction of the line of force is represented by the 
 twist in the muscles of the wrist, by which it is driven in. 
 
 
 FIG. 160. 
 
 177, Rotation of a Magnet Pole round a Current. 
 
 We infer from the last experiment that a magnet pole free 
 to move will rotate round a current. The experiment was 
 originally performed by Faraday by bringing the current 
 to bear only on one half of the magnet, carrying it away again 
 as soon as it reaches the centre. It is convenient to bend the 
 magnet, so that it may be pivoted on its middle point, the 
 current being brought to a mercury cup supported upon the 
 revolving magnet, and carried away by a bent wire which dips 
 into an annular cup of mercury, with which the battery wire 
 is connected. On passing a strong current, the magnet pole 
 rotates steadily, and on reversing the direction of the current, 
 the direction of rotation is reversed (Fig. 161). 
 
chap, v.] Electro- Magnetism and Dynamics. 269 
 
 178. Rotation of a Current round a Magnet Pole. 
 
 The third law of motion shows that whatever force a 
 
 Fid 161. 
 
 current exerts on a pole, the pole must exert an exactly 
 equal and opposite force on the current. Thus the system of 
 forces between a magnet pole and a current consists of a couple, 
 and the current, if free to move, will spin round the pole, 
 having the same direction of rotation relatively to the pole 
 that the pole has relatively to the current. These directions 
 of rotation are shown by the dotted lines in Fig. 162. 
 
 The rotation of a current round a pole can be shown 
 experimentally by pivoting a wire bent in the form of 
 an inverted letter U on the top of a vertical magnet, the 
 
270 
 
 Electricity. 
 
 [Book ill, 
 
 current being passed in through a mercury cup on the top 
 of the wire, and leaving it again by an annular cup which 
 surrounds the magnet lower down. If the magnet be of 
 
 N 'POLE 
 
 CURRENT 
 
 Fia. 162. 
 
 horse-shoe form, we may have two similar wires rotating in 
 opposite directions round its two poles (Fig. 163). Instead of 
 
 FIG. 163. 
 
 only one wire, we may have two or more soldered above, 
 forming a cage round the pole, or we may have a single 
 wire coiled in a spiral form, giving a pretty optical effect of 
 
chap, v.] Electro-Magnetism and Dynamics. 271 
 
 continually screwing up or down ; or we may vary the 
 experiment by passing the current into one annular cup and 
 out by the other, causing the wires to rotate in the same 
 direction round the opposite poles. 
 
 179. Movement of Current in a Magnetic Field. 
 
 A little reflection will show that the motion of the current can- 
 not depend on the mere magnet pole, but does depend on the 
 field of force immediately around the current. The observed 
 motion must, in fact, be the expression of a tendency on the 
 part of any moveable current to cut lines of magnetic force at 
 right angles, the direction of motion being reversed when either 
 the direction of the lines of force or of the current is reversed. 
 
 FIG. 164. 
 
 This is easily shown if we pass a current through a wire 
 freely suspended above and dipping in a cup of mercury. If 
 the poles of a strong horse-shoe magnet be brought near the 
 wire, so that the wire lies between them, or in any way cuts 
 the lines of force, the wire moves through the mercury until 
 contact is broken, falls back again, and so keeps up a vibrating 
 movement (Fig. 164). The direction of motion can be altered 
 
272 
 
 Electricity. 
 
 [Book in. 
 
 by reversing the poles or the direction of the current. If the 
 two poles be placed parallel to the wire no effect is produced. 
 This principle is further illustrated by Barlow's wheel. The 
 wheel consists of a brass wheel cut into a star with eight or 
 ten points. The points, when they come in succession to their 
 lowest position, dip into a mercury cup, and a current is sent 
 from the axis down the vertical radius to the mercury, whence 
 it returns to the battery. If now the poles of a magnet be 
 placed on opposite sides of the wheel, the wheel begins to 
 rotate, and by bringing the points successively into the mer- 
 cury cup, keeps up a continuous rotation as long as the 
 battery current continues. On reversing either the poles or 
 the current, the direction of rotation is reversed (Fig. 165). 
 
 FIG. 165 
 
 By means of this apparatus it is easy to study the direction 
 of motion of a conductor in a magnetic field. The movement 
 of the conductor is affected only by the lines of force which 
 cut through it, and the direction in which it tends to move is 
 at right angles to the plane containing the current and the 
 lines of magnetic force which cut it, The effect is greatest 
 when the current is placed so as to cut the lines of force at 
 right angles. The following is a convenient memoria 
 
chap, v.] Electro- Magnetism and Dynamics. 273 
 
 for remembering the relations of the three directions current, 
 lines of force, and movement of conductor : A figure swim- 
 ming in the current, and looking along the lines of force, is carried 
 to his left. For example, a person standing erect carrying a 
 current which flows from his heels to his head, and looking 
 magnetic northwards, i.e. along the lines of the earth's hori- 
 zontal force, is carried towards the west by the earth's 
 horizontal magnetic field. 
 
 Another illustration of these principles is afforded by the 
 D'Arvonsal Galvanometer, in which the coil carrying the 
 
 current to be measured is the 
 ' needle,' which moves in a 
 magnetic field made by two or 
 more fixed permanent magnets. 
 The coil is rectangular in 
 shape, and is held between two 
 wires, one from above and the 
 other from below, through 
 which the current is trans- 
 mitted. The vertical sides of 
 the rectangle are thus free to 
 move in a direction across the 
 lines of force, and the current 
 causes this motion, which is 
 checked by the torsion of the suspending wires. The move- 
 ment is read by means of a mirror attached to the moving 
 coil just as in the mirror galvanometer. Fig. 165A gives a 
 sketch of one form of the instrument. 
 
 FIG. 165A. 
 
 180. Methods of Suspending Currents. To con- 
 struct a circuit which shall be perfectly free to move, and yet 
 be in connection with the terminals of a battery, presents a 
 
 8 
 
274 
 
 Electricity. 
 
 [Book III. 
 
 mechanical problem of some difficulty. Ampere overcame it 
 by the invention of a stand which goes by his name, and 
 some modification of which is still used. After many trials, 
 the present writer has adopted the following method, which 
 will give satisfactory results in all the experiments described 
 with five Grove cells arranged for simple circuit, as in Art. 164. 
 The axis of the central stem consists of a wire C9nnected with 
 one binding-screw, and terminating in a mercury cup. It is 
 insulated by an ebonite cylinder from the outside, which con- 
 sists of a brass tube, connected with the second binding- screw. 
 On the brass tube slides an annular cup of mercury (Fig. 166). 
 The wire frames of various forms are pivoted in the central 
 mercury cup, and the other terminal dips slightly into the 
 
 FIG. 166. 
 
 mercury in the annular cup. The wires are so bent that the 
 centre of gravity is brought below the cup. To diminish 
 friction on the cup, the wire frame is also suspended by a few 
 fibres of unspun silk, by which nearly its whole weight is 
 borne (see Fig. 173), and the wire framework is left with 
 remarkable freedom of motion [The central stem is usually 
 
chap. v. Electro- Magnetism and Dynamics. 275 
 
 S 
 
 sold with a rather cumbrous arrangement for supporting the 
 wire frames, whose movements are then very sluggish.] 
 
 181. Effects of Terrestrial Magnetism on Move- 
 able Currents. By means of the double rectangle of Fig. 
 166, if the rectangle be made large enough (each not less than 
 10 in. by 8 in.), it will be found, on passing a current, that the 
 framework sets as a magnet would, but with its plane at right 
 angles to the magnetic meridian, the current ascending on the 
 west and descending on the east side in each rectangle. 
 
 The same effect may be shown rather more simply by a 
 coil of insulated wire (Fig. 167) wound ten or twelve times 
 round, with its terminals dipping, 
 one into a central mercury cup, and 
 the other into an annulus surrounding 
 it, from which cups wires go to the 
 battery. The coil measures about 4 
 in. by 3 in., and is supported by a 
 silk or cotton thread. On passing 
 the current the setting is quite unmis- 
 takeable, overcoming the torsion in 
 the suspending thread. 
 
 In this case a little consideration 
 shows that the figure swimming in 
 the current and looking along the 
 horizontal lines of magnetic force 
 (which alone affect this experiment) 
 is in all positions carried to its left 
 as far as the mechanical arrangements permit, in accordance 
 with Ampere's rule. If, however, we imagine, with Faraday, 
 the lines of magnetic force as having a real physical existence, 
 and distributed through the field of force in exceeding large 
 
 FIG. 167. 
 
276 
 
 Electricity. 
 
 [Book III. 
 
 but perfectly definite numbers, and in such a manner that 
 the number of lines of force which cut unit area round 
 any point in the field measures the strength of the field 
 perpendicular to that area, we can then represent the be- 
 haviour of this circuit rather more simply. The current 
 places itself at right angles to the lines of force (therefore 
 including as many lines of force as possible), and its direction 
 is related to that of the lines of force which it intercepts in 
 right-handed cyclical order. 
 
 By supporting a wire framework, free to rotate about a 
 horizontal axis at right angles to the magnetic meridian, and 
 passing a strong current, it has been shown that it sets at 
 right angles to the dipping needle. 
 
 By supporting a horizontal wire pivoted at one end, and 
 with its other end just dipping into a mercury basin, on which 
 it is supported by a cork float, it has been shown that on 
 passing a current through the wire it rotates under the 
 action of the vertical component of the earth's magnetism in 
 accordance with Ampere's rule. 
 
 182. Magnetic Properties of a Closed Current. If 
 
 we take a wire bent in the form of Fig. 168, in which the 
 
 
 
 PIG. 168. 
 
 current passes round the two equal rectangles (AB) in opposite 
 directions round A in a direction with the hands of a watch, 
 and round B in the contrary direction the whole system will 
 be astatic with reference to the earth. 
 
chap. v. ] Electro - Magnetism and Dynamics. 277 
 
 If we now take a magnet, and present its north pole to A, 
 it will be found that A is attracted by it, and if we present 
 the same pole to B it will be repelled. If we next present 
 the north pole to the back of A it will be repelled, and the 
 back of B will be attracted. If the south pole of the magnet 
 be used, these attractions and repulsions will again be reversed. 
 
 This experiment teaches us that the action of A and B in 
 the magnetic field are the same as if we were to substitute for 
 A a thin sheet of steel magnetised normally to its surface, 
 and having south polar magnetism on the side facing us, and 
 north polar magnetism on the opposite side, and for B a 
 similar sheet, only with magnetisms reversed. 
 
 If we have a series of such circuits closely following each 
 other, and parallel to each other as we may have by bending 
 a wire into circles separated by very short pieces of straight 
 wire, or into a close helix, with the wires brought back inside 
 
 Fia. 169. 
 
 (Fig. 169) we shall have a series of magnetic shells^magnetised 
 normally, all in the same direction, which will therefore be 
 equivalent to a series of slices cut from a bar magnet, and 
 should behave collectively, just as a bar magnet. Such an 
 arrangement is called a solenoid. 
 
 Place on the stand of Art. 180 a wire shaped as Fig. 170; 
 
278 
 
 Electricity. 
 
 [Book III. 
 
 then on presenting the north pole of a bar magnet we shall 
 find that it attracts one end and repels the other. 
 
 The current will not be strong enough to show the direc- 
 tive action of the earth's magnetism or the repulsion and 
 attraction between two similar solenoids, but if a coil of wire 
 be formed by closely coiling stout insulated wire from end 
 to end of a cylinder 6 inches long, and bringing the wire 
 through the cylinder, and again repeating the close coiling 
 till four or five layers have been obtained, this will be found 
 to act precisely as a weak magnet when presented to the ends 
 of the solenoid, the pairs of poles attracting and repelling just 
 as they would for two bar magnets. 
 
 FIG. 170. 
 
 The rules for the north and south poles of the solenoid will 
 be in accordance with what we said before ; that will be the 
 south pole in which the current, to an observer looking down 
 upon it, goes with the hands of a watch, and a north pole 
 in which the current goes against the hands of a watch (see 
 Fig. 171). 
 
 
 FIG. 171. 
 
 The behaviour of currents under magnetic force is some- 
 times illustrated by the floating battery of De La Rive. 
 This is a simple zinc-copper couple, connected by several turns 
 
chap, v.] Electro- Magnetism and Dynamics. 279 
 
 of insulated copper wire. The plates are mounted on the 
 under-side of a cork float, and put on a vessel of acidulated 
 water, which acts as the liquid of the cell (Fig. 172). By this 
 means the behaviour of a closed circuit under a magnet can 
 easily be exhibited. 
 
 FIG. 172. 
 
 By experiments, of which the above may be taken as types, 
 and others depending on quantitative measures, Ampere was 
 able to lay down as an experimental law that every closed 
 voltaic circuit carrying a current is identical in its behaviour 
 with a magnetic shell, magnetised normally, the current fol- 
 lowing the direction of the hands of a watch to an observer 
 looking down on the south polar face. The strength of the 
 equivalent current is directly proportional to the strength of 
 the magnetic shell, or to its magnetic moment per unit area. 
 
 *i83. Distinction between a Voltaic Circuit and a 
 Magnetic Shell. There is a very important difference 
 between the shell and the circuit. For if P, Q be two points 
 on the north and south side of a magnetised shell, a north 
 pole placed at P will be repelled by the action of the shell, 
 and carried round the edge to Q } where it will stop by impact 
 against the shell. If a small aperture were made in the shell, 
 
280 Electricity. [Bookm. 
 
 though too small to affect the force on a pole at any external 
 point, still in passing through this aperture the magnet pole 
 would experience a retarding force, against which the work 
 done by the pole between Q and P would just balance the 
 work done on it by the accelerating force it had experienced 
 up to Q, and it would reach P again with neither gain nor loss 
 of energy. This is no more than the assumption that mag- 
 netic forces among fixed magnets obey the law of conserva- 
 tion of energy. If, on the other hand, we have a voltaic 
 circuit, and P, Q be the corresponding points on opposite 
 sides of its plane, the pole passes freely from Q to P without 
 experiencing any retarding force, and reaches P again with 
 an increase of energy. This energy is of course derived, as 
 we shall see presently, from the current energy which has 
 its source in the chemical energy of the battery. 
 
 *i84. Absolute Electro-magnetic Units. This ex- 
 periment of Ampere is the key to the absolute electro- 
 magnetic system of measurement alluded to in Art. 154. 
 
 We define in this system the unit current of electricity, as 
 that current which, traversing any closed circuit, gives rise 
 to an electro-magnetic field identical in all respects with the 
 magnetic field due to a magnetic shell of unit strength, whose 
 edge coincides with the circuit. This is called the absolute 
 unit of current strength. 
 
 The absolute unit of quantity is the quantity of electricity 
 which passes per second in a current of unit strength. 
 
 The absolute unit of E.M.F. or potential difference is the 
 potential difference between two points such that unit work 
 is done in carrying the absolute unit of quantity from one 
 point to the other. 
 
cuap.v.] Electro- Magnetism and Dynamics. 281 
 
 The absolute unit of capacity is the capacity of a conductor 
 which, when charged with unit quantity of electricity, is at 
 unit potential. 
 
 The absolute unit of resistance is the resistance in a 1 circuit 
 in which the E.M.F. is the absolute unit of potential and the 
 current is the absolute unit of current. 
 
 These are not the units referred to above in Art. 154, 
 as some would be inconveniently large, and others incon- 
 veniently small. 
 
 The Coulomb, or practical unit of quantity, is y 1 ^- of the 
 absolute unit. 
 
 The Volt, or unit of potential, is equal to 10 8 , or one 
 hundred million absolute units of potential. 
 
 The Ampkre, or practical unit of current, is ^ of the abso- 
 lute unit. 
 
 The Ohm, or unit of resistance, is 10 9 , or one thousand 
 million absolute units. 
 
 The Farad, or unit of capacity, is 10~ 9 , or one thousand- 
 millionth of the absolute unit. The micro-farad, more com- 
 monly employed, is the millionth part of the farad, and there- 
 fore 10~ 15 , or one thousand-billionth of the absolute unit. 
 
 185. Attractions and Repulsions of Parallel and 
 Inclined Currents (Electro- Dynamics). To investi- 
 gate the action of one current upon another, the best form 
 of apparatus is that of Fig. 173, in which the current in 
 the two rectangles is astatic under the earth's magnetism. 
 If the battery wires be parallel and very near to the ex- 
 treme vertical currents, it will be found that the moveable 
 wire shows attraction where the currents run in the same 
 direction, bnt repulsion when in opposite directions. These 
 
282 
 
 Electricity. 
 
 [Book III. 
 
 actions will be made more visible if, instead of a single wire, 
 we use a current multiplier, or a coil of several circuits, each 
 rectangular in form, shown in Fig. 167. On presenting the 
 opposite sides of the multiplier, in which the currents are in 
 opposite directions, to one of the vertical wires on the stand, 
 the attraction and repulsion are more strongly marked. 
 
 FIG. 173. 
 
 By the same arrangement it can be shown that when 
 two finite currents are inclined to each other without cross- 
 ing, they attract when both run towards or both run away 
 
chap, v.] Electro- Magnetism and Dynamics. 283 
 
 from the common apex, but repel when one runs towards 
 and the other away from the apex. 
 
 The attraction and repulsion of parallel currents are 
 admirably shown by the arrangement of Fig. 174, which 
 consists of two flat spirals, each suspended by two wires, 
 through which the current is carried. On the base is a 
 
 Fio. 174. 
 
 simple form of contact breaker and commutator. On causing 
 the spirals to hang in parallel planes a short distance apart, 
 and passing the current so that it shall run in parallel direc- 
 tions round both spirals, they are attracted towards each 
 other. On hanging the spirals initially in contact, or nearly 
 
284 Electricity. [Book ILL 
 
 so, and passing the current so as to traverse them in opposite 
 directions, there will be a very marked repulsion. 
 
 The attraction of parallel currents is well illustrated by the 
 vibrating spiral. This consists of a spiral of moderately thin 
 copper wire suspended at its upper end and dipping at its lower 
 end into a basin of mercury (Fig. 175). On passing a current, 
 the successive turns of the spiral attract each other, draw the 
 point out of the mercury, and break the contact ; when the 
 lower end of the spiral falls back again into the mercury cup. 
 A vibratory motion is thus kept up as long as the battery 
 connection lasts. 
 
 These actions are easily explained in accordance with the 
 principles we have laid down, by regarding the parallel 
 
 FIG. 175. 
 
 currents as edges of two magnetic shells which face each other. 
 When the currents are in the same direction, the surfaces 
 oppositely magnetized will be directly opposed, and therefore 
 attraction ensues. If the currents are in opposite directions, 
 
chap, v.] Electro- Magnetism and Dynamics. 285 
 
 the surfaces similarly magnetized will oppose, and therefore 
 repel each other. 
 
 The same result will be arrived at also by considering 
 either current in the field of force due to the other. For 
 if A be a current, its lines of force will be more or less nearly 
 circles round it, and those circles will rise out of the paper 
 on one side and sink into it on the opposite (Fig. 176). If 
 another wire carrying a current be placed on the paper below 
 A, the figure swimming in the current and looking downwards 
 will be carried to his left, i.e. towards A ; and if the other 
 current be above A, the figure swimming in the current and 
 looking upwards will be carried to his left, that is, towards A 
 also. Thus on both sides, A will attract a current running 
 parallel to itself and in the same direction. 
 
 Lines of Force upwards. 
 A v 
 
 Lines of Force downwards. 
 FIG. 176. 
 
 The laws of inclined currents can be explained by taking 
 the equivalent magnetic shells, or by considering the resolved 
 part of the field of force of one current perpendicular to the 
 other. 
 
 186. Action of an Infinite Current on another 
 wholly on one side. If ABC represent a current, and 
 DE another at right angles to it (Fig. 177), then, apply- 
 ing the principle of inclined currents, we see that the current 
 in AB runs towards the apex, and that in DE runs away 
 from it, and therefore AB and DE repel each other ; while 
 those in BO and DE both run away from the apex, and 
 therefore attract each other. Hence, on the whole, DE, if 
 
286 
 
 Electricity. 
 
 [Book III. 
 
 free to move, will move parallel to ABC, and with the current 
 in ABC. 
 
 The same result is obtained if we consider DE as a current 
 in the field of magnetic force due to ABC. 
 
 B 
 
 FIG. 177. 
 
 This can be illustrated by a copper vessel (A), containing 
 copper sulphate, round which are coiled several strands of wire 
 (not shown in the figure), which constitute the continuous 
 current (Fig. 178). In the centre is an insulating stem which 
 
 Fio. 178. 
 
 bears a mercury cup on its top. On this is pivoted a wire, 
 which, extending horizontally both ways, is bent down at 
 right angles and reaches the copper sulphate near the cir- 
 cumference of the vessel. Suspended by these two wires is a 
 light copper ring, which dips into the copper sulphate. The 
 
chap, v.] Electro- Magnetism and Dynamics. 287 
 
 current, after traversing the coil round the copper vessel, 
 passes up the centre to the mercury cup, divides and descends 
 by the two wires to the copper sulphate, whence it returns 
 to the battery. The action of the continuous current on 
 both the horizontal and vertical parts of the current in the 
 poised wire causes it to rotate steadily, carrying with it the 
 copper ring which steadies the motion. 
 
 187. Equivalence of a Sinuous and Straight 
 Current. Ampere laid down the rule that a sinuous cur- 
 rent is equivalent to a straight current passing through it. 
 This can be shown by making a compound solenoid in which 
 the wire, coiled outside a tube in a helix, is carried through 
 the tube in a straight line, and this is done four or five 
 times, as described in Art. 182. We thus have an exterior 
 sinuous current of about 24 yards, and an internal straight 
 current in the opposite direction, whose length is about half a 
 yard. On placing this arrangement parallel to one of the 
 vertical wires in the suspended rectangle of Art. 185, and 
 passing the current through them both, we shall find they 
 are quite neutral to each other, the straight part just balanc- 
 ing the effect of the sinuous part. 
 
