Mining ' LIBRARY UNIVERSITY OF CALIFORNIA. Clas. MAGNETIC INDUCTION IN IRON AND OTHER METALS. BY J. A. EW1NG, li M.A., F.R.S., M.INST.C.E., PROFESSOR OF MECHANISM AND APPLIED MECHANICS IN THE UNIVERSITY OF CAMBRIDGE, FELLOW OF KING'S COLLEGE, CAMBRIDGE. THIRD EDITION, REVISED. UNIVERSITY OF / i F OR tjifc^ . THE D. VAN NOSTRAND COMPANY, 23, MURRAY STREET, AND 27 WARREN STREET. LONDON : THE ELECTRICIAN " PRINTING AND PUBLISHING COMPANY, LIMITED, SALISBURY COURT, FLEET STREET, E.G. JAPAN : Z. P. Maruya & Co. , 14, Nihonbashi Tori Sanchome, Tokyo. INDIA : Thacker, Spink & Co., Calcutta. Higginbotbam & Co., Madras. AUSTRALIA: George Robertson & Co., Melbourne, Sydney, Adelaide and Brisbane. All Rights lleserved. ? Printed and Published by THE ELECTRICIAN" PRINTING AND PUBLISHING co., LTD. 1, 2 and 3, Salisbury Court, Fleet Street, London, E.C. PREFACE. DURING recent years, and especially during the last ten, our knowledge of the physical facts of Magnetisation has made a marked advance. Perhaps no subject has profited more by the beneficent reaction of Practice on Science. The labours of a number of observers have made it possible to present a connected account of the phenomena of magnetic induction and of the distinctive qualities of the magnetic family of metals. There are still, of course, many questions for experiment to answer ; but a text-book of the subject may now be written with some degree of continuity and completeness. In attempting this task, the author has not ap- proached the matter from the standpoint of the scientific historian. He has been more concerned to tell of things discovered than of discoverers. In many instances, therefore, the work of early observers is passed over with no mention, or with the briefest, because later experiments are found to deal with the same points in a more conclusive or more exhaustive way. The author's aim has been to present the subject in sufficient detail to satisfy scientific students, as well as to meet the wants of those who may turn to the book in quest of data for application to matters of practice. Particulars, which will facilitate reference to the original 4 179327 IV. PREFACE. memoirs in which researches are described, have in all cases been given for the assistance of those who may wish to pursue the subject further than a short text- book can well take them. After an introductory chapter, which attempts to explain the fundamental ideas and the terminology, an account is given of the methods which are usually em- ployed to measure the magnetic qualities of metals. Examples are then quoted, showing the results of such measurements for various specimens of iron, steel, nickel, and cobalt. A chapter on Magnetic Hysteresis follows, and then the distinctive features of induction by very weak and by very strong magnetic forces are separately described, with further description of experimental methods, and with additional numerical results. The influence of Temperature and the influence of Stress are /lext discussed. The conception of the Magnetic Circuit is then explained, and some account is given of experi- ments which are best elucidated by making use of this essentially modern method of treatment. The book concludes with a chapter on the Molecular Theory of Magnetic Induction ; and the opportunity is taken to refer to a number of miscellaneous experimental facts, on which the molecular theory has an evident bearing. Throughout the book the author has endeavoured to familiarise the student' with the notion of intensity of magnetisation (|) as well as with the notion of magnetic induction (B)- It has been urged by some writers that the alternative which is in this way offered is unnecessary and confusing, and that if we keep "B" we may dispense with " |." The scientific value and the practical utility of " B " are so obvious that no one proposes to avoid using that. It is " | " that we are told must go. In this PREFACE. V. cry the author is by no means disposed to join. It is not too much to say