 If, on the other hand, the compound coil be approached 
 endwise to the current, its action is seen to be similar to 
 that of a bar magnet. 
 
 *i88. The Magnetic Field inside a Solenoid. One 
 
 of the most remarkable things about a solenoid carrying a 
 current is the great strength of the magnetic field inside it. 
 To explain this, we may notice that the lines of force due to a 
 straight current are circles, having their centre in the axis of 
 the current. If we have a large number of straight currents 
 
288 Electricity. [Bookm. 
 
 parallel to each other in a plane, to find the strength of field 
 at any given point, we must compound, according to the 
 parallelogram law, the strength of field due to each current 
 separately. This requires a mathematical investigation, but 
 we can easily see the general effect. Let the line of dots AB 
 (Fig. 179) denote the section of the paper by the currents 
 which pass down perpendicularly through the paper, and 
 extend indefinitely right and left. Let P be a point at 
 which we want to construct the line of force. The force 
 due to the current at A will be at right angles to AP, 
 and right-handed to the current; we denote it by F. We 
 can generally choose a current (B) such that PA = PB, and B 
 
 FIG. 179. 
 
 will give at P a force at right angles to BP equal to the force 
 due to A ', we denote it by F 1 . Now F, F 1 are equal, and 
 equally inclined to AB, and will therefore have a resultant 
 parallel to AB. The same will be true of each pair of currents 
 equally distant from P. The line of force at P will therefore be 
 parallel to AB, and the strength of field will be somewhat in- 
 creased by each single current. Of course, practically, the re- 
 mote currents will produce little effect, and if the currents be 
 finite with P near the middle, we may assume that the lines of 
 force are parallel to AB, that is to say, in the system we have 
 assumed the lines of force will cross the currents at right angles. 
 Suppose, now, one of the wires bent into a circle or closed figure. 
 
chap, v.] Electro- Magnetism and Dynamics. 289 
 
 The lines of force will no longer be circles, but will be closed 
 curves, being crowded together in the closed curve, and spread 
 out outside it, somewhat as in the drawing (Fig. 180)., in which 
 we represent the curves obtained when we pass a current down 
 one and up the other of two parallel wires near together. 
 
 
 FIG. 180. 
 
 Now, suppose each of the circles forming the band of cur- 
 rents we considered just now to be bent into a circle, and we 
 have the solenoidal arrangement. The lines of force must 
 now be a series of closed curves linked with the cylinder, 
 formed of the solenoid, entering by its south and leaving by 
 its north polar end. Externally the lines will be the same as 
 for a bar magnet (Art. 12), and the reasoning we used above 
 shows that all the circles conspire to give at all internal points, 
 except near the ends, a field whose lines of force are parallel 
 to the axis of the cylinder. These lines, moreover, are very 
 crowded, since all the lines pass through the cylinder, but 
 
 T 
 
290 
 
 Electricity. 
 
 [Book in. 
 
 are spread through the whole field outside it. The crowding 
 together of the lines explains on Faraday's hypothesis (Art. 
 181) the great relative strength of the field within the sole- 
 noid. In Fig. 181 a diagram of the lines of force is shown, 
 the two rows of circles being the section by the paper of the 
 solenoid wire. 
 
 oooooooooooooooooooooooooooo 
 
 FIG. 18L 
 
 This explains why a soft iron wire placed outside will be 
 magnetized very feebly and in the opposite direction to the 
 magnetization of the solenoid, while a wire inside will be very 
 strongly magnetized in the same direction. 
 
 189. Electro- Magnets. Temporary magnets of great 
 power are made by placing soft iron bars within helices 
 of wire, through which a current is transmitted. The soft 
 iron, while the current is passing, becomes a very strong 
 magnet, but instantly loses its magnetism when the circuit is 
 broken. This is easily seen by putting a stout soft iron wire 
 
chap.v.] Electro- Magnetism and Dynamics. 291 
 
 through a helix of insulated copper wire, when, on passing 
 the current through the helix, the iron wire will acquire the 
 power of picking up large quantities of brads or iron frag- 
 ments, dropping them again the moment that contact with 
 the battery is broken. 
 
 FIG. 182. 
 
 If a horse-shoe is made in soft iron, and a few dozen 
 strands of wire are coiled in opposite directions round the 
 two ends, on passing a current through the wire, a very 
 powerful electro-magnet is made, capable of supporting very 
 heavy weights when suspended from a soft iron armature 
 joining its poles (Fig. 182). 
 
292 Electricity. [Bookiii. 
 
 1 
 
 If a bar of steel be placed within the helix, the magnetism 
 induced is less strong than for an iron bar of the same size, 
 but is largely retained after the current is broken. Small bars 
 can be easily magnetized to saturation by placing them in a 
 helix and giving smart blows with a hammer while the cur- 
 rent is passing. 
 
 By the method just indicated temporary magnets can be 
 made of vast power compared even with the strongest per- 
 manent magnets. To obtain the best effects very nice adjusts 
 ments have to be made between the dimensions of the soft 
 iron core and the coils of wire which surround it. If the core 
 be too thick, only the outer parts are magnetized, while the 
 inner part contributes nothing to the strength of the pole. 
 There is again great difficulty in obtaining thick iron rods 
 which are well annealed throughout, without which the iron 
 is not soft. The core is therefore often made of a number of 
 thin rods of soft iron. By these means, with proper pre- 
 cautions, magnets of vast power have been made. 
 
 190. Paramagnetic and Diamagnetic Substances. 
 
 By means of the powerful electro-magnet possessed by the 
 Royal Institution, Faraday showed that almost all substances 
 were more or less susceptible to magnetic influence. He also 
 discovered two classes of substances very different in their 
 behaviour when under magnetic influence. The first class he 
 called paramagnetics, which in their properties are similar to 
 iron, nickel, and cobalt, so that when a bar of one of these 
 substances is suspended in the strong magnetic field between 
 the poles of the magnet, the bar sets with its length along the 
 lines of force, or, as he termed it, axially. The other class 
 he called diamagnetics, of which bismuth is a type. When a 
 
chap, v.] Electro- Magnetism and Dynamics. 293 
 
 bar of such a substance is suspended between the poles of the 
 magnet, it sets at right angles to the lines of force, or equa- 
 torially. This is illustrated in Fig. 183. He also discovered 
 that, while a small particle of a paramagnetic substance is 
 attracted by a magnetic pole, a small fragment of a diamag- 
 netic substance is repelled. On testing the polarity of a 
 
 FIG. 183. 
 
 diamagnetic substance placed in the magnetic field, he found 
 that the induced poles showed opposite polarity to those of a 
 paramagnetic, a pole of like name being next to either induc- 
 ing pole. 
 
 Faraday discovered that liquids and gases are, some para- 
 and others dia-magnetic. To show the action of magnetism 
 on liquids, he placed a drop of the liquid in a very thin 
 
294 Electricity. [Book in. 
 
 watch-glass supported between the poles of the electro- 
 magnet. On making contact with the battery, the shape of 
 the drop was altered. If a paramagnetic, the drop was 
 flattened, being drawn along the lines of force ; if a diamag- 
 netic, the drop was heaped up by the repulsion of the poles 
 and made more convex (see Fig. 184). 
 
 PARAMAGNETIC LIQUID. 
 
 DIAMACNETIC LIQUID. 
 FlO. 184. 
 
 To test the magnetism of a gas, he allowed it to escape 
 from a fine circular orifice between the magnetic poles, and 
 found that if paramagnetic it spread out like a fish-tail burner 
 along the lines of force, and if diamagnetic it spread out 
 across them. 
 
 A simple way of explaining the behaviour of diamagnetic 
 bodies depends on the magnetism of the air surrounding them. 
 Oxygen, at any rate, is a moderately strong paramagnetic, and 
 any substance less strongly paramagnetic than oxygen, when 
 immersed in it, would behave as a diamagnetic. For under 
 the induction of the magnetic field we should have, at say the 
 nominally north pole, a separation of north-polar magnetism 
 on the solid, and at the same time a separation of south-polar 
 magnetism in the oxygen in contact with it. If, then, the 
 paramagnetism of the oxygen be the stronger, the south pole 
 induced in the oxygen would overpower the north pole in- 
 
chap, v.] Electro- Magnetism and Dynamics. 295 
 
 duced in the solid, and we should have effectively a south 
 pole. In this way the general behaviour of diamagnetics can 
 be explained. 
 
 All diamagnetics have only very feeble magnetic properties, 
 and their demonstration requires a very strong electro-magnet. 
 With a moderate magnet, it is possible to show that a bar of 
 bismuth, carefully prepared without contact with iron tools, 
 sets equatorially when freely suspended by a silk fibre between 
 the poles of the electro-magnet, as in Fig. 183. A drop of 
 chloride of iron, or any iron salt (all of which are for liquids 
 powerfully paramagnetic), when placed in a watch-glass, and 
 laid between the poles, can be seen slightly to alter its con- 
 vexity when the current is passed. This is most easily 
 observed by watching the reflection in the drop of a window 
 bar or gas flame. 
 
 191. Electro-magnetic Toys. On the property of 
 electro-magnets suddenly acquiring, losing, or reversing their 
 magnetic properties with changes of the current, many con- 
 trivances are made, some mere toys, and others very useful 
 practical applications. One of the simplest depends on the 
 earth's directive effect on a magnet. If an electro-magnet be 
 pivoted on its centre, and a current transmitted, it will try 
 to set north and south. If, immediately on passing the 
 meridian, the current in the wire is reversed, the magnet will 
 move onward, and try to set itself in the opposite direction ; 
 and if a similar reversal of current be made each half revolu- 
 tion, the rotation will be continuous. This is carried into 
 practice by winding wire round a long thin iron rod, which 
 is pivoted in the centre of a wooden cup, the terminals of the 
 wire projecting downwards into the cup. The cup is divided 
 
296 
 
 Electricity. 
 
 [Book in. 
 
 into two halves by a wooden partition, shown in plan in 
 Fig. 186, of which each half is filled with mercury, the 
 convexity of the surface causing it to stand at a higher 
 level than the wooden partition. These two halves are 
 connected with the poles of a battery of one or two cells. 
 When the partition is in the magnetic meridian, and 
 the wires terminating the electro-magnetic coil, just dip 
 into the mercury but pass over the partition, its change of 
 polarity at each half rotation keeps up a constant rotation. 
 
 FIG. 186. 
 
 This commutator is used in a great number of electro-magnetic 
 toys. On placing it axially between the poles of a permanent 
 magnet, a short electro-magnet (Fig. 187, a\ whose terminals 
 dip into the commutator cup, can be made to rotate with 
 great rapidity. If the partition be placed in the equator of 
 the permanent magnet, a cage (Fig. 187, b) consisting of vertical 
 wires pivoted on its middle, one half dipping into each half 
 of the mercury cup, will keep up a constant rotation, as is 
 easily seen by considering the motion of the conductor in the 
 field of magnetic force, traversed by a current in one half 
 
chap.v.] Electro- Magnetism and Dynamics. 297 
 
 upwards, in the other downwards. Similarly a continuous 
 coil of wire (Fig. 187, c) pivoted between the poles will rotate 
 when the current is passed, this being an electro-magnet 
 without a core. 
 
 FIG. 187. 
 
 Sometimes the permanent magnet is replaced by an ex- 
 ternal coil of wire to carry the current, and we have the inner 
 coil rotating continuously. This we may explain either by 
 the electro-magnetic action of the two coils on each other, or 
 by the attractions and repulsions of parallel and inclined 
 currents on Ampere's principle. If the outer coil be free to 
 move, but its terminals dip into a fixed central cup and annulus 
 of mercury, in connection with the battery, while a commutat- 
 ing cup rotates with it, into which the terminals of the inner 
 coil dip, the two coils will continue rotating rapidly in opposite 
 directions. This arrangement is shown in Fig. 188. 
 
298 
 
 Electricity. 
 
 [Book III. 
 
 192. Electromotors. On similar principles have been 
 constructed a great number of electromotors, intended by their 
 
 Fio. 188. 
 
 inventors to replace steam by electricity as prime motive 
 power. None of them have as yet come into more than 
 limited use, owing chiefly to their great expensiveness com- 
 pared with steam-engines. Thus, weight for weight, zinc is 
 fifty times as expensive as coal, and it appears that only about 
 as much work can be obtained from a pound of zinc used 
 through the medium of an electro-magnetic engine, as from a 
 pound of coal used in a steam-engine. When electricity is 
 generated by steam power, and either distributed by wires or 
 stored in secondary batteries, it is probable that electromotors 
 will be employed much more widely for a variety of domestic 
 purposes, as well as for driving locomotives in underground 
 
chap.v.] Electro- Magnetism and Dynamics. 299 
 
 railways, and doing work in places where the products of com- 
 bustion of coal render the use of steam-engines unsuitable. 
 
 The first-made electromotors were obviously derived from 
 the action of the piston in a steam-engine, masses of soft 
 iron being attracted by electro-magnets, which were destroyed 
 at the end of the stroke by automatic contact breakers ; and 
 the backwards and forwards motion so produced was con- 
 verted into circular motion by the ordinary beam-and-crank 
 arrangement. The short distance through which an electro- 
 magnet exerts its power necessitated a very short stroke, 
 introducing mechanical difficulties. Models on this principle 
 are common. 
 
 Another form consists of masses of soft iron arranged on the 
 circumference of a wheel, round which are arranged a number 
 of fixed electro-magnets, having their poles very near its 
 circumference. These electro-magnets are made when the 
 piece of soft iron is approaching the magnet, and unmade 
 when immediately opposite to it. Thus each mass of soft 
 Jron^ when within about twenty degrees of an electro-magnet, 
 and approaching it, receives a pull which is sufficient to 
 send it on to within twenty degrees of the next magnet. 
 To this class belongs Froment's engine, of which the sketch 
 (Fig. 189) represents a model. The arrangement for throwing 
 the magnets alternately in and out of circuit consists of a 
 wheel of eight projecting teeth revolving with the rotating 
 wheel. Each projecting tooth, on coming in contact with a 
 spring, makes contact in the battery circuit, and so makes the 
 two electro-magnets. 
 
 Griscomb's Motor is a modern form of motor, weighing only 
 two or three pounds, and capable, when worked with four or 
 five Grove cells, of turning a sewing-machine, or a small saw. 
 
3oo 
 
 Electricity. 
 
 [Book in. 
 
 Its principle is that of a moveable coil rotating within a fixed 
 coil. The wires of each coil are wound on an iron frame- 
 work, making a long narrow coil like Siemens' armature, the 
 
 PIG. 189. 
 
 two opposite edges of the iron being north and south polar 
 when the current is passing. The inner coil is furnished 
 with a commutator, which reverses the current as soon as 
 
 FIG. 190. 
 
 opposite poles of the inner and outer coils are opposed. The 
 general appearance of the machine is shown (Fig. 190), in 
 which A represents the outer coil of wires, B one pole of the 
 
chap, v.j Electro- Magnetism and Dynamics. 301 
 
 fixed electro -magnet made by them, and G the commutating 
 arrangement by which the inner coil has the current reversed 
 each half revolution. Fig. 191 (i) shows the inner coil (Z>), 
 whose terminals are attached to the two halves of the spindle 
 (E), which are carefully insulated from each other. In 
 
 Fio. 191. 
 
 Fig. 191 (ii) the commutator is shown in plan, the current 
 being transmitted to the inner coil through the springs F and 
 G, which carry the friction rollers, working on the commu- 
 tator E. 
 
 The battery current enters at H, passes by F to E, through 
 the inner coil back to the upper half of E, on by G to K, from 
 
302 
 
 Electricity. 
 
 [Book III. 
 
 K through the outer coils to L, and from L back by a bind 
 ing-screw to the battery. 
 
 193. The Electric Bell. The next useful application 
 of electro-magnetism is shown in the electric bell, now widely 
 used for domestic and other purposes. The construction and 
 working of the bell is easily understood from the diagram (Fig. 
 192). The bell is an ordinary metal dome-shaped bell (A), and 
 
 B 
 
 PIG. 192. 
 
 the clapper (B) is moved by the electro-magnet (0). The clapper 
 is held by a spring, which has a piece of soft iron (D) attached 
 to it, this piece of soft iron acting as the armature of the 
 electro-magnet. 1 As soon as the current passes (in the direc- 
 tion shown by the arrows), the electro-magnet is made, and 
 attracts the armature, which carries with it the clapper, caus- 
 ing it to strike the bell ; the elasticity of the spring causes 
 a recoil of the clapper and prevents a dead sound. The 
 instant, however, that the armature is drawn forward, it 
 ceases to press the spring (E), and contact is by that means 
 1 In the instrument D is brought very near to the poles of the magnet. 
 
chap, v.] Electro- Magnetism and Dynamics. 303 
 
 broken, the magnet is unmade, and the elasticity of the 
 spring carries the armature away from the magnet again, re- 
 making contact with the battery, and sending up a vibratory 
 motion in the clapper, which causes the bell to continue ringing. 
 
 The battery usually consists of two or three Leclanche" 
 cells, and contact is made at a distance by pushing a small 
 button by which contact is made between two metal plates in 
 the frame- work of the button. 
 
 In mines and other places where bells are placed in damp and 
 dirty situations, the make and break of contact in the vibrating 
 bell is found inconvenient. A bell is then employed without 
 the break of contact and called a Tapper bell. Each time that 
 contact is made in the battery circuit the bell is sounded, 
 giving one stroke only, each time the push is pressed in. 
 
 194. The Electric Telegraph. The most important 
 application of these principles of electro-magnetism is found in 
 the Electric Telegraph, which we must now briefly describe. 
 
 The earliest attempts at telegraphy consisted in organising 
 a code of signals by the discharge of a Leyden jar through 
 a circuit, which would cause a spark or series of sparks 
 to be seen at the distant station. This was abandoned, 
 because it was found impossible to secure insulation in the 
 circuit in all weathers for electricity of high potential. Soon 
 after Oersted's discovery of the deflection of a magnet by 
 a current, it was seen that, by passing a current through a 
 circuit, a magnet at a distant station might be deflected. 
 At first it was proposed to use twenty-six wires and twenty- 
 six magnets, each representing one letter of the alphabet. It 
 was soon seen that by a properly arranged code of signals two 
 wires and two magnets were sufficient one to show deflec- 
 tions to the right, and another deflections to the left ; and, 
 
304 Electricity. [Book m. 
 
 still later, it was found that one needle, by reversing the 
 current, was sufficient to supply all signals required. 
 
 Formerly each magnet used required two wires to make 
 a complete circuit for the transmission of the current be- 
 tween two places, but now one of the two is replaced by the 
 earth. The ends of the wire at both stations are simply con- 
 nected with a metal plate sunk in permanently damp earth, 
 which, with the line wire, completes the circuit. 
 
 The essential parts in any system of telegraph are therefore 
 (1) the line joining the two stations; (2) the battery; (3) the 
 communicator ; (4) the indicator the last two at least being 
 at both stations, and different in all the systems of telegraphy. 
 
 195. The Line for Land or Marine Telegraph. 
 
 The character of the line depends on the conditions under 
 which it is to be used. If a land line, it may be either over- 
 head or underground; but if it passes under the sea or a 
 large river, some form of cable is used. 
 
 The overhead wires, seen in all parts of this country, are 
 made of galvanised iron, Jthinch in diameter (No. 8, B.W.G.). 
 The iron is coated with a thin layer of zinc, which, being the 
 more oxidisable metal, protects the iron from rust. The 
 external zinc is coated by a rust or oxide, but since zinc-oxide 
 is insoluble in water, it protects the interior from attack by 
 the weather. In towns, where a large amount of sulphur is 
 set free and brought down as acid in the rain, the oxide is 
 soon destroyed, and the iron rusts away. To prevent this, 
 wires in smoky neighbourhoods should be painted. This 
 wire has to be insulated, and must therefore be kept free from 
 all contact with buildings and trees. At intervals of from 90 
 to 100 yards, for a straight wire, it is supported on a larch 
 pole 5 or 6 inches in diameter by porcelain or glass sup- 
 
Chap, v.] Electro- Magnetism and Dynamics. 305 
 
 ports. These insulating supports, of which one form, seen in 
 section (Fig. 193), consists of a double umbrella for throwing 
 off the rain, and preventing surface leakage of electricity by 
 interposing as great a distance as possible between the wire 
 and the supporting post. When the wire has to be carried 
 into buildings or under ground, it is carefully coated with a 
 waterproof insulating material, generally gutta-percha. 
 
 For marine telegraphy the conditions are 
 very different. We need a very complete 
 insulation, through which water, under the 
 enormous pressure at the bottom of deep 
 sea will not force its way ; and also great 
 strength to withstand the strain brought on 
 the wire in laying it down in deep water, 
 and in lying, as it often must, on steep 
 slopes on the sea bottom. The cables most 
 commonly used consist, not of a single con- 
 ducting wire, but of a spirally twisted strand 
 of six or seven copper wires (Fig. 194), each about 1 mm. 
 (^th inch) diameter. These are the core, and are surrounded 
 by alternate layers of gutta-percha and Chatterton's compound 
 (a mixture of tar, resin, and gutta-percha), which form the 
 insulator proper. Kound the insulator is a layer of hemp, and 
 round this again a protecting sheath of about ten or twelve 
 steel wires, each coated with hemp. Near the shore end the 
 sheath of hemp and steel wire is made of very great thickness, 
 as a protection against breakage by the force of the waves 
 when in storm, but when the depth of about 100 fathoms is 
 reached a much thinner cable may be used. 
 
 196. The Battery. The battery most in use in this 
 country is some form of Daniell's. They are fitted up in 
 
 U 
 
306 
 
 Electricity. 
 
 [Book III. 
 
 troughs of about twenty cells, and will run for a considerable 
 time without further attention than filling up with water when 
 
 FIG. 194. 
 
 it has evaporated. They are the most constant of all cells, 
 and therefore best suited for circuits where almost continuous 
 work has to be done. On other circuits some variety of the 
 simple zinc-copper cell is still used, and Leclanche"'s are 
 gradually coming into use. In what was called the magneto- 
 telegraph, the battery was replaced by some form of magneto- 
 machine which generated the current. 
 
 197. The Single Needle Telegraph Communi- 
 cator. This consists of a commutator by which the current 
 
Electro- Magnetism and Dynamics. 307 
 
 can be rapidly changed in direction or put out of circuit 
 when no message is being sent, at the same time allowing 
 a current to pass through it from the distant end of the line. 
 
 FIG. 195. 
 
 The diagram (Fig. 195) shows such a commutator. It 
 consists of two brass springs, having ivory buttons on their 
 ends. When at rest they press upwards against two metal 
 
 / EARTH LINE 
 tl \ /EARTH 
 
 LINE. 
 
 BATTERY 
 
 a 
 
 BATTERY 
 
 + BATTERY 
 CC DEPRESSED 
 
 FIG. 196. 
 
 -f BATTERY 
 6 DEPRESSED 
 
 studs in the metal cross-piece. When either is depressed, it 
 is released from contact with this cross-piece, but presses on 
 one of the two metal studs on another metal cross-piece, 
 
308 
 
 Electricity. 
 
 [Book HI. 
 
 which passes under the ivory knobs. This throws the battery 
 into circuit, and, examining the arrows in the two figures 
 (Fig. 196), it will be seen that the current runs in opposite 
 directions through the line, according as or b is depressed. 
 
 When a is pushed down, the current goes in order: 
 battery a line earth b c battery. 
 
 When b is pushed down, the current goes in order : 
 battery b earth line a c 
 battery. 
 
 When neither a nor b is depressed, 
 a message will enter from the line, 
 and follow the course : line a c 
 b earth, or vice versa. 
 
 igS r . The Single Needle Indi- 
 cator. This consists of a coil of wire 
 (A, Fig. 197) similar to that used for 
 an astatic galvanometer. Its resistance 
 is made proportional to the line resist- 
 ance, consisting, for a short line, of a 
 few turns of moderately stout wire, 
 and, for a long line, of numerous 
 turns of very thin wire. The coils 
 are placed vertically, and within them 
 hangs a magnetic needle, also having 
 its axis vertical. This needle () is 
 deflected right or left according to 
 the direction of the current, and its 
 movement is shown by a long pointer Fl - 197< 
 
 (C) attached to it by a horizontal rod which passes through 
 the coil and registers the movements of the needle on a 
 
 B 
 
ciiap. v.] Electro- Magnetism and Dynamics. 309 
 
 dial outside. The motion of the pointer is usually checked 
 by two stops on the dial. (The dial is not shown in the 
 figure, being on the front of the instrument.) 
 
 199. Arrangement of Apparatus at Telegraph 
 Station. The arrangement of these parts at each station 
 can be understood from the diagram (Fig. 198), which shows 
 either the sending or receiving station. 
 
 AKIH 
 
 FIG. 198. 
 
 In addition to the essential parts described, there was 
 formerly an electric bell at each station to call the attention 
 of the clerk when a message is to be sent. This could easily 
 be done by a contact breaker, one branch of which contains 
 the bell, placed at any part of the line, between the communi- 
 cator and the earth, as shown in diagram (Fig. 198). The 
 clerk, when he leaves the telegraph-room, turns on his bell, 
 and any signal made by the clerk at the further end will then 
 cause the bell to ring. The bell is now seldom used, the click 
 of the needle against its stops being a sufficient call. 
 
 200. Codes of Telegraph Signals. The code of 
 
Electricity. [Book m. 
 
 signals consists in denoting each letter, numeral, or sign by a 
 certain number of deflections of the needle to the right, and a 
 certain number to the left, those letters which occur most 
 frequently being denoted by the fewest strokes. In the 
 printing telegraph, which we consider next, the same code is 
 used, the stroke to the left being denoted by a dot (), and 
 the stroke to the right by a dash ( ). The alphabet on the 
 two systems is given side by side : 
 
 Single Morse's Single Morse's 
 
 Needle. System. Needle. System. 
 
 A \l N / S] 
 
 B /SSN ---- III 
 
 C /s/s ---- P N//S ._ 
 
 /XS - Q 
 
 E \ R 
 
 F \\l\ ---- S 
 
 G //S - T I 
 
 H S\\N .... U \\/ 
 
 / \S ..- V \\\l 
 
 J s/// W \ll 
 
 K l\l X l\\l 
 
 L s/ss -.. F /s// 
 
 M II Z II \\ 
 
 For figures the following code is used : 
 
 Single Needle. Morse. 
 
 o ///// 
 
 2 \\/// 
 
 3 
 
chap, v.] Electro- Magnetism and Dynamics. 3 1 1 
 
 
 Single Needle. Morse. 
 
 4 
 
 VSVS/ 
 
 5 
 
 s\s\\ 
 
 6 
 
 /\svs 
 
 7 
 
 //V,v 
 
 8 
 
 ///x\ 
 
 9 
 
 ////s 
 
 This code will well repay the trouble involved in learning. 
 Depending on two signals of great simplicity, it has already re- 
 ceived various applications, and bids fair to become the universal 
 alphabet in cases where an ordinary written alphabet is un- 
 suitable. It can be made either visible by the movements of 
 a single finger, or audible by the use of two sounds of different 
 pitch, the longer movements or deeper sounds representing 
 the dashes, and the shorter movements or higher sounds the 
 dots. These considerations point to it, amongst other things, 
 as likely to supersede the deaf and dumb alphabet at present 
 in use. 
 
 *20I. The Morse Key. In Morse's printing telegraph 
 the message is written at the receiving station either by a 
 style indenting a paper strip, like a tape, or actually printed 
 in ink on the tape by contact with a narrow inked roller. 
 
 The communicator is a simple contact breaker, called the 
 Morse key. It consists of a brass lever (A) working on a 
 fulcrum in the middle, with a metal stud towards one 
 end, and an adjustable screw (D) at the other end. On 
 depressing the alternate ends of the lever, contact is made 
 with two metal studs (B and G) on the base (Fig. 199). 
 When the ivory knob attached to A is not depressed a spring 
 
3 1 2 Electricity. [Book in. 
 
 holds D constantly in contact with C. E and F are binding 
 screws connected with the fulcrum and the stud (7, and there 
 is a similar one on the opposite side connected with the stud 
 B. By means of these screws, B is connected with the local 
 battery, E with the line, and F with the indicator. 
 
 In receiving a message from the distant station, the key is 
 left alone, the current passing from the line through EA 
 C indicator - earth. 
 
 In sending a message A is depressed, breaking contact 
 with the home indicator at (7, and introducing the battery 
 current at B, which now proceeds by the course, battery 
 B AE line, to the distant indicator, and makes on 
 the indicator a dot or dash according to the length of time 
 during which the key is held depressed. 
 
 *202. The Morse Indicator. The Morse indicator is 
 made in a variety of forms, but consists essentially of two 
 parts, a train of clockwork, by 'which the paper tape is payed 
 out between two friction rollers from a large horizontal or 
 vertical wheel, on which it is coiled, and an electro-mag- 
 netic arrangement by which dots and dashes are made on 
 the strip as it passes, according to the will of the distant 
 operator (Fig. 200). The coil of paper on the vertical wheel is 
 
chap, v.] Electro- Magnetism and Dynamics. 3 1 3 
 
 shown at A, and .5, are the friction rollers between which it 
 passes by the action of the clockwork in the case (D), which 
 can be started or stopped at will by removing or applying a 
 detent. F is an electro-magnet round which the current from 
 the line passes. It has a soft iron core, and is wound with 
 numerous turns of fine wire, having a resistance which varies 
 
 FIG. 200. 
 
 from 50 to 500 ohms, according to the conditions of the 
 circuit. Opposite the poles of the electro-magnet is a soft iron 
 armature carried on a brass lever, which turns round a pivot, 
 and has its motion upwards checked by a screw (a), against 
 which it is held when no current is passing by a spring (6). 
 The lever carries on its further end a steel style, pointing 
 towards the tape, and so adjusted that when the soft iron 
 
314 Electricity. 
 
 armature is attracted by the electro-magnet, the style presses 
 gently on the paper and makes an indentation as long as 
 the current is passing. In modern instruments the style is 
 replaced by a narrow roller, which turns in a vessel contain- 
 ing printers' ink, and, when drawn up by the magnet, marks 
 with its edge the paper passing in front of it, thus perma- 
 nently printing the message sent. 
 
 *203. The Morse Relay. In long land lines the current 
 becomes much weakened by leakage, due to imperfect insu- 
 lation, and it is not strong enough to work the Morse indi- 
 cator. In this case there is used what is called a relay, which 
 at each make or break of contact in the line circuit makes or 
 breaks contact in a new battery circuit, in which the indicator 
 is included. 
 
 FIG. 201. 
 
 In the diagram (Fig. 201), A is an electro-magnet through 
 the coils of which the original current passes to earth. The 
 soft iron armature is carried by a brass arm which is lightly 
 suspended on a pivot (B\ and has its motion controlled by 
 the two screws, a, b, of which b is insulated by having its 
 
chap, v.] Electro- Magnetism and Dynamics. 315 
 
 point of ivory. When no current is passing, the arm is held 
 by the weak spiral spring c, in contact with b. On passing 
 the current the armature is attracted and brought into con- 
 
 tact with a, thus completing the circuit in the local battery, 
 in which circuit the indicator is included. Each time that 
 the current from the line passes through the relay, the local 
 
3 1 6 Electricity. [Book in. 
 
 battery transmits a current through the electro-magnet of the 
 indicator, the two working therefore completely in sympathy. 
 
 In the case of long land lines there are a series of " relay 
 stations" where the message is not received and retransmitted, 
 but passed on with renewed energy by means of a relay. One 
 terminal of the local battery is to earth, and the other is con- 
 nected through the relay with the continued line. By this 
 means there is a continuous telegraph, without retransmission 
 by hand between London and Teheran, there being five relay 
 stations on the road. 
 
 The arrangement at each station of key, relay, and indicator 
 can be understood from the diagram (Fig. 202), remembering 
 that the same must be repeated at each end of the line. 
 
 *204- Morse Sounder. The peculiar click made by the 
 armature either of the indicator or relay against its stops 
 enables an expert clerk to take down the message by ear as 
 it passes, only comparing afterwards with the tape to insure 
 accuracy. This depends on a slight difference in the click, 
 according as it is made by a momentary contact (for a dot), 
 or a prolonged contact (for a dash). On this principle is con- 
 structed the Morse Sounder, which is identical with the relay 
 in construction, but much smaller, and is used for military 
 telegraphy, or under conditions where economy of apparatus 
 is important. 
 
 *205- Electrostatic Induction in Cables. As soon as 
 marine cables of great length came into use it was found that 
 signals transmitted by them suffered a remarkable retardation, 
 the making contact with the battery for an instant at one end 
 causing at the other a gradual rising and sinking again of the 
 current, occupying several seconds. This would make the rate 
 
chap, v.] Electro-Magnetism and Dynamics. 317 
 
 of signalling very slow were it necessary to wait till each signal 
 had completely died away before transmitting the next. 
 
 The retardation is easily explained if we remember that the 
 core of the cable forms the inner coat of a Leyden jar of 
 enormous capacity, of which the conducting sea-water is the 
 outer coat. The effect of contact with the battery terminal is 
 to bring the core of the cable to a potential which, near the 
 battery, nearly equals the potential of the battery terminal. 
 This can only be done by charging the Leyden jar. In the 
 case of a long cable this charging takes a finite time, and on 
 breaking contact, the Leyden jar is discharged through the 
 receiving galvanometer, and this again occupies about the 
 same time. 
 
 The effect can be illustrated by the apparatus of Fig. 152, 
 in which one sheet of the condenser represents the cable and 
 the other the water. By means of a large number of such 
 condensers an artificial cable can be made, and all the effects 
 of a real cable exactly reproduced. 
 
 *2o6. Thomson's Marine Galvanometer. To over- 
 come the difficulty presented by the very slow rate of cable 
 signalling, Sir W. Thomson invented his Marine Galvanometer, 
 a variety of the reflecting galvanometer, in which the oscilla- 
 tions of the needle are damped, the needle simply deflecting 
 right or left when a current is transmitted, and returning to 
 its zero without making oscillations about it, as in the 
 common form of the instrument. This, of course, does not 
 obviate the retardation of the signals noticed above, but 
 enables the clerks by practice to interpret the indications of 
 the galvanometer without waiting for each signal to die away 
 before another is transmitted, each observation depending 
 
318 Electricity. [Book m 
 
 not only on the signal last sent, but on the twenty or thirty 
 preceding it. 
 
 *207. Thomson's Syphon Recorder. This is an in- 
 strument by which the messages sent through a cable are 
 made self-recording. It consists of a tape payed out vertically, 
 much as in the Morse Indicator. Opposite the tape is a fine 
 capillary glass tube bent somewhat in the form of the letter S, 
 whose upper end hangs in a vessel containing ink, and whose 
 lower end is opposite the middle of the tape. The ink vessel 
 is electrified by a small frictional machine, worked by the 
 clockwork which pays out the tape ; and, according to the 
 principle of the electrical watering-pot (Art. 93), the ink will 
 spurt out from the tube on to the tape, making a straight line 
 along it if the syphon remain stationary. The syphon tube 
 is attached by fine silk threads to the moving coil in a 
 D'Arvonsal galvanometer (Art. 179), by which it is deflected 
 right or left according to the direction and magnitude of the 
 current sent through the cable. By means of the attached 
 silk threads the movement of the syphon tube is made pro- 
 portional to the movement of the galvanometer coil, and the 
 syphon recorder therefore gives a permanent register of every 
 change in strength or direction of the line current. 
 
 *2o8. Step by Step, or ABC Telegraph. There is a 
 
 great variety of other telegraph machines used in various 
 parts of the world, including some in which the message is 
 actually printed in ordinary type. These depend on more 
 complex machinery, but involve no new principle in elec- 
 tricity. The only other form we shall refer to here is the ABC 
 telegraph, specially adapted for the use of persons who are 
 
chap, v.] Electro- Magnetism and Dynamics. 319 
 
 not familiar with any telegraphic code. The message is 
 received on a dial marked with the twenty-six letters of the 
 alphabet, a needle rotating always in the same direction, and 
 pausing at each letter which the distant operator wishes to 
 transmit. This and all other "step by step" telegraphs 
 require two parts, a manipulator at the sending station, and 
 an indicator at the receiving station, with, of course, the usual 
 line and battery. 
 
 The Manipulator (Fig. 204) consists of a dial marked with 
 the letters of the alphabet and two additional spaces, which 
 
 PIG. 204. 
 
 can be used to denote the beginning and ending of a sentence. 
 Over the letters moves an arm, rotating about the centre of 
 the dial, having attached to it behind the dial a toothed 
 wheel, the number of teeth being half the number of letter 
 and other spaces round the dial. The teeth, by pressing a 
 spring, make contact in the line battery, when the arm is 
 opposite each alternate letter. 
 
 The indicator (Fig. 205) contains an electro-magnet, fur- 
 nished with a soft iron armature. This armature carries a 
 long arm, whose end is formed to act as an escapement 
 against a toothed wheel having the same number of teeth 
 
3 20 
 
 Electricity. 
 
 [Book III. 
 
 as the wheel in the manipulator. The toothed wheel carries 
 an index hand, which moves over a dial whose divisions 
 correspond to those in the manipulator. Each time the 
 current passes the armature is attracted, and the detent 
 (Fig. 205, a) by its wedge-like action pushes on one tooth of 
 
 PIG. 205. 
 
 the wheel, and, on breaking, retains the next against the flat 
 end of the wedge. Thus in the making and breaking, the 
 index hand passes over two letters, just as in the manipulator. 
 
 To call attention to the instrument, a bell is attached to 
 the indicator (not shown in drawing), which can be put in or 
 out of circuit by a simple contact breaker. 
 
 There is also on the indicator a small button moving a 
 lever, by which the index hand can be moved over the letters 
 successively without employment of the current, by which 
 
chap, v.] Electro- Magnetism and Dynamics. 321 
 
 the manipulator and indicator can be brought to the same 
 letter initially. 
 
 To send a message the operator turns the manipulator arm 
 till it is opposite the letter he wishes to transmit, at which he 
 makes a pause. Each letter he passes over will be passed 
 over by the index hand in the indicator, which will also 
 pause at the letter over which he causes the manipulator 
 to make a pause, and so a message, letter by letter, can be 
 spelt out. The process is very slow, as it is often necessary 
 to turn the manipulator round nearly a whole circumference 
 between two letters, B and A, for instance, as it will only 
 work in one direction, The manipulator, again, must be 
 moved very slowly, as otherwise it will often pass over two 
 letters before the detent in the indicator has had time to set 
 more than one free, throwing the two parts of the instrument 
 out of correspondence. 
 
 208a. Telpherage. This was the name given to a special 
 contrivance due to the late Professor Fleeming Jenkin for 
 transmitting goods along a stout wire like a telegraph wire, 
 and supported in a similar manner. The line is divided into 
 equal lengths, separately insulated, and connected with the 
 positive and negative terminals of the battery or other gene- 
 rator. The goods are carried in buckets suspended below the 
 line, and hung from a grooved wheel which runs along the 
 line. A train of buckets (with an electromotor acting as 
 locomotive) is always slightly longer than one division of the 
 line, so that the foremost wheel is always on one section and 
 the hindmost on another. By means of these extreme wheels, 
 electrical communication is made to the electromotor, which 
 then keeps the train in motion. This method of transit was 
 
 x 
 
3 22 
 
 Electricity. 
 
 [Book III. 
 
 intended for use where small goods have to be carried, or ore 
 has to be brought from mines, under conditions where a per- 
 manent road or railway could not profitably be constructed. 
 
 *20p. Ampere's Theory of Magnetism. On observing 
 the intimate connection between a solenoid and a magnet, 
 Ampere introduced a hypothetical theory of the construction 
 of a magnet. He assumes that each molecule of magnetic 
 matter has an electric current constantly circulating round it. 
 When the body is unmagnetised these currents are in all direc- 
 tions, and neutralise each other's effect on external magnetism. 
 The act of magnetisation consists in setting the currents round 
 all the molecules in parallel planes and in the same rotational 
 direction. Thus any section across a magnet shows a series of 
 currents rotating round the molecules (Fig. 206). Assuming 
 these currents all of the same strength, the 
 current in two consecutive molecules will 
 be equal and opposite along the faces in 
 contact, and therefore will neutralise each 
 other, while the currents in the outer- 
 most molecules being in contact with the 
 air are not neutralised, but give a con- 
 tinuous current, or series of currents, round 
 the outside of the magnet. These currents 
 constitute a solenoid of which the succes- 
 sive turns are infinitely near together, and 
 are, according to Ampere, the source of its 
 magnetic properties, the Amperian currents being right- 
 handed, or in direction of the hands of a watch to an observer 
 looking down on the south pole, and left-handed to an ob- 
 server looking down on the north pole. 
 
 FIG. 206. 
 
chap, v.j Electro- Magnetism and Dynamics. 323 
 
 All the relations between a magnet and electric currents 
 can, by means of the Amperian hypothesis, be reduced to 
 the actions of currents on each other, but they can be easily 
 explained by actions in the magnetic fields of the magnets, 
 demonstrable by experiment, while the Amperian currents 
 are only hypothetical. 
 
 210. The Magnetic Tick. That the magnetization of 
 a bar is accompanied by some molecular movement is proved 
 by the magnetic tick which accompanies its magnetization 
 and demagnetization. The sound can be easily heard by 
 
 FIG. 207. 
 
 stretching a soft iron wire, about 1 metre long and a milli- 
 metre in diameter, over a sounding-board (Fig. 207 Z>, shows 
 a section), and surrounding the wire, through nearly its whole 
 length by a narrow glass tube, which is supported out of 
 contact with the wire. Eound the glass tube is closely 
 
324 Electricity. (Bookin. 
 
 wound moderately stout insulated copper wire two or three 
 layers in depth. On connecting the ends of the copper wire 
 with the terminals of a battery of four or five Grove cells, 
 and placing any contact breaker in the circuit, a sound is 
 heard from the wire each time that contact is made or 
 broken. 
 
 On this principle a telephone capable of transmitting musical 
 notes is easily constructed. The notes are sung or sounded 
 through a mouthpiece into a box (A), whose upper surface is 
 closed by a thin sheet of metal (B) stretched tightly. Near 
 its centre is adjusted a screw (C) whose point all but touches 
 the metal membrane, and does touch it at each vibration of 
 the membrane, when a note is sounded into the mouthpiece. 
 The note depends simply on the number of vibrations per 
 second, and each of these vibrations makes and breaks contact 
 in a voltaic circuit. This circuit includes the electro-magnet 
 D, which gives the magnetic tick for each make and break of 
 contact, and reproduces the note sounded. 
 
 This telephone is commonly but inaccurately called by the 
 name of Eeis, who, about 1860, invented a telephone which 
 transmitted articulate speech as well as musical tones. His 
 receiver was on the principle of the receiver described above, 
 consisting of a knitting-needle surrounded by a coil of wire 
 mounted on a sounding-board. His transmitter was formed 
 on the model of the drum and bones of the human ear, and 
 he was thus led to an instrument identical in principle with 
 the carbon transmitter of the present telephone. (See Philipp 
 Eeis, Inventor of the Telephone, by Prof. S. P. Thomson, D.Sc.) 
 
CHAPTER VI. 
 CURRENT INDUCTION. 
 
 211. Work done in the Electro-Magnetic Field at 
 Expense of the Current. In the experiments of the last 
 chapter, where movements of conductors or magnets take 
 place under electro-magnetic force, it appears from theory 
 that the work done during the movement is accompanied by 
 a diminution of the current while the movement lasts./ This 
 falling off in most cases is so small, compared to the total 
 current passing, that it is rather difficult to show, either by 
 including a rough galvanometer in the main circuit, or a 
 delicate one in a branch circuit. It can be shown by passing 
 the current from five Grove cells continuously through two 
 electro-magnets of horse-shoe form, and including a glow 
 lamp in the circuit. If the electro-magnets be now held, one 
 immediately above the other, with contrary poles opposed at 
 a distance of one or two inches, and the upper be allowed to 
 fall on to the lower, a momentary decrease in the light will 
 be noted, showing a slight falling off of the current. On 
 lifting up suddenly the upper magnet, and separating it from 
 the lower, there will be a slight increase of the current, shown 
 by increased light from the lamp. 
 