that in stating the magnetic qualities of a metal the quantity "|" is of primary importance. The facts of saturation, the molecular theory, and the phenomena of magneto-optics, all demonstrate its phy- sical reality and its fundamental interest. The author would take this opportunity to repeat an acknowledgment, already made elsewhere, of the assist- ance most willingly and ably rendered by a number of his pupils in carrying out experiments on some of the subjects with which this book deals. Messrs. Tanaka- date, Fujisawa, Tanaka, and Sakai, in Japan, and Messrs. W. Low, Cowan, D. Low, and Frew, in Dundee, have been skilful and sympathetic collaborators, whose interest was as lively as their patience was inexhaustible. A reminder of how far the subject still is from finality comes, as the last pages are passing through the press, in the announcement by Prof. J. J. Thomson of his demonstration that iron continues to be strongly susceptible to magnetisation by such rapid alternations of magnetic force as occur in a Leyden-jar discharge ; and that the damping-out of the electric oscillations when the discharge traverses a coil with an iron core proves magnetic hysteresis to play an important part, notwithstanding the excessive frequency of the reversals. Independent experiments made by Prof. Trowbridge point to the same conclusion. Prof. Thomson's use of vacuum-globes without electrodes as induction secon- daries opens up new possibilities of magnetic research, which he has himself been the first to turn to account. A2 PREFACE TO THE THIRD EDITION. IN this Edition a number of references are given to advances which the subject has made since the book was originally published, and a Chapter is added on " Practical Magnetic Testing." J. A. EWING. Cambridge, rpoo. CONTENTS. CHAPTER I. INTRODUCTORY. SECTION. PAGE. Introductory 1 .... 1 Magnetic Poles, Axis, and Moment . . . . . . 2 .... 2 Magnetic Field and Magnetic Force . . . , . . 3 .... 3 Lines of Magnetic Force . . . . . . . . . . 4 .... 4 Uniform Magnetic Field . . . . . . . . . . 5 .... 6 Continuity of the Magnetic State . . . . . . 6 .... 7 Intensity of Magnetisation . . . . . . . , . . 7 .... 7 Kelation of I to Pole- Strength 8 8 King Magnet 9 .... 8 Lines of Magnetisation .. .. .. .. .. 10-11 .... 9 Magnetic Force within the Metal . . . . .. .. 12 .... 11 Magnetic Induction . . . . . . . . . . 13 .... 12 Distinction between Magnetic Induction and Magnetic Force within the Metal 14 .... 12 Particular Cases . . . . . . . . . . . . 15 .... 13 Magnetic Permeability . . . . . . . . .. 16 .... 14 Permeability of Paramagnetic and Diamagnetic Substances 17 .... 16 Illustrations of Permeability 18 .... 16 Magnetic Susceptibility 19 .... 18 Connection of the Ideas of Permeability and Susceptibility 20 .... 18 Caution with regard to the Use of the Ideas of Perme- ability and Susceptibility 21 .... 19 Influence of the Form of Bodies on the Magnetisation induced in them 22 .... 20 Long Rod placed Lengthwise in a Uniform Field . . 23 .... 21 Analogy of Induced Magnetisation to Electric Conduction 24 .... 22 Cases in which the Magnetisation is Uniform : Ellipsoid 25 .... 23 Magnetisation of an Ellipsoid 26 .... 24 Distribution of Free Magnetism in a Uniformly Mag- netised Ellipsoid 27 .... 25 Moment of Ellipsoid . . . . . . . . . . ' . . 28 . . . . 27 Application to the Case of a Sphere 29 .... 27 Application to the Case of a Short Ellipsoid . . . . 80 .... 29 Viil. CONTENTS. SECTION. PAGE. Application to the Case of a Long Cylindrical Eod of Cir- cular Section Magnetised Transversely in a Uniform Field 31 .... 30 Case of a Thin Disc Magnetised in the Direction of the Thickness by a Uniform Field 32 .... 31 Long Ellipsoid: Influence of the Length on the Mag- netising Force 33 .... 31 .Residual Magnetism and Eotentiveness 34 .... 32 Self-Demagnetising Force . . . . . . . . 35 .... 33 Self -Demagnetising Force in Ellipsoids . . . . . . 36 .... 34 CHAPTER II. MEASUREMENTS OF MAGNETIC QUALITY: THE MAGNETOMETRIC METHOD. SECTION. PAGE. Methods of Measuring Magnetic Quality . . . . . . 