 *2i2. Theoretical Explanation of foregoing Experi- 
 ment. It will be worth while considering how the fall in 
 
 325 
 
326 Electricity. [Book ra. 
 
 the current is a source of energy. Let I be the current when 
 the machine is at rest, and /' the current when the same 
 machine is in motion. Let also E be E.M.F. of the battery, 
 and R the resistance, which is the same in both cases. The 
 energy given out from the battery is in the two cases El 
 and El' (Art. 169), and the heat generated measured in 
 mechanical work is RP and RP* (Art. 169) each per second. 
 If T be the time in which a gram of zinc is consumed in the 
 battery with current I, it will require a longer time, namely, 
 
 j/ T, when the current is /'. Hence the heat given out per 
 gram of zinc consumed will be in the two cases RP T and 
 RI'* x y,r, and this latter is equal to RII'1\ which is neces- 
 sarily less than RPT, if /' is less than /. But the energy 
 given out from the battery must in both cases be the same, 
 since equal amounts of zinc are dissolved. Hence, when the 
 machine is in motion there is less energy given out in heat 
 than that abstracted from the battery by R(I*-H')T per 
 gram of zinc used. This energy, then, does the work in the 
 machine. 
 
 When work is done against electro-magnetic forces, the 
 current is increased, the work done on the system being 
 evolved from it as increased heat in the circuit. 
 
 213, Induced Currents. Returning to any of the 
 apparatus of last chapter, in which we have the movement 
 of currents in a magnetic or electro-magnetic field, we replace 
 the battery by a sensitive galvanometer, of course removed 
 to a distance from the magnet. On moving the current 
 or magnet by hand, the galvanometer shows a current, 
 
Chap. VI.] 
 
 Current Induction. 
 
 327 
 
 and the direction of the current changes with a change 
 in the direction of the movement being always opposite to 
 the current which would have caused the actual movement. 
 These are called induced currents ; they correspond with the 
 falling off in the current noticed above, and may, in fact, be 
 regarded in an algebraical sense as a falling off in the current, 
 when that current is zero. 
 
 We accordingly find that the induced current is opposite in 
 direction to the current which would have caused the motion, 
 or that the electro-magnetic effect of the induced current is 
 always to oppose the motion taking place in the field. This 
 principle is known as Lenz's law, which we will illustrate 
 further before making a more formal statement of the law. 
 
 Taking the apparatus for showing the rotation of a magnet 
 pole round a current, or of a current round a magnet pole 
 
 FIG; 208. 
 
 (Figs. 161 and 163), we obtain an induced current on rotating 
 the apparatus by hand, and if we examine its direction it 
 
328 Electricity. [Book in. 
 
 will be opposite to that which would have caused the motion. 
 Thus, on rotating the north pole with the hands of a watch, 
 the current will be upwards, it being remembered that a 
 downward current would cause this rotation (Fig. 208). 
 
 In Barlow's wheel in the same way the rotation by hand 
 will call up a current related to the lines of force and direction 
 of rotation, as shown in Fig. 209. The induced current is 
 perpendicular to the plane containing the lines of force and 
 the direction of motion of the conductor, and on comparing 
 with the rule for the motion of a conductor carrying a current 
 given in Art. 179, we have the rule: A figure placed in a 
 conductor looking along the lines of force, and carried mechanic- 
 ally to its left, will experience a current which enters by its 
 head and leaves by its heels. 
 
 FIG. 209. 
 
 In the electromotors of Art. 191-2, the currents can be 
 obtained by turning round the moving parts. When the 
 magnetism is wholly due to electro-magnets, the residual 
 magnetism in the iron cores never fails to start a current 
 which can be shown by the galvanometer. 
 
 214. Induced Currents in a Wire Coil moving in a 
 Magnetic Field. The foregoing and all other cases of 
 induced currents are best studied in connection with Faraday's 
 
chap, vi.] Current Induction. 329 
 
 conception of Lines of Force, already explained (Art. 181). 
 Take a small coil, consisting of a few turns of wire, and connect 
 its ends with a delicate galvanometer. If this coil be sud- 
 denly transferred into the strongest part of the field of an 
 
 FIG, 210. 
 
 electro- or permanent magnet, it will be found to be traversed 
 by an induced current. In Fig. 210 the coil in position a is 
 in a weak part of the field, and traversed by few lines of force, 
 and by being transferred to b it is at once traversed by many 
 more lines. The induced current will in this case tend to 
 oppose the change that is to say, it will tend to diminish the 
 number of lines intercepted by causing a current whose own 
 lines of force would be in the opposite direction. This is the 
 same as saying that the induced current is left-handed to the 
 lines of force in the field. On moving the coil out of the 
 strongest part of the field the induced current is reversed. 
 
 In a similar way, whatever cause alters the number of lines 
 of force embraced by the coil will produce an induced current 
 in the coil left-handed to the lines of force when they are 
 increasing, and right-handed to them when they are decreas- 
 ing. This may be done by simply turning the coil about a 
 
330 Electricity. [Book in. 
 
 diameter, as from a position b to a position c, when the lines 
 of force pass parallel to the face of the coil, but are not 
 intercepted by it. In this case the lines intercepted have 
 diminished from maximum to zero, and a right-handed current 
 is the result. If the rotation be still continued, the opposite 
 face will meet the lines of force, and to a person looking on 
 this face the current appears reversed, and therefore, to a 
 person who still looks on the original face, the current is 
 continuous. Otherwise, if we keep our attention fixed on 
 the same face of the coil, the lines of force diminish from 
 maximum to zero and again increase to maximum, but with 
 a negative sign, owing to the direction of the field being 
 reversed relatively to this face of the coil. This would be 
 represented algebraically as a constant decrease through 
 the half-revolution ; the current being consequently right- 
 handed to the lines of force throughout. During the other 
 half-revolution in returning to position 5, the current is left- 
 handed to the lines of force. 
 
 If the coil has a large diameter, the earth's magnetic 
 field will be sufficient for this experiment. Lay the coil on 
 the table and simply turn it once over, and a current will 
 pass, due in this case to the vertical component of the 
 earth's magnetic field. If it be placed vertically at right 
 angles to the meridian, and turned once about a vertical 
 diameter, the horizontal component will alone influence the 
 experiment. If it be placed at right angles to the dip, and 
 rotated about a diameter, the whole magnetic field of the 
 earth will be employed. 
 
 These experiments are often shown by means of Delezenne's 
 Circle. It consists of a coil fastened to a framework, the ends 
 of the wire being connected with the split ring a (Fig. 211), 
 
Chap. VI.] 
 
 Current Induction. 
 
 which with the springs makes a commutator reversing the 
 current in the galvanometer relatively to the coil when its 
 plane is parallel to the dip. The current is thus made con- 
 tinuous *n the galvanometer through a whole revolution. 
 
 FIG. 211. 
 
 The change in the number of lines of force may also be 
 brought about by change in the magnetism of the magnet, as 
 may be shown by making or breaking contact in the electro- 
 magnet, or even by shunting part of the current. 
 
 In Fig. 181 is shown a sketch of the lines of force for a 
 solenoid carrying a current. If, now, a secondary coil of wire 
 be slid on over the primary solenoid, it will embrace all the 
 lines of force contained in the original or primary solenoid. 
 Fig. 212 shows the arrangement in which the primary coil 
 connected with the battery can be slid into the secondary 
 coil connected with the galvanometer. On thrusting the 
 primary in, a left-handed, and on withdrawing it, a right- 
 handed current will be shown in the galvanometer. Similar 
 
332 
 
 Electricity. 
 
 [Book III. 
 
 effects can be obtained by placing the primary within the 
 secondary coil* and simply making and breaking contact. 
 
 FIG, 212. 
 
 If an iron core be placed inside the primary, these effects 
 will be all much increased, since the presence of the iron 
 increases greatly the strength of the field, or the number of 
 lines of force embraced by the coil. In the case of magnetised 
 iron or steel it is now usual to consider the lines of force as 
 passing through the metal much as in the solenoid, forming 
 a system of closed curves, the directions being within the 
 magnet from south to north, and outside from north to south. 
 Thus, whether air or iron occupy the magnetic field, the 
 behaviour is of the same kind, and different only in degree. 
 
 A coil of wire slid on over a permanent magnet will embrace 
 all its internal lines of force, and an induced current is caused 
 by moving the coil on to the magnet. If the embracing 
 coil be very large compared to the magnet, the effect is dim- 
 inished, since the lines of force which pass out from the mag- 
 
chap, vi.] Current Induction. 333 
 
 net and back again through the circuit must be omitted in 
 summing up the number of lines included. A current in the 
 opposite direction, and of much smaller magnitude, will be 
 caused by moving the coil up to the centre of the magnet, 
 but wholly outside it : since in this case the lines of force 
 included are much fewer in number, and traverse the coil in 
 the opposite direction. 
 
 A similar explanation applies to the flat spirals of Fig. 174, 
 when one has a current passed through it, and the other, con- 
 nected with a galvanometer only, is moved from or towards 
 it. As the spirals approach there is an induced current 
 opposite in direction to the battery current, and as they 
 recede the induced current is in the same direction as the 
 battery current. 
 
 215. The Extra Current or Galvanic Spark. On 
 
 making and breaking the battery circuit, a bright spark is 
 noticed to pass between the terminals at the instant of making 
 and breaking. This cannot be due to the battery current, as 
 it only occurs momentarily when that current is made or 
 broken, and we shall find it has a much higher E.M.F. than 
 the battery current itself. On including a large coil of wire 
 or an electro -magnet in the circuit, the intensity of the spark 
 is very much increased, causing a brilliant flash if contact be 
 broken in a mercury cup. 
 
 This is no doubt the effect of an induced current in the 
 conductor itself, which behaves in this respect just like any 
 other conductor in the field, experiencing an induced inverse 
 current on closing, and an induced direct current on breaking 
 the battery circuit. 
 
 These currents were discovered by Faraday, and by him 
 were called the inverse and direct extra current respectively. 
 
334 
 
 Electricity. 
 
 [Book III. 
 
 To exhibit their directions by the galvanometer is not 
 easy, as they occur with the battery current, in the same 
 conductor. Faraday showed the direct extra current by 
 arranging a circuit containing a battery and an electro-magnet 
 (C in Fig. 213), and placing a galvanometer in a branch 
 
 FIG. 213. 
 
 circuit AGB (by means of the mercury cups A and B), 
 which was therefore traversed by a certain fraction of the 
 battery current, causing the needle to deflect. By laying a 
 piece of cork or a brass weight on the galvanometer card he 
 blocked the needle, retaining the needle at zero, while the 
 battery current was passing. Contact was broken by lifting 
 the battery wire out of the mercury cup A or B, and the 
 direct extra current passed round the closed circuit ACBG. 
 Assuming the battery current to pass through the electro- 
 magnet in the direction ACB, and through the galvanometer 
 in the direction AGB, the direct induced current traverses 
 the galvanometer in the opposite direction to the battery 
 current. On breaking contact, therefore, the needle swings 
 
chap, vi.] Current Induction. 335 
 
 away from its stop, thus proving the existence of the extra 
 current. 
 
 The high E.M.F. of the extra current may be shown in a 
 variety of ways. Thus, if the galvanometer in Fig. 213 be 
 replaced by the two hands of the operator, one finger being 
 placed on each cup, a sharp pricking sensation is felt when- 
 ever contact with the battery is made or broken in the mercury 
 cups. This sensation is increased by rapidly making and 
 breaking contact, as by rubbing the end of the battery wire 
 over the surface of a file, one end of which is held in the 
 mercury cup. That these effects are not due to the direct 
 battery current is shown by passing it through the body, 
 when no sensation whatever is produced. 
 
 The direct extra current has always much higher E.M.F. 
 than the inverse, though the same amount of electricity 
 must pass in both. This is why the spark on breaking is 
 always much brighter than on making contact with the 
 battery. 
 
 >)- 
 
 2l6. Lenz's Law. All induced currents, such as we have 
 
 been experimenting upon, obey the Law of Lenz, to which 
 we have already alluded. It may be stated thus : If either a 
 conductor forming part of a closed circuit be moved in the magnetic 
 field, or the field in which the conductor is placed undergo any 
 change of strength, during the movement or change the conductor 
 is traversed by a current, whose electro-magnetic effect is to oppose 
 the movement of the conductor or the change in the field. 
 
 The following are but cases of the general law, which we 
 have already illustrated by experiment : 
 
 (1) If a north pole approach a closed circuit, the number 
 of lines intercepted is increasing and the induced current 
 
336 Electricity. [Book in. 
 
 being left-handed to the lines of force, makes the face, opposite 
 to the north pole, also north-polar, so as to resist the advance 
 of the pole. 
 
 (2) If a linear conductor forming part of a closed circuit 
 be moved across the lines of force, so that a figure in the 
 conductor looking along the lines of force is carried by the 
 motion to its left, the induced current will enter by its head 
 and leave by its heels. These directions are conveniently 
 remembered by extending the thumb and forefinger of the 
 right hand, and bending the second finger up at right angles 
 to the plane of the palm. If the thumb denote the direction 
 of the lines of magnetic force, and the second finger the 
 direction of the motion of the conductor, the forefinger points 
 in the direction of the current. 1 It is also convenient to 
 remember that the direction of the induced current is at 
 right angles to the plane which contains the lines of force and 
 the direction of motion. 
 
 (3) If a closed conductor carrying a current approach 
 towards a closed conductor not carrying a current, a current 
 will be induced in the latter conductor in opposite direction 
 to the battery current. 
 
 (4) If a conductor be moved so as to include fewer lines 
 of magnetic force, there will be a right-handed induced 
 current whose electro-magnetic effect is to increase the 
 number of lines of force. 
 
 (5) If the strength of a current, or the magnetism of a 
 magnet, be diminished, every conductor in its field will 
 experience a current right-handed to the lines of force. 
 
 (6) If the current be established in a conducting circuit, 
 
 1 See Munroe and Jamieson's Pocket Book of Electrical Rules and 
 Tables, 
 
chap, vi.] Current Ind^lct^on. 337 
 
 an inverse extra current will be developed in the circuit 
 itself. 
 
 It is almost superfluous to remark that in each case a 
 reversal of the direction of motion or of the change also 
 reverses the direction of the induced current. 
 
 217. Currents induced in Solid Conductors moved 
 in the Magnetic Field. For the development of induced 
 currents it is not necessary to have wires forming closed 
 circuits, since induced currents occur whenever a conducting 
 mass is moved through a magnetic field across the lines of 
 force. This is easily shown by the resistance experienced in 
 drawing a metal sheet between the poles of a strong electro- 
 magnet. A piece of copper (usually shaped like a saw), on 
 being drawn through air between the poles of the electro 
 magnet, feels to the operator as if it were being drawn 
 through some viscous fluid like honey or treacle. This is 
 obviously due to the induced currents in the metal sheet which 
 oppose the motion. 
 
 The same thing is often shown by suspending a copper cube 
 by a fine string between the poles of the electro-magnet. 
 After putting torsion on the string, by rotating the cube 
 several times, it, when left to itself, with the magnet unmade, 
 spins rapidly round, untwisting the string. If while the string 
 is untwisting contact be made with the battery, the cube is 
 rapidly pulled up, as if it were meeting with resistance in the 
 air; but on breaking contact again, it goes on spinning as 
 before. 
 
 Before Faraday's discovery of induced currents, Arago had 
 observed that if a horizontal copper disc be rotated rapidly, 
 a magnet needle suspended by a fibre over its centre is 
 
 Y 
 
338 
 
 Electricity. 
 
 [Book in. 
 
 deflected in the direction of rotation, and if the rotation is 
 rapid enough, the magnet also spins round, following the 
 motion of the disc. 
 
 The explanation of these currents (eddy currents as they 
 are called), is that in every part of a conductor moving 
 
 through a magnetic 
 field there is an electro- 
 S J^^^T^) ) I motive force at right 
 angles to the plane con- 
 taining the lines of force 
 and direction of motion, 
 strongest in the strong- 
 est part of the field. 
 FlG 214 - A strong current, there- 
 
 fore, passes in this part of the field, the closed circuits which 
 carry the current being distributed over the whole surface of 
 the conductor, but not penetrating it to any great depth. 
 
 The figure shows such currents for the simple case of a 
 strip of metal drawn through a magnetic field, from right 
 to left of an observer who looks down on the south pole. 
 
 In practical electricity these eddy currents lead to heating 
 of the metal masses, and represent a wasteful expenditure of 
 energy. They are usually prevented by building up all 
 moving masses of metal of sheets insulated from one another. 
 The planes of the sheets should be parallel as far as possible 
 to the lines of force and to the direction of motion of the mass. 
 
 218. Dead Beat Galvanometer. It will now be easy 
 to understand the ' damping ' effect observed in some galvano- 
 meters in which the needle moves directly from zero to its 
 final position, and back again to zero almost completely with- 
 
Chap. VI.] 
 
 Current Induction. 
 
 339 
 
 out oscillation, thus saving much time in taking observations. 
 
 Fio. 215; 
 
 This is specially noticeable in the D'Arvonsal Galvanometer 
 
34O Electricity. [Book in. 
 
 (Art. 179), in which a coil of wire wound on a strip of copper 
 oscillates in a strong magnetic field, which induces currents 
 in both parts to check the motion of the needle. 
 
 The same is the case in Sir W. Thomson's Marine Galvano- 
 meter, the number of coils of wire being so great that the 
 swing of the needle is damped by the induced currents its 
 movement calls up. 
 
 219. Magneto-Electric Machines. This name is 
 given to machines in which a coil of wire is made to rotate in 
 the field of a strong permanent magnet, in which currents are 
 induced. 
 
 Of these, Clarke's machine was one of the earliest; it is 
 very simple in construction, and still continues more or less 
 in use for medical purposes. 
 
 It consists (Fig. 215, a) of a single horse-shoe magnet, or a 
 battery of three magnets, in front of the poles of which 
 revolve on a spindle passing between them two bobbins of 
 wire (BC) containing soft iron cores. 
 
 The bobbin when opposite the south pole is traversed by 
 lines of force passing from us through it, and when opposite 
 the north pole the lines of force are in the opposite direction. 
 Thus through the half revolution it will experience a right- 
 handed current, due to the algebraical loss of lines of force. 
 Exactly the opposite will be the case with the opposite 
 bobbin passing simultaneously from the north to the south 
 pole, the current being left-handed owing to a constant 
 algebraical gain of lines of force. 
 
 The arrangement of the bobbins is shown in section in 
 Fig. 215, b. The wires from the bobbins are brought to a pair 
 of common terminals in such a manner that both bobbins tend 
 
chap, vi] Current Induction. 341 
 
 to send a current in the same direction through the external 
 circuit. One of these terminals is connected with the metal 
 spindle, on which fits closely an ebonite cylinder carrying on 
 its surface two metal ferrules, whose arrangement depends on 
 the use to which the machine is to be put ; they are shown by 
 D and E. One of them (D) should be connected by a screw 
 which passes through the ebonite with the metal spindle, and 
 thus with one terminal of the bobbins. The other terminal 
 is insulated from the spindle but connected with the ferrule 
 E. The current is carried away from the ferrules by metal 
 springs which continuously press against them as they revolve 
 (Fig. 215, a). 
 
 If the ferrules are complete circles running side by side 
 round the ebonite cylinder, the machine gives alternating 
 currents. If D and E be the two halves of one ferrule 
 insulated from each other, so that the same spring which is in 
 contact with D during one half its revolution is in contact 
 with E during the other half-revolution, it is a commu- 
 tator reversing the current at each half-revolution, and so 
 making a continuous current in the external circuit ; just as 
 in Delezenne's Circle (Fig. 211). 
 
 For medical purposes the principal current is short-cir- 
 cuited, and when at its strongest is suddenly broken, thus 
 bringing in the direct and inverse extra current in the external 
 circuit, of which we have already noticed the high E.M.F. and 
 remarkable physiological action. This is accomplished where 
 the two half ferrules D and E are separated by a spiral line, 
 making D broad where E is narrow, and vice versa. When 
 the E.M.F. is smallest the contact springs press one on D and 
 the other on E ; but when the E.M.F. is greatest both at once 
 press on D or E and the current is short-circuited. When 
 
342 
 
 Electricity. 
 
 [Book III. 
 
 the induced current is strongest one spring passes over the 
 spiral line, suddenly breaking the short-circuit. 
 
 220. The Dynamo. Great attention has been paid in 
 recent years to the perfection of machines known as Dynamos, 
 for the generation of electrical currents, on the principles 
 foreshadowed in Clarke's machine. These machines are of 
 different types of construction, according as they are intended 
 to yield continuous or alternating currents. We can only 
 briefly indicate their chief features. 
 
 221. Continuous Current Machines. These consist 
 
 Fio. 215A.1 
 
 FIG. 215s. 
 
 Fio. 215c. 
 
 of field-magnets, composed in all the more powerful machines 
 
 1 This and most of the diagrams in relation to Dynamos are copied 
 from Prof. S. P. Thompson's standard work on Dynamo-Electricity, 
 and Machinery. The author wishes to record his thanks to Prof. 
 Thompson for his great kindness in allowing him to use them. The 
 following figures are also derived from that source : Figs. 216-219, 
 222, 236A, and 236c. 
 
c&ap. VL] Ciirrent Induction. 343 
 
 of massive iron cores, round which the exciting coils are 
 wound. Continuous with the cores are iron pole-pieces, 
 which are hollowed just large enough to admit of the rotation 
 of the armature within the hollow. The armature consists of 
 wire coils variously arranged in different types of machine. 
 The terminals of these coils are brought to a collector or 
 commutator of many sections fixed to the spindle of the 
 armature, but insulated from it and from each other. Against 
 this collector presses two * brushes ' made of copper, which 
 carry away the currents induced in the armature. 
 
 In the figures N S denote the pole-pieces, A the armature, 
 B the brushes, C the collector. In the older machines 
 called Magneto-Dynamos, the field-magnets consisted of steel 
 permanent magnets, which are often still employed in hand 
 machines. This arrangement is shown in Fig. 21 5A. When 
 electro-magnets were introduced for field-magnets they were 
 at first excited by a battery or an independent Magneto- 
 Dynamo. It was soon found, however, that the excitement 
 could as well be made by diverting the whole or part of the 
 current generated in the armature round the field-magnet 
 coils. We thus obtain the two types now in use, the series 
 dynamo (Fig. 215B), in which the whole of the current passes 
 round the field-magnets, and the shunt Dynamo (Fig. 215c), 
 in which the field-magnet coils form a shunt circuit. 
 
 It would at first sight appear that no magnetic field exists 
 initially to start the current, but in practice there is always 
 found to be sufficient residual magnetism in the magnet cores 
 to start a current, which rapidly rises just as the electrical 
 separation rises in an inductive electrical machine. 
 
 There are also methods in use combining the series and 
 shunt, adapting the dynamo to special purposes. 
 
344 
 
 Electricity. 
 
 [Book III. 
 
 222. Field- Magnets. These are made in a great variety 
 of forms. Sometimes two straight electro-magnets joined by 
 an iron yoke-piece are employed (Fig. 216A). In others we 
 have a pair of magnets with consequent poles (Fig. 216B). 
 Or, again, we have sometimes a variety of the simple horse- 
 shoe magnet (Fig. 216c). The most important thing is to 
 
 A FIG. 216. 
 
 have enough iron in the cores to give a field of sufficient 
 strength for the required machine without magnetising the 
 iron near to saturation, which is found to be wasteful. 
 It is also found important to have, as nearly as possible, a 
 complete magnetic circuit of soft iron, formed by cores, yoke- 
 piece, pole-pieces, and armature, with the narrowest air 
 spaces mechanically possible (see Art. 235A). 
 
 223. Armatures. These are made in a very great variety 
 
 FIG. 217. 
 
 of forms, but those most in use at present belong to the Drum 
 
chap, vi] Current Induction. 345 
 
 or Ring types. The simplest element of the drum winding 
 consists of a single loop of wire rectangular in form (Fig. 217), 
 with its ends connected to a two part commutator or collector. 
 It is shown in the position in 
 which the lines of force of the 
 field -magnet cut it at right 
 angles, and in which therefore 
 it intercepts the maximum num- 
 ber of these lines, while the 
 dotted portion shows that in 
 which it intercepts no lines of 
 force. / 
 
 An element of a ring arma- FIG. sis. 
 
 ture is shown in Fig. 218, in which a coil of wire connected 
 with a two-part commutator is placed on a ring. In this case 
 also the coil is supposed to be in the position in which the 
 maximum number of lines of force intercept it, and where, 
 consequently, the commutator comes into action. 
 
 In both these arrangements the current in each half-re- 
 volution rises from zero to a maximum, and sinks again 
 to zero. To remedy this irregularity other sets of loops 
 are so placed that one set comes into action just as another 
 declines, and one set is in the most when the other is in the 
 least advantageous position. Four such coils continuously 
 wound (that is, the end of one coil being connected with 
 the beginning of the next), and connected at their junc- 
 tion with the parts of a four-parted collector or commutator, 
 are shown, both of the drum and ring form (Figs. 219 a, 
 and 219 6). 
 
 The number of such coils can, of course, be increased with 
 advantage to the uniformity of the current. 
 
346 Electricity. [Book HI. 
 
 The ring and drum formed armatures are both provided 
 with iron cores, which help to complete the magnetic circuit 
 of the field-magnets, and by their induction increase the 
 strength of the field in which the coils are moving. These 
 
 FIG. 219A. FIG. 219s 
 
 cores, as has been pointed out (Art. 2*7), should be laminated 
 in planes parallel to the lines of force and direction of motion. 
 This is secured by building up the drum or ring of cir- 
 cular discs or rings of iron stamped out and clamped together, 
 but insulated from each other. 
 
 224. The Gramme Machine. This is a good example 
 of the ring type of armature. It consists of a cylindrical 
 ring (Fig. 220, a) made of soft iron, upon which is coiled 
 a continuous wire, forming in itself an unbroken circuit. 
 This coil, at thirty-two points equally distributed along it, has 
 wires soldered to it (AB . . .), which are in connection with 
 thirty -two separate copper pieces ((7), carefully insulated from 
 each other by mica plates, and surrounding the spindle of 
 
Current Induction* 
 
 347 
 
 FIG. 220. 
 
348 
 
 Electricity. 
 
 [Book III. 
 
 the armature. Against this cylinder of separate copper pieces, 
 above and below it, press two metal brush collectors, which 
 are connected with the terminals (FG) of the machine. 
 
 It is interesting to notice that the Gramme machine can 
 be used very effectively as a motor. Taking the dissected 
 diagram (Fig. 221), the current enters by the terminal (A), 
 and through the brush (7 enters the coils at 6, where it is 
 divided, part going through the coils on the semicircle bca, 
 and part through those on the semicircle bda. These parts 
 unite again at a, and pass by the brush D to the terminal .B, 
 by which the current returns to the battery. 
 
 FIG. 221. 
 
 The wire coiled round the iron core of the semicircle adb 
 tends to make it a magnet of horse-shoe type, having a south 
 pole at a, and a north pole at b. In the same way, the cur- 
 rent in coils round the iron core of acb being in the opposite 
 
chap, vi.] Current Induction. 349 
 
 direction, also make a south pole at a and a north pole at b. 
 Thus the iron circular core has a double south pole at a and 
 a double north pole at b. These will be repelled and attracted 
 by the poles of the permanent magnet, a being driven in the 
 direction ac, and b in the direction bd. This process is re- 
 peated as each successive portion of the coil comes in contact 
 with the brush, and a continuous rotation is maintained in 
 the direction acbd. 
 
 By the application of Lenz's law we might deduce the action 
 as a dynamo from that as motor. 
 
 225. Alternating Current Machines. In these ma- 
 chines the current given by the armature suffers very rapid 
 
 FIG. 222. 
 
 alternations of direction. This is generally obtained by 
 allowing the coils of the armature to pass through a succession 
 of magnetic fields, in which the lines of force are alternately 
 in opposite directions. The field-magnets consist of a series of 
 poles alternately N and S, arranged in a crown on two fixed 
 
350 Electricity. [Book in. 
 
 plates. The armature is of disc form, carrying coils of wire 
 with or without iron cores, arranged near its circumference so 
 as to pass alternately between the poles of the field-magnets. 
 The general arrangement of the coils and magnets will be seen 
 by studying Fig. 222, in which the arrangement is shown 
 diagramatically. It is obvious that on passing each pole the 
 E.M.F., and therefore the current^ is reversed in each coil. 
 The direction of the current round the successive coils will 
 be also opposite, but by fitting them together as indicated the 
 current is made continuous through all the coils. 
 
 For exciting the field-magnets a small continuous current 
 machine is commonly used, though there are various contriv- 
 ances by which the current from one or more coils in the 
 armature is separately rectified by a suitable commutator, 
 and used for charging the field-magnets. 
 
 This general arrangement is used in the Wilde, Siemens, 
 Gordon, Ferranti, and many other alternate current dynamos 
 now widely used for electric lighting. 
 
 226. The Incandescent Electric Lamp. One of the 
 great uses for dynamo-machines is the generation of electricity 
 for lighting purposes, and it will be convenient to say here a 
 few words about this application. There are two distinct 
 modes of lighting, by incandescent or glow lamps, and by 
 the arc lamp, besides one or two other methods which hold 
 an intermediate position between these two. 
 
 All the incandescent lamps (Fig. 223) at present in use 
 consist of one or more filaments of carbon (a), of horse-shoe 
 form, attached at their ends to stout platinum wires 6, T, 
 which are fused through the glass of the small globe d. These 
 globes are exhausted by a Sprengel mercury pump, and then 
 
tfhap VI.] 
 
 Current Induction. 
 
 351 
 
 hermetically sealed. By different inventors the whole vege- 
 table kingdom has been ransacked to find the fibre which 
 yields the most suitable carbon filament. These are heated 
 (air being excluded) to expel water and gases, and then 
 compressed in a mould. The chief difference between the 
 lamps in use is the source and mode of preparation of the 
 carbon filament and the nature of the residual gas. 
 
 PIG. 223. 
 
 Among the advantages these lamps offer for domestic illumi- 
 nation is the absence of the poisonous products of combustion 
 which make gas-lighted rooms absolutely fatal to plants, and, 
 in the absence of perfect ventilation, deleterious to human 
 health. The heating effect is small, since, although the carbon 
 filament is at a very high temperature, its mass is so small 
 that the quantity of heat given out never makes even the globe 
 unpleasantly warm to the touch. The light can be placed in 
 any position, as under water, or in contact with inflammable 
 materials, even in mines, where the air itself forms an in- 
 flammable comoound, without danger of fire. Even if the 
 
352 
 
 Electricity. 
 
 [Book III. 
 
 globe were accidentally broken, the carbon would be burnt 
 up and the light extinguished instantaneously, before any 
 material, however near (except an inflammable gas), could 
 come in contact with its heated filament. Moreover, the low 
 
 E.M.F. of the current makes 
 insulation a matter of great ease, 
 and removes the peculiar dangers 
 incident to electrical apparatus of 
 high potential when carelessly 
 handled. 
 
 227. The Arc Lamp. With 
 arc lights, the light appears between 
 the extremities of two carbon rods, 
 which are kept at a slight distance 
 apart in air. The carbons are both 
 burnt away, though unequally, that 
 forming the positive terminal the 
 more rapidly. To prevent the re- 
 duction and extinction of the light 
 by the consuming of the carbons, 
 various forms of automatic regu- 
 lator have been invented. The 
 principle of them can be under- 
 stood from the very simplest 
 that of the Browning lamp (Fig. 224). Its simplicity 
 depends chiefly on the fact that the lower carbon is fixed, 
 but its position can be regulated by hand by means of the 
 milled head (A\ which, acting on a lever, raises or de- 
 presses the lower carbon, which should be negative. The 
 upper carbon is held by a brass rod (J5), which slides freely 
 
 Pro. 224. 
 
chap, vi.] Current Induction. 353 
 
 in the upper framework, and naturally slides down until it 
 rests on the lower carbon. The sliding rod is pressed by a 
 small detent (D) at the end of a lever, whose opposite end 
 (E) forms the armature of a small electro-magnet (F). The 
 current passes through this electro-magnet to the positive 
 carbon, and across the arc to the negative. As soon as the 
 current passes, the detent presses on the sliding rod, and by 
 its friction prevents the carbon from falling ; but as the car- 
 bons are consumed, the resistance grows greater, the current 
 falls off, and the detent loses its hold, causing the carbon to 
 slide down. In a properly regulated lamp, the friction of 
 the detent and the strength of the electro-magnet are so well 
 balanced always that the carbon falls regularly, with but 
 small flickering of the light. 
 
 228. Source of the Voltaic Arc. The carbons must 
 be at first in contact. The current, encountering great resist- 
 ance at the point of contact, heats the carbons red hot, 
 making the air round them also hot, and therefore rarer, and 
 a better conductor. As the carbons burn away, the current 
 is still maintained by a series of disruptive discharges through 
 the hot air. These disruptive discharges are accompanied by 
 a stream of particles of carbon in an incandescent state, which 
 fly from the positive to the negative pole, as is proved by the 
 fact that the positive burns away about twice as fast as the 
 negative carbon, and by the form of the carbons, the positive 
 being regularly pointed, but with a hollow extremity, and 
 the negative irregularly convex, 
 
 22p. Arrangement of Lamps. Lamps may be ar- 
 ranged either in multiple arc, in which each lamp is connected 
 
354 
 
 Electricity. 
 
 [Book III. 
 
 with stout copper leads, the current being divided between 
 all the lamps (Fig. 2 25 A), or in series (Fig. 225B), in which 
 
 FIG. 225A. 
 
 PlO. 225B. 
 
 the negative terminal of each lamp is connected with the 
 positive of the next. In the former case we require only 
 E.M.F. sufficient for a single lamp, with sufficient quantity 
 to supply all the lamps in parallel. In the latter case we 
 require a high E.M.F., but quantity only sufficient for a 
 single lamp. 
 
 The relation between a dynamo and the external circuit 
 is practically identical with that between a battery and its 
 circuit. Where the external resistance is high (as when 
 lamps are in series), we wind the armature with great length 
 of thin wire, making the internal resistance large too ; but 
 where the lamps are in multiple arc, the whole resistance is 
 
chap, vi.] Current Induction. 355 
 
 but a fraction of that of a single lamp, and the coils of the 
 armature are wound with short lengths of thick wire, the 
 successive coils being often themselves placed in parallel. 
 The latter arrangement is that now almost exclusively 
 used, both dynamos and secondary batteries being made of 
 extremely small resistance. The whole E.M.F. of the 
 dynamo will then be effective in each 'branch of the divided 
 circuit, and each lamp will draw its own supply from the 
 source of electricity quite independently of the others. The 
 only practical limit is attained when the total resistance of 
 the many branches becomes comparable with the internal 
 resistance, and the current then is insufficient to supply all 
 the branches. 
 
 For this reason lamps are constructed, not of a given resist 
 ance, but of a given voltage, which means that they are used 
 in connection with a source of electricity, having the specified 
 E.M.F. 
 
 230. Theory of Self-regulation of Lamps in 
 Parallel. Let E be the E.M.F. of the source, r its internal 
 resistance, and let the external resistance consist of n lamps, 
 each of resistance R in parallel. Then the external resistance 
 
 is . Hence Ohm's formula gives 7= = n 
 
 n 
 So long as nr is very small compared with R, we shall have 
 
 7=^=- and there will be a current = to supply each of the 
 
 lamps, or there will be as much current through each of 
 twenty lamps as through a single lamp. 
 
 Where, however, nr is no longer negligible on account of 
 
356 Electricity. [Book ra. 
 
 the largeness of w, the total current does not increase propor- 
 tionally with the increasing number of lamps, and the illumi- 
 nation in each lamp declines as more are added. 
 
 231. Induction Coils. We have already noticed the 
 great E.M.F. possessed by certain induced currents, com- 
 pared to that of the battery current by which they are in- 
 duced. In the construction of an induction coil the aim is 
 to heighten as far as possible the E.M.F. , so as to give us 
 results comparable with those obtained by statical electricity. 
 The principle is this : Make a primary circuit by a stout 
 wire coiled a few times round a bundle of soft iron wires, 
 so as to make the strongest electro-magnet possible for the 
 dimensions. Kound this place a secondary coil consisting 
 of a vast number of turns of thin wire. If we rapidly 
 make and break contact in the battery circuit, each time the 
 electro-magnet is made or unmade, an inverse or direct 
 current passes in the secondary coil. The E.M.F. of this 
 current depends on (1) the strength of the magnetic field; 
 
 (2) the number of turns in the wire of the secondary coil ; 
 
 (3) the rapidity with which the current in the primary is 
 made and broken. 
 
 The parts in an induction coil (Fig. 226) are, in addition to 
 the battery, (1) a commutator (A\ by which the current is 
 admitted, and by which its direction can be reversed ; (2) a 
 contact breaker (B\ for alternately making and breaking 
 contact in the primary; (3) a condenser ((7), which makes 
 the breaking of contact more sudden ; (4) the primary 
 coil and core ; (5) the secondary coil, with insulated sliding 
 terminals (GH). 
 
Chap. VI.] 
 
 Current Induction. 
 
 357 
 
 The Commutator (Fig. 226). This usually consists of a solid 
 ebonite cylinder, having holes at either end for admitting a 
 
 FIG. 226. 
 
 spindle in two parts. Upon its surface are fastened two 
 brass plates connected by wires with the two ends of the 
 
 -GULF 
 
 Fro. 226A. 
 
 spindle, and against them press brass springs, which, by bind- 
 
358 
 
 Electricity. 
 
 [Book III. 
 
 ing-screws, are connected with the battery. The two up- 
 rights in which the spindle works are insulated from each 
 other, but connected with the contact breaker. 
 
 The Contact Breaker. This in large coils is an indepen- 
 dent engine, but in small coils is worked by the electro- 
 magnet of the primary coil. The end (A) (Fig. 227) 
 of the core is a powerful magnet pole, and attracts the 
 hammer-shaped piece of soft iron (B) which is carried by 
 a stiff spring (G). On this stiff spring opposite to B is a 
 
 BAT 
 
 BAT 
 
 PIG. 227. 
 
 metal stud, which makes contact by pressing against the 
 adjustable screw D. The passing of the current makes the 
 electro-magnet, which attracts B, and breaks the circuit in 
 doing so. B continues rapidly vibrating backwards and 
 forwards. The opposed surfaces must be of platinum, as any 
 other metal is rapidly oxidised, and the oxide acts as a 
 non-conductor to the current. 
 
Chap. VI.] 
 
 Current Induction. 
 
 359 
 
 The Condenser (Fig. 228). This is made of sheets, of tinfoil, 
 separated by silk or stout paper soaked in paraffin ; the alter- 
 nate sheets are connected with the opposite terminals of the 
 contact breaker. It is usually folded in a case, forming the 
 
 FTG. 228. 
 
 base of the instrument. The object of it is to reduce the 
 direct extra spark in the primary coil induced by making 
 and breaking contact. Without a condenser we have a bright 
 spark between the screw and stud each time contact is broken, 
 which, by prolonging the current, increases the time occupied 
 in destroying the magnet, and thus diminishes the E.M.F. of 
 the induced current. With a condenser the first effect of the 
 extra spark is to charge the condenser, and its E.M.F. is 
 thus rendered so low that hardly any spark passes, the con- 
 denser being discharged again by the extra spark on making, 
 which is in the opposite direction. 
 
 FIG. 229. 
 
 The Primary Coil (Fig. 229). This is composed of a few 
 thicknesses of stout copper wire (B) surrounding a bundle of 
 soft iron wires (A). The inner coil is connected with the 
 battery through the contact breaker. 
 
3 6 Electricity. [Book in. 
 
 The Secondary Coil. This (C) is coiled outside the primary 
 coil, very great care being taken to secure good insulation on 
 account of the high E.M.F. of the current passing through it. 
 Each wire is separated from its neighbour by some hard 
 insulator, and care taken that no two parts of the coil at 
 a great difference of potential shall be near to each other. 
 This is accomplished by dividing the secondary coil into 
 compartments by partitions of vulcanite, the coils in suc- 
 cessive compartments being connected in series, and the 
 current passing from the inside to the outside of one com- 
 partment, and from the outside to the inside of the next. 
 The length of wire on some secondary coils is as much as fifty 
 miles. The ends of the wire of the secondary coil are con- 
 nected to terminals which can be adjusted by a pair of in- 
 sulated handles. 
 
 232. Experiments with the Induction Coil. By 
 
 large induction coils, sparks of length up to 2 feet have been 
 obtained. They appear continuous, but their discontinuous 
 character can be shown by rotating a coloured disk or a spoked 
 wheel under the illumination of the spark, and it will be seen 
 the colours or spokes do not blend, but stand separately, as 
 they could not do were the light continuous. When the 
 spark passes through a wide air space, the effect is probably 
 due almost wholly to the direct induced current, as this, by 
 its higher E.M.F., can break through a greater air space than 
 the inverse. This is shown if we connect the terminals of a 
 Leyden jar with the terminals of the secondary circuit, which, 
 if there be a large break in the wire through which the spark 
 has to pass, will be charged by the direct current, but with- 
 out this break the direct and inverse current passing in equal 
 quantities neutralise each other. 
 
chap, vi.] Current Induction. 361 
 
 If we connect the platinum electrodes of a voltameter with 
 the terminals, water will be decomposed, but mixed gases 
 will be given off at both electrodes. If, however, we leave an 
 air space across which the spark breaks, we shall find the 
 gases, separated by the direct current only, collected at the 
 electrodes. 
 
 The power of the secondary spark can be much increased 
 by connecting the terminals with the inner and outer coats of 
 a Leyden jar. This condenses the spark, making fewer and 
 shorter sparks pass, but those sparks are of much increased 
 intensity. By this means metals and other substances can be 
 deflagrated for spectroscopic examination or other purposes. 
 
 Many chemical combinations can be made by the spark 
 from an induction coil. Thus a minute spark is sufficient to 
 cause hydrogen and oxygen to combine with explosive 
 violence, forming water. The passage of the current through 
 an hermetically sealed tube of air causes the oxygen and 
 nitrogen to combine, forming nitrous oxide. 
 
 233. Discharge through rarefied Gas, When the 
 discharge takes place in air or any gas or vapour in a highly 
 rarefied state, we obtain remarkable luminous appearances. 
 A stream of coloured beams, formed of the gas in a state of 
 incandescence, appears to flow from the positive to the negative 
 terminal, and by examination with the spectroscope gives 
 the spectrum of the gas. Frequently the stream of light has 
 a stratified appearance, not yet well understood. The best 
 way of observing these phenomena is by Geissler's tubes. 
 These are made of glass tubes and bulbs (Fig. 230), in various 
 shapes, with platinum wires fused through them at two points. 
 After being filled with some gas, as air, hydrogen, etc., they are 
 
362 Electricity. [Book in. 
 
 exhausted by the mercury pump, and hermetically sealed. On 
 connecting their terminals with the secondary coil, remark- 
 able streams of light are observed, more like the play of the 
 Aurora Borealis than any other natural phenomenon. In fact, 
 it is more than probable that the Aurora Borealis is produced 
 by a cause exactly analogous to these secondary discharges. 
 We have noticed that it always accompanies a magnetic 
 storm, during which the magnetic elements all over the 
 earth show sudden changes, and earth currents appear in the 
 earth, either as the cause or consequence of these magnetic 
 changes. If we remember that air at a sufficient height must 
 be, on account of its rarity, a conductor of electricity, we 
 might expect currents to pass in this conducting envelope, 
 induced by changes in the earth's magnetism. 
 