37 .... 35 Classification of Methods : Magnetometrio and Ballistic 38 .... 36 Magnetometric Method 39-40.. 37-39 Details of Magnetometric Method , 41 .... 40 Demagnetising by Eeversals . . . . . . . . 42 ... 46 Adjustment of the Current required to balance the Ver- tical Component of the Earth's Field 43 .... 46 To find the Directing Force at the Magnetometer . . 44 .... 47 Example of a Test of Iron by the Magnetometric Method 45 .... 49 Magnetisation Curve 46 .... 52 Residual Magnetism and Coercive Force 47 .... 52 Correction of the foregoing results to allow for the Re- action of the Specimen on the Magnetising Field 48 .... 54 Differential Susceptibility and Differential Permeability. . 49 .... 56 Supplementary Remarks on the Magnetometric Method 50 .... 56 CHAPTER III. MEASUREMENTS OF MAGNETIC QUALITY: THE BALLISTIC METHOD. SECTION. PAGE. The Ballistic Method 51 ..., 59 Earth Coil . . . . 52 .... 60 Use of a Solenoid and Current for Standardising the Bal- listic Galvanometer 53 .... 62 Damping and Calibration of the Ballistic Galvanometer 54 .... 63 Ballistic Tests of Rings and Rods 55 .... 64 Calculation of B from Ballistic Measurements . . . . 50 .... 66 Magnetic Force in Rings . . . . . . . . . . 57 .... 66 Bar and Yoke 58 67 Hopkinson's Application of the Bar and Yoke . . 59 .... 69 Double Bars and Yokes 60 69 Example of the Ballistic Method 61 .... 70 CONTENTS. IX. CHAPTER IV. EXAMPLES OF MAGNETISATION. SECTION. PAGE. Ballistic Method Using Keversals : Magnetisation of an Iron King (Eowland) 62 .... 73 Cyclic Process of Magnetisation : Long Iron Wire . . 63 .... 75 Magnetisation of Iron Hods of Various Lengths . . . . 64 . . . , 77 Wrought-Iron Bar 65 79 Magnetisation of Mechanically Hardened Iron . . . . 66 .... 80 Magnetic Qualities of Steel 67 .... 82 Magnetisation of Pianoforte Steel Wire 68 .... 83 Cast Iron . . . , . . 69 85 Non-Magnetic Steels 70 85 Nickel 71 .... 86 Cobalt 72 .... 88 Curves of Permeability and Susceptibility . . . . 73 .... 88 Susceptibility Curves for Wrought-Iron Wire . . . . 74 .... 88 Permeability Curves for Nickel.. 75 .... 91 Permeability Curves for Cobalt 76 .... 92 CHAPTER V. MAGNETIC HYSTERESIS. SECTION. PAGE. Magnetic Hysteresis 77 .... 93 Effects of Hysteresis 78 .... 94 Dissipation of Energy through Magnetic Hysteresis . . 79 .... 99 Heating Effect of a Cyclic Process 80 102 Values of fHd I 81 .... 103 Dissipation of Energy by JReversals of Moderately Strong Magnetisation 82 .... 105 Influence of Speed on Magnetic Hysteresis . . . . 83 .... 108 Steinmetz Coefficient of Hysteresis 83A 111 Effects of Vibration 84 .... 112 Experiments on the- Effects of Vibration in the Mag- netisation of Soft Iron Wire 85 .... 114 Magnetic Curve Tracer 85A 118 CHAPTER VI. MAGNETISM IN WEAK FIELDS. SECTION, PAGE. Permeability with respect to Small Magnetic Forces . . 86 124 Lord Bayleigh's Experiments . . . . . . . . 87 .... 126 Magnetic Viscosity under Small Forces 88 .... 127 Further Experiments on Time Lag in Magnetisation 89 .... 131 Molecular Accommodation .. .. 90 ... 135 CONTENTS. CHAPTER VII MAGNETISM IN STRONG FIELDS. SECTION. PAGE. Magnetisation in Strong Fields 91 .... 136 The Isthmus Method 92 .... 138 Early Experiments, using the Isthmus Method . . . . 93 .... 139 Later Experiments, using the Isthmus Method . . 94 .... 143 Theory of the Isthmus Method : Form of Cone to give Maximum Concentration 95 .... 145 Greatest Magnetising Force producible by means of Cones 96 .... 147 Form of Cone to give most Uniform Field . . , . 97 .... 148 Further Experiments with Wrought Iron .. .. 98 .... 150 Cast Iron and Steel in very Strong Fields . . . . 99 151 Hadfield's Manganese Steel in Strong Fields . . . . 100 .... 153 Nickel and Cobalt in Strong Fields . . . . . . 101 .... 153 Summary of Conclusions from Isthmus Experiments . . 102 .... 155 Apparatus for applying the Isthmus Method. . . . 103 .... 156 Experiments by Du Bois -with Strong Fields. Optical Method 104 .... 