 Fm. 230. 
 
 234. Graham Bell's Telephone. One of the most 
 wonderful applications of induced currents in modern times 
 is found in Professor Graham Bell's telephone, which first 
 brought the telephone into general use. 
 
 To understand the telephone, we will first show two experi- 
 ments to prove the effect on which the telephone's action de- 
 pends. Take a narrow bobbin (Fig. 231 ) of thin wire, and place 
 it round the pole of a bar magnet, supported horizontally, in- 
 cluding a sensitive galvanometer in the circuit. On taking 
 a piece of thin plate iron, 2 or 3 inches in diameter, and 
 moving it towards the pole, we have an induced current 
 
Chap. VI.] 
 
 Ciirrent Induction. 
 
 363 
 
 in one direction, and on moving it away from the pole, we 
 have the induced current in the opposite direction. The 
 origin of these currents is easily understood. The iron plate 
 
 FIG. 231 
 
 becomes a magnet under the induction of the permanent 
 magnet, and on moving it towards the permanent magnet it 
 acts inductively upon it, altering its magnetism, and there- 
 fore causing an induced current. 
 
 Remove now the galvanometer, and replace it by a similar 
 magnet, also surrounded near one of its poles with a narrow 
 bobbin of thin wire (Fig. 232). Opposite the pole of this 
 magnet suspend an equal iron plate (E) with a long straw 
 
 FIG. 232. 
 
 pointer attached (the suspension may be a pin passing through 
 the straw), placed so as not to be drawn into contact with 
 the magnet pole. If we now take the former iron plate (A), 
 
364 Electricity. [Book in. 
 
 and move it about backwards and forwards with a regular 
 vibratory motion, we shall soon see the suspended plate 
 vibrating in sympathy with our movement of the first 
 plate. This is an exaggerated model of a pair of Bell tele- 
 phones, the first acting as transmitter, and the second as 
 receiver. 
 
 To understand how sounds are transmitted by this apparatus 
 we must remember that every sound consists of pulses com- 
 municated to the air, or the medium which conveys the sound, 
 the number of these pulses per second defining the pitch of 
 the note. It is clear, then, from the experiment, that if the 
 plate A be made to vibrate at a certain definite rate, the plate 
 B will vibrate at exactly the same rate, and therefore in 
 unison with it. That is to say, the note given out from B 
 will be of exactly the same pitch as the note sounded at A. 
 But the instrument does more, reproducing not only the 
 pitch, but also what musicians call the quality of the note, 
 as well as the very complex modification and superposition 
 of notes on which articulate speech depends. These produce 
 on the transmitter a very complicated system of movements, 
 which are by the induced currents absolutely copied at the 
 receiver, the only difference being that the sound is very 
 much weaker, and its quality is affected by the natural vibra- 
 tion of the metal plates, which gives the sound a peculiar 
 nasal intonation. 
 
 The actual construction of the instrument, in which trans- 
 mitter and receiver are identical, is shown in section, Fig. 233. 
 A is a magnet about 4 inches long, and \ inch in diameter. 
 Kound one pole is wound a coil of wire (B\ whose resistance is 
 from 70 to 350 ohms. The magnet and coil are protected by a 
 wooden case ((7), of which the thin part serves for holding the 
 
Chap. VI] 
 
 Current Induction. 
 
 365 
 
 instrument in the hand. At the 
 broad end is the mouth-piece, 
 consisting of a wooden ring, con- 
 cave inwards, shaped like the 
 mouth of a stethoscope, and im- 
 mediately behind it a plate of 
 ferrotype iron (E) (i.e. the iron 
 plate used in the process known as 
 ferrotype photography), loosely 
 held by three screws, which leave 
 it free to vibrate. At a very 
 small distance behind this plate 
 is the pole of the magnet, whose 
 distance must be regulated by a 
 screw (F), and carefully adjusted 
 in each instrument. From the 
 coil the wires are brought through 
 the wooden case to two binding- 
 screws. 1 
 
 With two of these instruments at opposite ends of a circuit 
 hundreds of miles in length, conversation can be carried on, 
 but the sound given out is so feeble that it is inaudible unless 
 the ear be placed in close proximity to the mouth of the 
 receiver. The instrument is also peculiarly liable to dis- 
 turbance from induction in the circuit ; the make or break 
 of contact in a telegraph wire, parallel to the telephone 
 wire, but 20 feet distant, causing a harsh grating sound 
 in the telephone, altogether overpowering the conversa- 
 tion. This is prevented by using a double wire, the return 
 
 1 It will be noticed that this instrument differs from the Reis 
 receiver (Art. 210) only in the addition of the iron plate. 
 
366 Electricity. [Book m. 
 
 wire being united with the direct, though of course insulated 
 from it. 
 
 It will easily be seen that the telephone of Graham Bell is 
 a very sensitive galvanoscope, and may be substituted for a 
 galvanometer in many cases where a delicate adjustment is 
 required, as in Wheatstone's bridge, while it forms an essen- 
 tial feature in many pieces of apparatus required for special 
 investigations, as the microphone, the induction balance of 
 Professor Hughes, and the tasimeter of Mr. Edison, all of 
 which followed rapidly on the invention of the telephone. 
 
 235. The Microphone. The Microphone consists essen- 
 tially of two pieces of carbon resting loosely one upon the 
 other. A very simple form is that shown (Fig. 234), in which 
 two square bars of gas carbon are fastened to an upright piece 
 of wood, and joined by another square bar, also of gas carbon, 
 tapering at its ends, which rest loosely in sockets sunk in the 
 horizontal bars. On passing a battery current, great resistance 
 is encountered at the loose contacts, and any vibration in the 
 instrument makes rapid alterations in these contacts, therefore 
 rapid alterations in the resistance, and therefore again rapid 
 alterations in the current. These are easily observed by simply 
 including a Graham Bell telephone in the circuit. If the 
 wooden base of the microphone be scratched with the finger- 
 nail a very harsh grating sound is produced in the telephone, 
 while the ticking of a watch is heard with remarkable 
 loudness. In more sensitive forms of the instrument 
 the walk of a fly over it is said to suggest the tramp of a 
 regiment. 
 
 The forms of the microphone are infinite. A jar of cinders 
 having electrodes sunk in it, resting on a vibrating plate, 
 
Chap. VI.] 
 
 Current Induction. 
 
 367 
 
 has been used with success, as also a heap of nails, or any 
 conductors or semi-conductors piled loosely together. 
 
 FIG. 234. 
 
 The invention of the microphone following rapidly on that 
 of the telephone, led to attempts to use some form of the 
 microphone as a transmitter, and the telephone as a receiver 
 only. This idea though present in the loose platinum contact 
 of the Reis receiver has received its practical accomplish- 
 ment in the loud-speaking Gower-Bell Telephone, used in the 
 Telephone Exchange. The transmitter is a wooden plate, on 
 the under-side of which is suspended a microphone (Fig. 235) 
 of peculiar form. The transmitter also contains a small 
 electro-magnet, which is included with the microphone in 
 the battery circuit. This seems to act by heightening the 
 
3 68 
 
 Electricity. 
 
 [Book III. 
 
 extra current which accompanies each change in the main 
 current. The receiver is a telephone of peculiar construction. 
 
 FIG. 235. 
 
 The inside is shown (Fig. 236, b), in which A is a strong 
 permanent magnet, over whose poles are two coils of wire 
 
 FIG. 236. 
 
 (B) with soft iron armatures. The varying strength of the 
 current in the coils alters the magnetism of the cores, and 
 
chap, vi.] Current Induction. 369 
 
 causes vibration in the plate of thin sheet-iron, which is 
 adjusted so as to be all but in contact with them. The plate 
 is held in the outside case (Fig. 236, a), which has an aperture 
 in the centre, through which the sound caused by the vibra- 
 tion of the plate escapes. 
 
 The sound from the Gower-Bell telephone is much louder 
 than that obtained from the ordinary Bell telephone, but it 
 can only be heard when the ear is placed within a few inches 
 of the receiver. 
 
 235a. Experiments on the Magnetic Circuit. We 
 
 now return to the magnetic circuit already alluded to in con- 
 nection with dynamo construction. The whole subject has 
 been ably treated by Prof. S. P. Thompson in the Cantor 
 Lectures, from which we select the following illustrative 
 experiments : 
 
 Take an electro-magnet made of soft iron in horse-shoe 
 form, excited by coils of wire carrying current round its arms 
 in the ordinary manner ; it is also furnished with an armature 
 of soft iron. Exploring coils, con- 
 sisting each of a few turns of 
 wire, are wound, one round the 
 soft iron core (A) at the middle 
 of the magnet or top of the 
 horse-shoe, a second (B) round 
 one pole, and a third (0) round 
 the middle of the armature. 
 These coils are all equal, and 
 connected in turn with a sensi- 
 tive mirror galvanometer. The 
 throw of the galvanometer ob- 
 
37 Electricity. [Book in. 
 
 tained by reversing the current in the exciting coils measures 
 the number of lines of force embraced by the exploring coil, 
 or, as it is called, the magnetic flux through it. 
 
 The coil A embraces all the lines of force, and we will first 
 assume it to be connected with the galvanometer. When the 
 armature is attached there is found to be a much greater 
 magnetic flux through A than when the armature is separated 
 even by a millimetre of air space, and the further it is removed 
 the smaller and smaller the flux becomes. This experiment 
 shows that the air resists the flow of magnetic lines through 
 it, as compared with an equal space occupied by iron, the 
 intensity of magnetisation of the iron, therefore, depend- 
 ing not only on the amount of iron present, but on the other 
 material through which lines of force have to be forced. This 
 leads to the idea of resistance offered by various materials to 
 the flow of magnetic lines through them, such magnetic resist- 
 ance depending, like electrical resistance, on the shape of the 
 bodies, and the materials of which they are made. Iron is, 
 of course, the best conductor, but different varieties differ 
 very much, non-magnetic bodies being all not very different 
 from air. The term permeability is applied to denote the 
 magnetic conductive power of different materials ; its reci- 
 procal representing their specific resistance. In a magnet of 
 bar form the lines of force leak out more or less sideways, and 
 the coil B is placed to measure the number of lines which 
 traverse it under different conditions. The coils B and A being 
 equal, the throws obtained by connecting them alternately 
 with the galvanometer gives a comparison of the number of 
 lines traversing them under the same conditions of magnet 
 and armature. It is always found that the magnetic flow 
 through B is less than through A, but attaching the armature 
 
chap, vi.] Current Induction. 371 
 
 brings them up much nearer to equality, and the further it 
 is removed the more unequal they become. 
 
 The number of lines again which traverse C are always 
 smaller than those which traverse #, owing to leakage into 
 air, but the proportion is again increased in very high degree 
 by attaching the armature. 
 
 If a permanent magnet were used, and exploring coils 
 wound round it as described, the number of lines of force 
 shown by A is not altered by removing the armature, the 
 number of lines being fixed by the initial magnetism ; but the 
 indications of leakage shown by B and G are similar in char- 
 acter to those described above. 
 
 In the Cantor Lectures are also very interesting experiments 
 on the tendency of the magnetic circuit to reduce its resist- 
 ance. Thus a piece of iron, free to move, places itself in the 
 strongest part of the field, so as to transmit the greatest 
 possible number of lines of force through the smallest 
 possible resistance. A hollow coil of wire will suck in, 
 for the same reason, a rod of soft iron balanced over its 
 centre, when an exciting current is passed through the coil. 
 
 We have, too, the paradoxical experiment, which Prof. 
 Thompson calls the Electro-magnetic Pop-gun. A short 
 electro-magnet is made, whose core consists of a tube of iron 
 about two inches long. A piece of iron, about an inch long, 
 is placed in the mouth of the tube. On turning on the 
 current the piece of iron is expelled with some force. Here 
 the magnetic circuit tries to complete itself, lengthening the 
 core by pushing out the small piece of iron, and so affording 
 a shorter air space for lines of force to traverse. 
 
 235!?. Ammeters and Voltmeters.-~In connection 
 
372 
 
 Electricity. 
 
 [Book in. 
 
 with practical uses of electricity new forms of direct reading 
 galvanometers for registering the number of amperes trans- 
 mitted, and the volts between two points in a circuit, have 
 been invented under the names given above. One form for 
 continuous current use is shown in horizontal plan. NS are 
 
 the poles of a permanent 
 magnet, along the equator of 
 which runs a helix of wire 
 A, A, composing the circuit. 
 Within this helix is a soft 
 iron needle (5), connected 
 with which, and above it, is a 
 pointer ((7), which registers 
 the number of amperes or 
 volts. The action is as fol- 
 lows: The needle of soft 
 iron is held by induction 
 along the axis NS of the per- 
 manent magnet. When a 
 current passes the needle is 
 deflected and takes up an in- 
 clined position. The needle being of soft iron, and not a 
 permanent magnet, displacement alters its magnetisation. 
 As a consequence the tangent principle does not apply, and 
 by suitable adjustment the deflection becomes practically pro- 
 portional to the number of volts or amperes which are then 
 read off directly. 
 
 If for an ammeter the coil is short and of very stout wire, 
 and the instrument is placed in the circuit. If for a volt- 
 meter the coil is of thin wire, and high resistance, forming a 
 shunt circuit between the two points where it is inserted. 
 
 FIG. 236B. 
 
chap, vi.] Current Induction. 373 
 
 If its resistance is high enough not sensibly to alter the 
 currents in the rest of the circuit, it directly indicates the 
 E.M.F. between these two points in volts (see Art. 165). 
 
 For alternate current machines the above type of instru- 
 ment cannot be used, as current and E.M.F. are both con- 
 stantly changing their direction. In this case instruments 
 are used whose indication depends on the square of the 
 current, which is always of the same sign. Two principles 
 are used the heating effect and the electro-dynamic attraction 
 and repulsion of portions of the same current. Professors 
 Ayrton and Perry have made very efficient instruments 
 depending on the heating effect of a current on a spiral made 
 of a wide metal shaving, in which if one end be left free, 
 heating causes a rotary movement in a needle attached to 
 the free end. 
 
 2350. Transmission of Electrical Power. Trans- 
 formers. Since the energy given out per second from a bat- 
 tery or dynamo is measured by the product of an E.M.F. and 
 a current strength (Art. 169), to any rate of working or horse- 
 power there will be a certain equivalent of electrical energy, re- 
 presented by this product. Thus the same horse-power would 
 supply 4 amperes at 1000 volts, or 40 amperes at 100 volts. 
 If this amount of power had to be transmitted to a distance 
 through a metal conductor, the current of 40 amperes would 
 generate 100 times as much heat as the current of 4 amperes 
 (for heat given out is proportional to current strength squared), 
 or for the same degree of heating the section must be 100 
 times as great. Thus it is obviously more economical to 
 transmit the power as 4 amperes at 1000 volts, rather than as 
 40 amperes at 100 volts. It is more economical, therefore, to 
 
374 
 
 Electricity. 
 
 [BooklH 
 
 transmit electrical energy at a high E.M.F. and low current 
 strength, rather than at a low E.M.F. and high current 
 strength. 
 
 The consumer who uses the current delivered from the 
 distant generator will require it at a higher strength and 
 a proportionally lower E.M.F, Transformers were invented 
 to make this possible, and they are very largely in use where 
 the alternate current system of distribution prevails. 
 
 An efficient form of transformer consists of a gramme ring 
 wound with two sets of coils placed in sections side by side, 
 but well insulated from each other. The high potential 
 current is passed through one set of coils, consisting of 
 
 long thin wire, the transformed 
 current is received from the other 
 set of coils, which are composed of 
 relative short and stout wires. The 
 current yielded by the transformer 
 (which is a form of induction coil) 
 is induced by the rapid reversal of 
 the magnetism in the ring, and 
 since leakage of lines of force from 
 a ring is practically nil, the energy 
 (measured in watts) given out by 
 
 the transformer is nearly the same as that abstracted 
 from the primary circuit. Thus, by properly arranging the 
 resistances of the two sets of coils, any relation between the 
 value of the current strength and E.M.F. can be obtained, 
 subject to the condition of constancy of their product. 
 
 FIG. 23Co. 
 
Questions on Book III. 375 
 
 QUESTIONS ON BOOK III. 
 CHAPTERS I. IV. 
 
 1. Given that one litre of hydrogen at normal temperature and 
 pressure * weighs '08957 grams : find what volume of hydrogen is 
 given off for each gram of zinc consumed in each cell of the battery. 
 
 ANS. -343 litre. 
 
 2. A litre of oxygen weighs 1 '4298 grams. Find the weight of zinc (^ 
 consumed in each cell of a battery before 100 cub. cm. of oxygen have 
 been collected in a voltameter. 
 
 ANS. -581 gram. 
 
 3. In a decomposition of copper sulphate, it is found that '59 gram 
 of copper is separated. Find the amount of zinc consumed in each 
 cell of the battery. _ 
 
 ANS. '606 gram. 
 
 4. Four Grove cells in compound series are used to decompose 
 hydrochloric acid. Find the total weight of zinc used in obtaining 
 one gram of chlorine. 
 
 ANS. 3*66 gram. 
 
 5. In the decomposition of hydrochloric acid find the volumes of 
 hydrogen and chlorine respectively separated when one gram of zinc 
 has been consumed in each cell of the battery. One litre of hydrogen 
 weighs -08957 gram. - , * ^ jJi\+ - 3 * ? c < 
 
 ANS. 343 cub. cm. of each. *"/ 0"/f 7 
 
 1 It will be assumed throughout this Exercise that gases are at 
 normal temperature (0 C. ) and pressure (760 mm. of mertury). 
 
3 7 6 Questions on Book III. 
 
 6. Draw the potential gradient for three cells in compound circuit 
 and no external resistance. Show from the gradient that the current 
 is the same as for a single cell. '"Jv-C*/* \ 
 
 7. Draw the potential gradient for three cells in compound circuit, 
 each separated from the next by a wire whose resistance equals that 
 of a single cell, a point midway between two cells being to earth. 
 
 
 
 8. Draw the potential gradient for one cell and for three cells in 
 simple circuit having the same external resistance. Show that if 
 the external resistance be large the current is nearly the same in 
 
 9. In a certain circuit the potential difference between the extremi- 
 ties of a resistance of 300 ohms is equal to 16 volts. Find the whole 
 E.M.F. if the total resistance in the circuit is 2400 ohms. 
 
 10. Find the current strength in a circuit with E.M.F. of 9 '8 volts 
 and resistance 5 ohms. 
 
 ANS. 1'96 amperes. 
 
 11. Find the resistance in a circuit if an E.M.F. of 10 volts gives a 
 current of 1 "6 amperes. 
 
 ANS. 6 '25 ohms. 
 
 12. Find the E.M.F. if the current strength in the circuit be 3 '5 
 amperes, and the resistance 24 ohms. 
 
 ANS. 84 volts. 
 
 13. It is found experimentally that one coulomb of electricity sets 
 free '0000105 gm. of hydrogen. Find in amperes the strength of a 
 current which has yielded '035 grm. of hydrogen in two minutes. 
 
 ANS. 27 "7 amperes. 
 
 14. Find the weights of silver, chlorine, and copper which will be 
 set free by one coulomb of electricity. 
 
 ANS. -001134 gram silver; '0003727 gram chlorine ; '0003318 gram 
 copper. 
 
 15. A current of two amperes passes for five minutes through a 
 voltameter : find the total weight of water decomposed. 
 
 ANS. '0567 grams. 
 
 \ 
 
Questions on Book III. 377 
 
 16. A battery of several cells is included in a circuit with a volta- 
 meter and tangent galvanometer. After passing the current for five 
 minutes, '098 grams of hydrogen were collected, and the average read- 
 ing of the tangent galvanometer taken each ten seconds was 55. 
 Find the current in amperes, and find the constant multiplier re- 
 quired to convert the galvanometer indication into current measure 
 in amperes. 
 
 ANS. 31'1 amperes: 21'8 nearly. 
 
 17. A battery of five cells when short-circuited with a galvanometer 
 of no resistance gives a deflection of 9. On introducing 20 ohms 
 resistance the deflection sinks to 3. Find the internal resistance of 
 the battery. 
 
 ANS. 10 ohms. 
 
 18. A single cell when short-circuited gives in a galvanometer 45, 
 and when 2 '5 ohms are introduced it falls to 26^. Find the sum 
 of the resistances of the battery and galvanometer, and calculate the 
 galvanometer reading when five more ohms are introduced. 
 
 ANS. 2'5 ohms: 184 nearly. 
 
 19. Using a sine galvanometer whose resistance is '3 ohm, a battery 
 gives 72 when short-circuited. On introducing 15 ohms resistance 
 the deflection falls to 36. Find the resistance of the battery. 
 
 ANS. 24 ohms. 
 
 20. A battery short-circuited gives 54 deflection to a sine galvano- 
 meter. Find the reading of the galvanometer when the total resist- 
 ance is doubled. 
 
 ANS. 24 nearly. 
 
 21. A circuit, including battery and tangent galvanometer only, 
 gives a deflection of 63. On introducing 20 ohms additional resist- 
 ance, the reading is 42, and on introducing a coil of unknown 
 resistance in place of the 20 ohms, the reading is 25 : find the 
 resistance of the coil. 
 
 ANS. 54*5 ohms. 
 
 22. The resistance of the battery is known to be 24 ohms, and of 
 the tangent galvanometer '5 ohm. On short-circuiting the reading is 
 42. On introducing a coil of wire the reading sinks to 25. Find 
 the resistance of the coil. 
 
 ANS. 22-8 ohms. 
 
Questions on Book III. 
 
 23. A battery cell gives a resistance of 4'5 ohms, and the (tangent) 
 galvanometer resistance is nil. On short-circuiting, the reading of 
 the galvanometer is 144. Find the reading on introducing 5 ohms 
 resistance. 
 
 ANS. 7. 
 
 24. Find the resistance of a silver wire one metre long, and sectional 
 area '0007791 sq. cm. (British Wire Gauge, No. 30). 
 
 ANS. '195 ohm. 
 
 25. Find the sectional area of a copper wire of which one meter 
 offers resistance 1 ohm. 
 
 ANS. '0001642 sq, cm. 
 
 26. Find the length of a mercury column one sq. mm. in section, 
 whose resistance is 1 ohm. 
 
 ANS. 1'04 metre. 
 
 27. Find the ratio of the resistance of silver and platinum wires of 
 the same dimensions. 
 
 ANS. 1 to 6-02. 
 
 28. Find the internal resistance of a cell containing dilute sulphuric 
 acid (5 per cent, acid), the plates measuring 12 cm. by 8 cm., and 
 being separated by 2 cm. 
 
 ANS. '1 ohm nearly. 
 
 29. Find the resistance of an iron telegraph wire, 30 kilometres long, 
 and whose sectional area is '1051 sq. cm. (B. W. G., No. 9). 
 
 ANS. 280 '5 ohms. 
 
 30. Four cells, each of E.M.F. 1*8 volt, and resistance 1-5 ohm, 
 with a galvanometer of 3 ohms resistance, are fitted up in compound cir- 
 cuit with an external resistance of 23 ohms. Find the current strength. 
 
 ANS. '225 ampere. 
 
 31. Compare the current with that obtained from one cell with the 
 same e.xternal conditions. 
 
 ANS. As 55 : 16. 
 
 32. Six cells, each of E.M.F. T07 volt, and resistance 3'6 ohms, 
 with a galvanometer of '4 ohm resistance, are fitted up in simple 
 circuit with an external resistance of one ohm. Compare the current 
 with that obtained from one cell with the same external conditions. 
 
 ANS. As 5 to 2. 
 
Questions on Book III. 379 
 
 33. Five Bunsen cells, each of E.M.F. 1'8 volts, and internal re- 
 sistance 1*2 ohms, are used in compound circuit with a resistance of 
 24 ohms : find the current in absolute measure, 
 
 ANS. '03 in absolute electro-magnetic units. 
 
 34. Will it be better to arrange six Daniell cells in simple or com- 
 pound circuit, the resistance of each cell being '6 ohm, and the 
 external resistance 2 '4 ohms ? 
 
 ANS. Compound series. 
 
 35. Twenty-four cells, each of E.M.F. 1'6 volt, and of 2'4 ohms 
 resistance, are arranged in four rows. If the external resistance be 
 6 ohms, find the current strength. 
 
 ANS. 1 ampere. 
 
 36. Calculate the best arrangement of 48 cells, each of internal Q^-A 
 resistance 1'5 ohms when the external resistance is 12 ohms. 
 
 ANS. Either two rows or three rows. 
 
 37- Find the resistance in a divided circuit whose two branches 
 offer resistances 6 ohms and 30 ohms respectively. 
 ANS. 5 ohms. 
 
 38. What resistance is offered by a divided circuit of three branches, 
 in which there are resistances of 6, 8, and 24 ohms ? 
 
 ANS. 3 ohms. 
 
 39. The plates of a cell whose E.M.F. is 1-9 volt, and whose /- 
 resistance is 2 '8 ohms, are joined by three wires whose resistances 
 are 2, and 3, and 6 ohms respectively. Find the current in each 
 branch. 
 
 ANS. '25 ampere ; *16 ampere ; '083 ampere. 
 
 40. Find how many grams of water would be heated 1 C. by ~ 
 immersing in it a wire coil whose resistance is 7 ohms, and passing I 
 a current of '3 ampere for five minutes, supposing all the heat 
 communicated to the water. 
 
 ANS. 45 grams. 
 
 41. Eight Daniell cells, of each of which the E.M.F. is 1 volt, and 
 resistance 3 "5 volts, are arranged in compound circuit, and the ter- 
 minals joined by a wire of 35 ohms resistance, which is immersed in 
 
380 Questions on Book III. 
 
 a kilogram of water. Find the rise in temperature of the water after 
 the current has passed for ten minutes, supposing no heat to escape. 
 ANS. -08 C. 
 
 CHAPTERS V. AND VI 
 
 42. A straight bar magnet is placed in the field of a straight wire 
 traversed by a voltaic current. Explain the position which the 
 magnet will take up. If the direction of the current be reversed, 
 what change will take place in the magnet's position ? 
 
 43. A vertical wire carrying a current is brought near to different 
 parts of a magnet, suspended so as to move horizontally. Explain at 
 what parts of the surface attraction or repulsion will be shown. 
 
 44. A vertical wire carries an upward current. In what direction 
 would it be carried if free to move under the earth's magnetic field ? 
 
 45. A horizontal wire carries a current from east to west. In what 
 direction would it move under the action of the earth's magnetism ? 
 
 46. A straight wire is pivoted at one end so as to move freely in a 
 horizontal plane, and is traversed by a current which flows from the 
 pivot. Find the direction in which it will move under the earth's 
 magnetism. 
 
 47. A straight and thin bar magnet is held parallel to the surface 
 of water on which is a De la Rive's floating battery. Describe the 
 position which the floating battery would take up under the magnetic 
 force. 
 
 48. If a straight wire carrying a current be placed over the water 
 near the floating battery, what position will it take up ? 
 
 49. Describe how a coil of wire, traversed by a current, would place 
 itself if suspended between the poles of a horse-shoe magnet. 
 
 50. Show that a galvanometer could be constructed by means of a 
 coil of wire traversed by the current suspended between the poles of 
 a powerful horse-shoe magnet. 
 
Questions on Book III. 18 1 
 
 51. How would a coil of wire, traversed by a current, place itself 
 if suspended within the core of another coil traversed by the same 
 current ? 
 
 52. A beaker is placed on one pole of an electro-magnet and filled 
 with liquid, which is traversed by a current from the centre to the 
 circumference. What motion would be observed in the liquid ? 
 
 53. A wide beaker is placed on one pole of an electro-magnet of 
 horse-shoe form, and filled with dilute acid. At the bottom of the 
 acid is put a zinc plate, and near its surface a copper plate, from both 
 of which insulated wires pass to outside. Show that on connecting 
 these wires together the liquid will begin to move. 
 
 54. When a wire is dipped into a small mercury cup on the pole of a 
 magnet, and the current passed through it, the mercury is often seen 
 to be rapidly rotating. How do you explain this ? 
 
 55. The two rails of an ordinary railway are insulated from each 
 other, but connected with the two terminals of a powerful battery, so 
 that the current passes through the rails to wheels and axles of the 
 carriages placed upon the line. Show that if the current were strong 
 enough, the carriages would move along the line under the magnetic 
 field of the earth, the direction of motion depending on the direction 
 of the battery current. 
 
 56. A vertical wire, forming part of a closed conductor, is moved 
 rapidly from east to west : show the direction of the induced cur- 
 rents. 
 
 57. A horizontal wire, forming part of a closed circuit, is placed 
 east and west, and carried towards the north. What will be the 
 direction of the induced current ? 
 
 58. A copper hoop in a vertical plane is rapidly rotated about a 
 vertical diameter, and a magnet is suspended horizontally at its centre. 
 Show that the induced currents in the hoop will cause the magnet 
 to be deflected in the direction of the rotation. 
 
 59. A metal sheet, held vertically, is drawn between the poles of 
 an electro-magnet, its upper and lower edges being pressed by fixed 
 springs which are connected with an external galvanometer. Draw 
 a diagram showing the direction of the current in the galvanometer. 
 
382 Questions on Book ///. 
 
 60. A stream of liquid is flowing between the poles of an electro- 
 magnet. In what position would you place electrodes to test for an 
 induced current in the liquid ? 
 
 61. A soft iron horse-shoe coiled with wire has its extremities placed 
 opposite the poles of a horse-shoe magnet. If the ends of the wire 
 be connected with a galvanometer at a distance, what currents will 
 be observed on drawing the horse-shoe away from the magnet and 
 moving it towards the magnet again ? 
 
 62. Show that the swing of a compass-needle will be " damped " by 
 hanging in a metal box. 
 
 63. If insulated wire be coiled round a metal cylinder, show that 
 induced currents will travel round the cylinder at every change of 
 current in the wire. How would you prevent these currents without 
 abandoning metal as the material of which the cylinder is made ? 
 
BOOK IV. 
 THERMO-ELECTRICITY. 
 
 236. Definition of Thermo-Electricity. If two rods 
 of different metals be soldered at their ends, and not in 
 contact elsewhere, on bringing the junctions to different 
 temperatures, a current of electricity flows round the cir- 
 cuit made by the two metals. To this current, and the 
 phenomena which accompany it, is given the name of Thermo- 
 Electricity. 
 
 237. Elementary Experiments. The phenomenon, 
 which was discovered in 1821 by Professor Seebeck of Berlin, 
 is very easily shown by a strip of copper bent down at its 
 
 FIG. 237. 
 
 ends, and soldered to a bar of bismuth (Fig. 237), a magnet 
 being pivoted so as to swing freely between the copper and 
 
384 
 
 Electricity. 
 
 [Book IV. 
 
 bismuth. After placing the compound bar in the magnetic 
 meridian, so that the needle remains parallel to it, we observe, 
 on heating one junction with a spirit-lamp, that the needle 
 is immediately deflected, the direction of the deflection 
 proving that a current flows from the bismuth to the copper 
 through the hot junction. If, instead of heating with a 
 spirit-lamp, we cool this junction with ice, the magnet will be 
 deflected in the opposite direction. 
 
 The apparatus is made more sensitive by being arranged as 
 in Fig. 238, with a galvanometer of low resistance between 
 the binding-screws which are attached to the copper. In 
 this case the heat of the finger applied to one junction will 
 cause a considerable deflection in the galvanometer. 
 
 FIG. 238. 
 
 238. The Thermopile. To still further increase the 
 sensitiveness, a number of couples are arranged in compound 
 series (Fig. 239, a), and are folded together as in Fig. 239, b, 
 to bring all the junctions of the same kind into a small area, 
 generally in form a square. The instrument then forms the 
 
Book IV.] 
 
 Thermo- Electricity. 
 
 335 
 
 essential part of a thermopile (Fig. 240), whose terminals 
 are joined in circuit with a delicate galvanometer of low re- 
 
 FIG. 239. 
 
 sistance. The cone of polished metal attached is useful in 
 experiments on radiant heat to limit the area from which the 
 radiations proceed on to the face of the thermopile. The 
 
 FIG. 240. 
 
 metals employed in the thermopile are usually bismuth and 
 antimony, which of all the more common metals give the 
 
 2B 
 
386 Electricity. [Book iv. 
 
 highest E.M.F. at ordinary temperatures, though a couple of 
 bismuth and tellurium would be of much higher power. 
 
 With a good thermopile a considerable deflection will be 
 given to the galvanometer by holding the hand a yard from 
 one face ; otherwise a heated poker, or the blackened surface 
 of a vessel containing hot water (Leslie's cube), may be em- 
 ployed. It was by help of the thermopile that Melloni and 
 Tyndall carried out their researches on radiant heat, and 
 that astronomers have been able to detect and measure the 
 heat reaching us from the moon and the brighter fixed 
 stars. This shows that it is in skilful hands infinitely the 
 most delicate thermometer we possess. 
 
 239. Thermo-electric Power and Diagram. Seebeck 
 thought that, with a given couple, the E.M.F. of the thermo- 
 electric current was proportional to the difference of tempera- 
 ture. Such is only the case if the mean of the temperatures 
 of the hot and cold junctions be constant. Thus, for each 
 pair of metals we may determine at each temperature the 
 E.M.F. in a circuit made of these metals, one junction being 
 half a degree above and the other half a degree below the 
 assigned temperature. This E.M.F. per degree of temperature 
 at a given temperature is defined to be the thermo-electric 
 power of that pair at that temperature. 
 
 Professor P. G. Tait, by measuring the E.M.F. of pairs of 
 metals through the whole range of mercury thermometers, 
 has shown that in each pair the change in thermo-electric 
 power is proportional to the change in temperature. If, 
 therefore, we construct a figure in which horizontal lines re- 
 present temperatures, and vertical lines the thermo-electric 
 powers of a given couple, the extremities of the vertical lines 
 
Book IV.] 
 
 Thermo- Electricity. 
 
 387 
 
 would all lie on a straight line. Thus, in Fig. 241, if the base 
 line represent any metal (say lead), the thermo-electric power 
 of a lead-copper pair would be given by a line such as P P, 
 and of a lead-iron pair by such a line as Q f Q, the lead being 
 positive to the iron through the part of the diagram where 
 the iron line is above the base line, and negative where be- 
 low it. 
 
 U M' M > 
 
 FIG. 241. 
 
 Moreover, it appears from experiment that if at a given 
 temperature we observe the thermo-electric power of two 
 metals A ~B, and also that of a pair C, then their difference 
 will always give us the thermo-electric power of the pair A C. 
 Consequently, if we draw one ordinate MPQ through the dia- 
 gram for the temperature OM, so that PM represents on our 
 assigned scale the thermo-electric power of Cu Pb, and QM 
 that of Fe Pb, then QP will represent the thermo-electric 
 power of Fe Cu on the same scale. 
 
 Thus, taking as base line any metal (and there are theo- 
 
388 Electricity. [Bookiv. 
 
 retical reasons for choosing lead), each of the metals will be 
 represented through ordinary temperatures by a straight line, 
 and the thermo-electric power of any pair of metals can be 
 at once taken from the diagram by drawing an ordinate 
 through the assigned temperature, and measuring the dis- 
 tance between its section with the lines of the two metals. 
 Such a diagram has actually been constructed by P. G. Tait, 
 and Fig. 241 is a rough copy of the actual lead, copper, 
 and iron lines in his thermo-electric diagram. 
 
 To find the E.M.F. of a given pair with junctions at the 
 assigned temperature, we have only to find the thermo- 
 electric power at the mean of the two temperatures, and 
 multiply it by the range. Thus, if we require to find the 
 E.M.F. of the Fe Cu pair with junctions at temperatures 
 denoted by M, M' t the thermo-electric power at the mean 
 temperature is (PQ + P'Q'\ and the E.M.F. is therefore 
 %(PQ + P'Q 1 ) x (OM- OM'\ But by ordinary geometry this 
 expresses the area of the trapeze Q'Q PP. Since throughout 
 the range copper is positive to iron, the direction of the 
 current is from copper to iron, through the hot junction, or 
 in the direction P'PQQ'. 
 
 It will be noticed in the diagram that the Fe and Cu lines 
 intersect at a point N, whose temperature is about 284 C., 
 and therefore well within the range of experiment. 
 
 At this point Fe and Cu are neutral to each other, below 
 that temperature Cu being + to Fe, and above it to Fe. 
 The existence of such a point was demonstrated first by 
 J. Gumming 1 soon after Seebeck's discovery. On arranging a 
 
 1 Late Professor of Chemistry in the University of Cambridge. 
 There is reason for believing that he independently discovered 
 Thermo-electricity. 
 
Book iv.] Thermo- Electricity. 389 
 
 Fe-Cu couple brazed together at the junctions, and arranged 
 as in Fig. 238, on heating one junction and leaving the other 
 at the air temperature, the current in the galvanometer is 
 seen to rise slowly to attain a maximum, when the tempera- 
 ture of the hot junctions is about 284, and then slowly to 
 sink again as the heating is continued. 
 
 This is quite in accordance with what the rule given above 
 teaches us, since, if the hot junction were above, and the 
 cool below the neutral temperature, the trapezium would de- 
 generate into two triangles, of which that to the right must 
 be subtracted from that to the left. 
 
 240. Electro-motive Force of Thermo-electric 
 Currents. On account of the extreme smallness of the 
 E.M.F. in these currents, the most convenient unit is the 
 microvolt or millionth part of a volt. The following table of 
 thermo-electric values, or values of the thermo-electric power 
 at temperature f C., was constructed by Professor Everett, 
 from P. G. Tait's Thermo-electric diagram (Trans. R.S.E., 
 1873). Bismuth and antimony, which are added to Professor 
 Everett's list, have been calculated from Tait's data. It is 
 assumed that each metal forms a couple with lead, and 
 the signs + and denote that the metal is respectively 
 positive or negative to lead ; when it is positive, the current 
 passes from the assigned metal to lead through the hot junc- 
 tion. The range of temperature through which these values 
 may be assumed is from 18 C. to 416 C., with the 
 exceptions zinc up to 373 C., and German silver, to 175 C. 
 (The calculation of the values involves the assumption that 
 the KM.F. of a Grove cell is 1-97 volt.) 
 
390 
 
 Electricity. 
 
 [Book IV. 
 
 THERMO-ELECTRIC VALUES IN MICROVOLTS or METALS AT f C. 
 
 REFERRED TO LEAD. 
 
 Iron, . 
 
 Steel, . 
 
 Soft Platinum, 
 
 Hard Platinum, 
 
 Alloy Platinum and Nickel, 
 
 AUoy Platinum, 95% 
 
 Iridium, 5% 
 
 Alloy Platinum, 85% 
 
 Iridium, 15% 
 
 German Silver, 
 
 Zinc, . 
 
 Cadmium, 
 
 Silver, 
 
 Gold, . 
 
 Copper, 
 
 Tin, 
 
 Aluminium, 
 
 Palladium, 
 
 Bismuth, 
 
 Antimony, 
 
 - 17-34 + -0487 * 
 -11-39 + -0328 
 + -61 + -Oil t 
 
 - 2-6 +-0075* 
 
 - 5'44+ 'Oil t 
 
 - 6-22 + -0055 t 
 
 - 5-77 
 
 + 12-07 + -0512 t 
 
 - 2-34- -024 t 
 
 - 2 -66- -0429 t 
 
 - 2-14- -015 t 
 
 - 2-83- '0102 * 
 
 - 1 '36- -0095 t 
 + -43 - -0055 t 
 
 77 - '0039 t 
 
 6'25 + -0359 t 
 
 62-84+ '1084 t 
 
 - 35 -03- '2246 t 
 
 Since the values vary greatly with the specimens of the 
 metals employed, these values are only true in a general 
 sense. 
 
 The above table enables us to solve many problems in 
 the thermo-electric behaviour of pairs of metals. Thus the 
 neutral point can be found by equating the thermo-electric 
 values of the two metals concerned. The thermo-electric 
 power at any temperature is given by simply subtracting 
 the thermo-electric values and substituting the value for /. 
 
Book iv.] Thermo- Electricity. 39 J 
 
 The E.M.F. of a couple of two metals is found by taking 
 their thermo-electric value at the mean of the temperatures 
 of the hot and cold junctions, and multiplying by the range 
 of temperature. 
 
 Example 1. To find the neutral temperature of iron and 
 zinc, we have from the table 
 
 -17-34 +-04872!= -2-34 --024*. 
 .-. -0727 =15. .-. 2=206 0. 
 
 Example 2. To find the thermo-electric value of an iron- 
 zinc couple at temperature 100 C. 
 Thermo-electric value for iron-zinc 
 
 = (-17-34 + -0487 0-(-2-34- -024 t) 
 
 = -15 + -0727 t 
 
 = 773 microvolts, when 2=100. 
 
 Example 3. To find the E.M.F. of an iron-zinc couple 
 when the junctions are at 15 C. and 185 C. respectively. 
 
 The mean of 15 C. and 185 is 100, and thermo-electric 
 value at 100 of iron-zinc =7 -7 3 by last example. 
 
 .-. E.M.F. = 7-73x (185-15) 
 = 7-73x170 
 = 1314 microvolts. 
 
 241. Thermo-electric Diagrams for Higher Tem- 
 peratures. P. G. Tait has pushed his investigations into 
 the thermo-electric behaviour of metals to temperatures far 
 above the range of a mercurial thermometer. He finds in 
 several metals, especially iron and nickel, that the lines are 
 by no means straight. Thus iron has two neutral points 
 with lead, and it has certainly two and probably three neutral 
 
392 Elettricity. [Book iv. 
 
 points with the platinum-iridium compound, whose line in 
 the diagram is parallel to the lead line. In working pro- 
 blems, therefore, temperatures outside the range named must 
 not be considered as having any physical meaning. 
 
 242. Thermo-electric Currents in circuits of one 
 Metal. Magnus has shown that if a circuit is formed of one 
 metal homogeneous throughout, no unequal heating can pro- 
 duce thermo-electric currents. In the case of a single metal, 
 when two parts are of different structure, as in hard and soft 
 iron, a current is produced just as if they were two metals, 
 on heating unequally the discontinuous portions. It seems 
 that any cause which gives rise to molecular change in the 
 wire may also give rise, on unequal heating, to currents of 
 electricity. Thus if part of a wire be twisted, or hammered, 
 or knotted, or magnetized, and heat applied on one side of 
 the changed part, currents can usually be detected in the 
 wire. 
 
 *243. The Peltier Effect. On the general principle of 
 conservation of energy, it is clear that the thermo-electric 
 current is developed at the expense of the heat at the hot 
 junction the tendency of the current, when no other work 
 is done, being to neutralise the differences of temperature 
 in the circuit, the hot junction being cooled, and perhaps 
 the cold junction heated. 
 
 That this is actually the case was proved by Peltier, who 
 showed that when a current from a voltaic element is passed 
 round a bismuth-antimony couple, that junction in which the 
 current goes from bismuth to antimony is cooled, and the 
 opposite junction heated ; that is to say, the current cools 
 
Book IV.] 
 
 Thermo- Electricity. 
 
 393 
 
 that junction which, when heated, gives a current in the 
 direction of the battery current. 
 
 This is called the Peltier effect, and may be shown by two 
 bars, one of bismuth (AB, Fig. 242) and the other of anti- 
 mony (CD), arranged in a cross, and soldered at the junction 
 E. If the current from one or two elements be sent from 
 
 PlG. 242. 
 
 A to 0, it cools the junction. This cooling is best shown by 
 arranging the cross so that C, D are over mercury cups, and 
 the cross rocking on two Y's at A and B^ either or D may 
 dip into a cup, but not both at once. If a galvanometer be 
 connected with B and the mercury cup at D, and after passing 
 the current in direction AEC, the cross be rocked, there will 
 be a current in the galvanometer in the direction DEB, thus 
 proving a cooling at E. 
 
 *244. Theoretical Measure of the E.M.F. of a 
 Thermo-electric Couple. If a battery be included in 
 
394 Electricity. [Book iv. 
 
 any circuit of several metals it is theoretically easy to suppose 
 that the battery current continues until the thermo-electric 
 E.M.F. (caused by the heating and cooling of the junctions 
 and other parts of the circuit, according to Peltier's law), 
 balances the E.M.F. of the battery, when all current ceases. 
 If we also suppose the current very weak and the resistance 
 in the circuit inappreciable, the heat generated frictionally 
 (Art. 169) will be very small, and we may treat the whole 
 heat evolved as that due to the Peltier and similar effects. 
 The energy given out by the battery has in this case been 
 used up in heating and cooling the different parts of the circuit, 
 and must therefore be equivalent to the total heat evolved, 
 counting that absorbed negative. Now the energy given out 
 from the battery is measured by E I t, when E is the 
 E.M.F., I the current strength, and t the time. If I and t be 
 each unity, the E.M.F. is the measure of the energy given out, 
 and therefore equals the energy developed in the circuit per 
 unit time by unit current. Thus if we allow unit current 
 to pass round the circuit for unit time, the total heat evolved 
 (counting that absorbed negative), according to Peltier's law, 
 is equivalent to the E.M.F. of the thermo-electric circuit. 
 
 *245. The Thomson Effect. Professor Cumming 
 observed that at the temperature 284 C., at which the 
 iron and copper are neutral to each other that is, at the 
 temperature represented by the point N on Fig. 241 the 
 Peltier effect vanishes. 
 
 From this Sir W. Thomson argued that if the hot junction 
 in an iron-copper couple be at 284 C., and the other at 
 any lower temperature, no heat is absorbed at the hotter 
 junction. "We therefore have a thermo-electric current with- 
 
Book iv.] Thermo- Electricity. 395 
 
 out any source of energy, unless heat is absorbed according 
 to Peltier's law, but at other parts of the circuit than the 
 junctions. This absorption can only be in the passage of the 
 current from hot to cold, or from cold to hot, parts of the 
 same metal. On experimenting with an unequally heated 
 conductor of copper, it is found that the electric current, going 
 from hotter to colder parts, transfers heat from the hotter to 
 the colder parts ; if the conductor were of iron, the transfer 
 of heat would be from the colder to the hotter parts ; heating 
 and cooling being reversed with the direction of the current. 
 Thus in a copper conductor the electric current tends to 
 neutralise differences of temperature, but in an iron con- 
 ductor it tends to exaggerate them. This electrical convection 
 of heat, called the Thomson effect, has been proved by numer- 
 ous experiments to exist in nearly all metals, but to vanish 
 or become exceedingly small in lead and in certain alloys, 
 whose lines on the diagram are parallel to the lead line. 
 
 It is the vanishing of the Thomson effect which gives the 
 theoretical reason for choosing lead as the base line of the 
 diagram. 
 
 246. Thermo-electric Batteries. On account of the 
 low resistance of thermo-electric couples, it has been proposed 
 to construct batteries of numerous elements, arranged in com- 
 pound series, to be used for telegraphy, electro-plating, and 
 other purposes, but none of them have at present come into 
 general use. 
 
 a 
 che 
 
 . length 
 
396 Questions on Book 
 
 QUESTIONS ON BOOK IV. 
 
 1. Find the temperature of the neutral point of lead and soft 
 platinum. 
 
 ANS. -56C. 
 
 2. Find the temperature of the neutral point of iron and copper. 
 ANS. 274 C. 
 
 3. Find the general thermo-electric value for a metal whose thermo- 
 electric power at O c C. is - 2'14, and at temperature 50 C. is - 2'89. 
 
 ANS. -2-14- -015 t. 
 
 4. Find the E.M.F. of a soft platinum and iron pair, the tempera- 
 tures of whose junctions are 15 C. and 175 C. 
 
 ANS. 2299 microvolts. 
 
 5. Find the number of bismuth-antimony pairs which will be re- 
 quired to give E.M.F. of 1 volt, the junctions being at temperatures 
 C. and 100 C. 
 
 ANS. 87. 
 
 6. Show that in a couple formed of two metals whose lines on the 
 thermo-electric diagram are parallel to each other, the E.M.F. is 
 
 " v / directly proportional to the difference in temperature of the junctions. 
 
 7. Show that if in any couple the temperature of the hot junction 
 | is at the same distance above the neutral temperature that the cold 
 
 junction is below it, no current will appear. 
 
APPENDIX I. 
 
 ABSOLUTE UNITS IN CG.S. SYSTEM. 
 
 247. Units and Measures. The description of every 
 physical quantity consists of a number, and a concrete thing 
 of the same nature as that which is being described. Thus if 
 we say a certain distance is 20 inches, the numerical part 
 (twenty) expresses the ratio of the length to another length 
 (the inch), the description presupposing a common understand- 
 ing as to the nature of the inch. In this case the measure is 
 twenty, and the unit an inch. If instead of the inch we wish 
 to make the foot our unit, the measure is altered ; in fact, 20 
 inches equals f feet; or, again, equals -| yards. Thus we 
 observe that the change of a unit changes all measures ex- 
 pressed in that unit, and the change in the measure is 
 inversely proportional to the change in the unit. 
 
 248. Fundamental Units. The fundamental units, 
 from which all other units are derived, are those of length, 
 mass, and time. There is great diversity in the units of these 
 adopted in different countries, but the greatest care is taken 
 by all civilised states to legalise one, and only one, unit with 
 which all measures must be compared. Our own standard of 
 length is the yard, and is denned by Act of Parliament as the 
 distance between two transverse lines on two gold plugs in a 
 bar of bronze deposited in the office of the Exchequer, the 
 measure being taken when the bar is at 62 F. 
 
 The French standard of length is the metre, whose length 
 
 897 
 
Electricity. [A PP . 
 
 was made to equal, as nearly as possible, the ten-millionth part 
 of the quadrantal arc of the earth in the longitude of Paris ; but 
 since such a measurement can only be made within tolerably 
 wide errors of observation, the definition of the unit is the 
 distance between the ends of a bar of platinum made by 
 Borda, when the bar is at the temperature of melting ice. 
 The subdivisions of the metre are the tenth or decimetre, the 
 hundredth or centimetre, and the thousandth or millimetre. 
 For all scientific purposes the French system of measure is 
 used, owing largely to its being a decimal system. The unit 
 of length we adopt is the centimetre. Its length, referred to 
 British inches, is "3937043, or rather more than one-third of 
 an inch. 
 
 The British unit of mass is defined in the same way, as the 
 mass of a certain weight of platinum deposited in the office 
 of the Exchequer, and denominated the Imperial Standard 
 Pound Avoirdupois. The grain troy is defined as the seven- 
 thousandth part of the pound avoirdupois. 
 
 The French standard is the mass of the Kilogramme des 
 Archives, made of platinum by Borda, and representing as 
 nearly as possible the mass of a cubic decimetre of distilled 
 water at temperature 4 C. 
 
 The thousandth part of this, or the mass of a cubic centi- 
 metre of distilled water at 4 C., is chosen as the standard 
 of mass, and called the gramme. This is found to contain 
 15 -43234874 grains troy. 
 
 These are defined in their respective Acts of Parliament as 
 standards of weight; but we see they are masses of metal, 
 and their weights depend on the attractive force of the 
 earth at the particular place where they are weighed, and 
 their weight must change as they are carried either to 
 places of different altitudes or different latitudes. If, how- 
 ever, any material body be balanced by an ordinary pair of 
 scales in vacuo against the standard weight, it will also 
 balance wherever the experiment be repeated, since the 
 
i.] Absolute Units in C.G.S. System. 399 
 
 change of terrestrial gravitation will be equal on both the 
 weight and its counterpoise. Thus it appears that in our 
 ordinary commercial transactions, carried on by scales and 
 weights, we are really dealing with masses, and not with 
 weights, the so-called standards of weight being standards of 
 mass. 
 
 The unit employed for time is always the second of our 
 mean-time clocks. Since no clock-work can be made to go 
 uniformly for ever, the standard unit of time cannot be 
 denned as the second on a particular clock from which it can 
 always be reproduced. The regulation of the clock depends 
 on astronomical observations, and the constancy of the second 
 through vast lapses of time assumes that the rotation of the 
 earth is at a uniform rate, and also that the earth always 
 takes the same time for its orbital revolution. It is by no 
 means probable that either of these assumptions is true, though 
 no doubt both are sensibly true during hundreds of years. 
 
 249. Mechanical Units. Having established these 
 three fundamental units of length, the centimetre ; of time, 
 the second ; and of mass, the gramme, we are able to express 
 in terms of them every physical quantity whatever. 
 
 There are certain dynamical quantities which constantly 
 recur in all physical science, whose nature and measurement 
 we must briefly explain. 
 
 (1) Velocity is a property possessed by every moving 
 particle at each instant of its motion. To define it we must 
 know three things the position of the particle in space, the 
 direction of its motion, and its speed, or the rate with which it 
 is moving. To represent the rate of motion we usually state 
 the distance the particle would go supposing it to retain its 
 present rate of motion for a certain time. Thus in speaking 
 of the motion of a railway train we usually state it in 
 miles per hour, meaning that if it continue moving for an 
 hour at its present rate it will go so many miles in the 
 
4 Electricity. [App. 
 
 hour ; not of course assuming that it has actually gone that 
 distance in the hour, or will go that distance in the next hour. 
 If we speak of the rate of a body falling under gravity, or 
 of a cannon ball, we usually state it in feet per second. 
 
 It is very convenient for practical purposes to have many 
 units of measurement, but for scientific purposes it is con- 
 venient to have only one, or at any rate to have units which 
 may be with the least possible trouble converted into our 
 assumed fundamental units. Thus we measure all velocities 
 in centimetres per second, and we speak of a velocity of one 
 centimetre per second as our unit velocity. Velocities can 
 then be expressed by simple numbers a velocity of 1000 
 meaning that the body is moving at the rate of 1000 centi- 
 metres per second. 
 
 (2) Acceleration and Retardation. If the velocity of a 
 particle is not uniform, it is at each instant either quickening 
 or slackening its speed. To discover this we must observe the 
 velocity at both ends of a certain interval, and find out 
 whether it has changed during the interval, and if so, by how 
 much. Thus acceleration is usually measured by the increase 
 in velocity per second, not implying that the acceleration is 
 uniform during a second, but only representing the amount 
 by which the velocity would increase, supposing the increase 
 to go on uniformly for one second. An acceleration of 1000 
 would then mean that the body would have a velocity of 
 1000 cm. per second greater at the end than at the beginning 
 of a second during which the same acceleration was main- 
 tained. The unit of acceleration is therefore an acceleration 
 of one cm, per second every second. 
 
 The best illustration of uniform acceleration is afforded by 
 a body falling in vacuo near the surface of the earth. The 
 acceleration of gravity at the level of the sea in the latitude of 
 Paris is found to be 981, and will be sensibly the same at all 
 altitudes which differ by only a few hundreds of yards or 
 metres. This means that any particle falling toward the 
 
i.] Absolute Units in C.G.S. System. 401 
 
 earth increases its velocity by 981 cm. per second per second, 
 and if it be projected upwards from the earth it will suffer 
 retardation, or will lose velocity at exactly the same rate. 
 
 In England, feet and seconds have till recently been com- 
 monly used as units of length and time, and in terms of them 
 the measure of gravitation at London is taken to be 32 '2, 
 denoting that the velocity of a falling body increases by 32 -2 
 feet per second per second. 
 
 (3) Force is commonly denned as that which changes or 
 tends to change a body's state of rest or motion. This com- 
 prises all such physical magnitudes as weights, pressure, 
 tension, strains, etc. By the weight of a body we denote the 
 pull exerted by the earth upon it, or by it upon the earth, for 
 these two are equal and in contrary directions. We have 
 noted that, if unopposed, the weight of any body whatever 
 will alter its state of rest or motion in the vertical line by 
 981 units of velocity per second. Thus the change of motion 
 caused by gravitation is independent of the mass of the body 
 experimented on, but the pull of the earth, or the Force of 
 gravitation, is not independent of mass. For all experience 
 shows that if we suspend by a string a small mass, the string 
 assumes a state of tension, which prevents gravitation from 
 causing change of state ; but if we suspend a larger mass the 
 string can no longer bear the strain, and breaks, allowing 
 gravity to produce its change of state in the body. We are 
 thus led to see that the description of a force must express 
 the mass of the body as well as the acceleration it will, if un- 
 opposed, produce in the body. Thus a force of 10 Ibs. must 
 mean a force which would produce in a mass of 10 Ibs. the 
 same acceleration as gravity, that is, an acceleration of 32 '2 
 feet per second per second, and this is shown experimentally 
 to be the same as would produce in a mass of 1 Ib. an 
 acceleration of 322( = 32'2xlO) feet per second per second, 
 or in a mass of 322 Ibs. an acceleration of 1 foot per second 
 per second. 
 
 2 C 
 
4 2 Electricity. [App. 
 
 For scientific purposes we take our cm., gm. and second as 
 fundamental units of reference, and define our unit force as 
 the force which will produce in 1 gm. unit acceleration, or a 
 velocity of 1 cm. per second per second. This unit of force 
 we call a dyne, 1 and the weight of a gram in the latitude 
 of Paris and at the level of the sea is 981 dynes. 
 
 (4) Work. Work is said to be done whenever a mass is 
 carried through space in opposition to a force. Thus Watt 
 took as standard the work done in raising a pound against 
 the attraction of the earth through 1 foot, and this he called 
 a "foot-pound," It must be noticed that no work is done in 
 moving a body at right angles to the force acting on it, as, for 
 instance, in carrying a body horizontally, unless it be done 
 against the resistance of the air or friction, since, could the 
 body be started on a perfectly smooth and level surface in 
 vacuo, it would move on for ever without the expenditure on 
 it of any work whatever. 
 
 " In the absolute system we use cm. dynes instead of foot- 
 pounds, the cm. -dyne being the work done in opposing 
 through a centimetre the force of 1 dyne, or in carrying 
 1 gram through a centimetre in oppositibn to a force which 
 unopposed would give it unit acceleration. This unit is 
 commonly now called an erg. 2 To find the number of ergs in 
 a foot-pound we notice that 1 Ib. mass =453*5 9 3 gm. mass, 
 and 1 foot =30 '48 cm., and the acceleration of gravity =981 
 units. Hence in carrying 1 Ib. through a foot against earth's 
 pull, we carry 453*593 grams through 30*48 cm. against 
 981 units of force, which is the same work as expended in 
 carrying 453*593 x 30*48 x 981 grams through 1 cm. against 
 unit force, that is to say, 1 foot-pound equals 13,560,000 
 ergs nearly. 
 
 (5) Energy, Kinetic and Potential. The power of doing 
 work in an agent is called its energy, and the amount of 
 energy is simply measured by the number of units of work it 
 
 1 Greek, 8vvafjus= force. 2 (-reek, fpyov = 
 
i.] Absolute Units in C.G.S. System. 403 
 
 is capable of doing. We may first have energy due to a 
 body's motion. A bullet flying through the air, on striking 
 against a block of wood, sinks into it till it is brought to 
 rest. The energy of the bullet caused it to do work, in 
 overcoming the resistance of the wood to disintegration, or 
 against the molecular cohesion of the wood. Now it can be 
 demonstrated mathematically that for every such case the 
 amount of work done by the moving body before it is brought 
 to rest equals half the product of the mass of the body 
 into the square of its velocity. If different parts of the 
 body are moving with different velocities, the total energy 
 may be taken as the sum of the energy of each particle 
 computed as explained above. This kind of energy, which a 
 body has in virtue of its motion, is commonly called Kinetic 
 Energy. 
 
 A body may, secondly, have energy, in virtue of position or 
 of work having been expended upon it, which is retained in 
 the body, and can be recovered at any future time. Thus 
 when a stone is carried up to a height and placed on the edge 
 of a cliff, work has been expended in carrying the stone, 
 without any change in the stone, except in respect to position 
 relatively to gravitation. A very slight touch may dislodge 
 the stone, and it will, in falling down, acquire kinetic energy, 
 which, when it reaches the level from which it was carried, 
 will exactly equal that expended in raising the stone. In 
 every form of catapult or bow used in archery, work is first 
 done against molecular forces in compressing the spring or 
 bending the bow; and on loosing the trigger or detent, a 
 large share of this energy is concentrated on the arrow or 
 other projectile, which thus acquires a high velocity. Were it 
 mechanically possible to bring all parts of the machine except 
 the projectile absolutely to rest at the instant when the pro- 
 jectile leaves it, the energy of the projectile would numerically 
 equal the work done in compression. This kind of energy is 
 often called Potential Energy. 
 
Electricity. [App. 
 
 The same general principles apply to other physical pheno 
 mena. Thus if work be expended in heating a body, the 
 energy of the heat is numerically the same as the work 
 expended in heating it. If work be done in making an 
 electrical separation or an electric current, the energy of 
 the separation or of the current is the same as the original 
 work done. These are only illustrations of the great principle 
 of conservation of energy, of which we find many applications 
 in electrical and magnetic phenomena. 
 
 (6.) Rate of Working. The rate at which an agent works is 
 in practice expressed in horse power. The horse power was 
 denned by Watt to be the rate of working of an agent which 
 does 33,000 foot-pounds of work per minute. In conformity 
 with our notation, we should naturally express the rate of 
 working in ergs per second. To convert the horse power into 
 ergs per second, we notice that the horse power is 550 foot- 
 pounds per second, and the foot-pound is 13,560,000 ergs. 
 Hence the horse power is 550 x 13,560,000 = 7-46 x 10 9 ergs 
 per second. 
 
II.] 
 
 Table of Natiiral Sines. 
 
 405 
 
 APPENDIX II. 
 
 TABLE OF NATURAL SINES AND TANGENTS OF 
 ANGLES FOR EACH DEGREE. 
 
 ^ 
 
 1 
 
 Q 
 
 S 
 3d 
 
 Tangent. 
 
 I 
 
 d 
 
 i 
 
 +3 
 
 d 
 
 ! 
 
 i 
 
 Tangent. 
 
 1 
 
 2 
 3 
 
 018 
 035 
 052 
 
 018 
 035 
 052 
 
 31 
 32 
 33 
 
 615 
 530 
 545 
 
 601 
 
 625 
 649 
 
 61 
 
 62 
 63 
 
 875 
 883 
 891 
 
 1-804 
 1-881 
 1-963 
 
 4 
 5 
 
 6 
 
 070 
 087 
 105 
 
 070 
 
 087 
 105 
 
 34 
 35 
 36 
 
 559 
 574 
 588 
 
 675 
 700 
 727 
 
 64 
 65 
 66 
 
 906 
 914 
 
 2-050 
 2-145 
 2-246 
 
 7 
 8 
 9 
 
 122 
 139 
 156 
 
 123 
 141 
 158 
 
 37 
 38 
 39 
 
 602 
 616 
 629 
 
 754 
 
 781 
 810 
 
 67 
 68 
 69 
 
 921 
 927 
 934 
 
 2-356 
 2-475 
 2-605 
 
 10 
 
 174 
 
 176 
 
 40 
 
 643 
 
 839 
 
 70 
 
 940 
 
 2-748 
 
 11 
 12 
 13 
 
 191 
 208 
 225 
 
 194 
 213 
 231 
 
 41 U 
 
 42 
 43 
 
 656 
 669 
 682 
 
 869 
 900 
 933 
 
 71 
 72 
 73 
 
 946 
 951 
 956 
 
 2-904 
 3-078 
 3-271 
 
 14 
 15 
 16 
 
 242 
 259 
 276 
 
 249 
 268 
 287 
 
 44 
 
 45 
 46 
 
 695 
 707 
 719 
 
 966 
 1-000 
 1-036 
 
 74 
 75 
 76 
 
 961 
 966 
 970 
 
 3-487 
 3-732 
 4-011 
 
 17 
 18 
 19 
 
 292" 
 
 309 
 326 
 
 306 
 325 
 344 
 
 47 
 48 
 49 
 
 731 
 743 
 755 
 
 1-072 
 Mil 
 1-150 
 
 77 
 78 
 79 
 
 974 
 
 978 
 982 
 
 4-331 
 4-705 
 5-145 
 
 20 
 
 342 
 
 364 
 
 50" 
 
 766 
 
 1-192 
 
 80 
 
 985 
 
 5-671 
 
 21 
 
 22 
 23 
 
 358 
 375 
 391 
 
 384 
 404 
 425 
 
 51 
 
 52 
 53 
 
 788 
 799 
 
 1-235 
 1-280 
 1-327 
 
 81 
 82 
 83 
 
 988 
 990 
 993 
 
 6-314 
 7-115 
 8-144 
 
 24 
 25 
 26 
 
 407 
 423 
 438 
 
 445 
 
 466 
 488 
 
 54 
 55 
 66 
 
 809 
 819 
 829 
 
 1-376 
 1-428 
 1-483 
 
 84 
 85 
 86 
 
 995 
 996 
 998 
 
 9-514 
 11-43 
 14-30 
 
 27 
 28 
 29 
 
 454 
 469 
 485 
 
 510 
 532 
 554 
 
 57 
 58 
 59 
 
 839 
 848 
 857 
 
 1-540 
 1-600 
 1-664 
 
 87 
 88 
 89 
 
 999 
 999 
 999 
 
 19-08 
 28-64 
 57-29 
 
 30 
 
 500 
 
 577 
 
 60 
 
 866 
 
 1-732 
 
 90 
 
 1-000 
 
 cc 
 
Printed by T. aud A. CONSTABLE, Printers to Her Majesty, 
 at the Edinburgh University Press. 
 
91826^ 
 
 o 
 in 
 
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