158 Eesults of Optical Measurements 105 .... 161 Magnetisation of Magnetite 106 162 Experiments with Ellipsoids 107 .... 163 CHAPTER VIII. EFFECTS OF TEMPERATURE. SECTION. PAGE. Effects of Temperature on Magnetic Quality : Loss of Magnetic Quality at a High Temperature . . . . 108 .... 1^6 Change of Physical State at the Critical Temperature 109 .... 167 Effects of Temperature Below the Critical Point . . 110 .... 168 Hopkinsnn's Experiments on the Magnetisation of Iron at Various Temperatures Ill .... 170 Whitworth's Mild Steel 112 173 Whitworth's Hard Steel 113 .... 174 Hopkinson's Experiments with Nickel . . . . 114 .... 175 Effects of Temperature within the Atmospheric Eange 115 .... 178 Effects of Varying Temperature, the Magnetic Force being Constant 116 .... 180 Experiments in Alternate Heating and Cooling of Mag- netised Iron 117 .... 181 Hysteresis in the Kelation of Magnetic Susceptibility to Temperature 118 .... 184 Hopkinson's Experiments with Nickel-Iron Alloys . . 119 .... 186 Eesearches on Effects of Temperature by Dr. Morris 119A .... 190 "Ageing" of Iron by Prolonged Exposure to Moderate Temperature 119u .... 193 CONTENTS. ft CHAPTER IX. EFFECTS OF STEESS. SECTION. PAGE. Effects of Stress : Introductory 120 .... 197 Effects of Longitudinal Pull on the Susceptibility and Retentiveness of Nickel . . . . . . . . 121 .... 193 Effects of Longitudinal Push on the Susceptibility and Retentiveness of Nickel . . . . . . . . 122 .... 202 Effects of Cyclic Variation of Longitudinal Stress on the Magnetism of Nickel .. -^ .. .. 123 .... 206 Effects of Longitudinal Pull in Iron 124 .... 209 Annealed Iron under Pulling Stress . . . . . , 125 .... 209 Hardened Iron under Pulling Stress , . . . . . 126 .... 212 Effects of Applying Longitudinal Pull to Magnetised Iron 127 216 Hysteresis in the Effects of Stress . . . . . . 128 .... 219 Influence of Vibration on the Effects of Stress . . . . 129 .... 222 Effects of Loading Annealed Iron . . . . .. 130 222 Effects of Longitudinal Stress in Cobalt 131 .... 222 Kelation between the Effects of Stress on Magnetism, and the Effects of Magnetism in changing the Dimensions of Magnetic Metals . . . . . . 132 .... 224 Residual Effects of Stress applied before Magnetising . . 133 .... 225 Experiments showing Residual Effects of Stress . . 134 , . . . 226 Other Evidences of Hysteresis in the Effects of Stress. . 135 .... 230 Effects of Torsion on Magnetic Quality . . . . 136 231 Effects of Torsion due to Magnetic Aeolotropy .. .. 137 .... 232 Production of Longitudinal Magnetism by Twisting a Circularly Magnetised Wire . . . . . . 138 .... 234 Torsional Strain Produced by Combining Circular with Longitudinal Magnetisation . . . . . . . . 139 .... 236 Transient Currents produced by Magnetising Twisted Rods, or by Twisting Magnetised Rods .. .. 110 .... 237 Effects of Combined Pull and Torsion on the Magnetisa- tion of Iron and Nickel 141 240 Effects of Cyclic Twisting in Nickel, when Associated with Longitudinal Pull 142 244 Strain caused by Magnetisation 143 .... 249 Modification of the Results by applying Tensile Stress 144 .... 252 Stress due to Magnetisation . . . . . . . . 145 .... 254 Tractive Force in Divided Magnets . . . . . . 146 .... 254 Relation of Tractive Force to Magnetisation . . . . 147 .... 257 Determination of Magnetisation by Measuring the Tractive Force 148 .... 259 CONTENTS. CHAPTEB X. THE MAGNETIC CIRCUIT. SECTION. PAGE. The Magnetic Circuit 149 .... 262 Tubes of Magnetic Induction. Definition of Magnetic Flux and of a Perfect Magnetic Circuit . . . . 150 .... 263 Imperfect Magnetic Circuit .. .. .. .. .. 151 .... 265 Line-Integral of Magnetic Force, or Magnetomotive Force 152 .... 265 Value of the Line-Integral of Magnetic Force . . . . 153 .... 266 Equation of the Magnetic Circuit 154 .... 268 Particular Cases : Continuous Ring wound uniformly and otherwise . . 155 .... 271 King Magnet with an Air Gap . . 156 .... 275 Comparison of a Split-King with an Ellipsoid . . . . 157 .... 276 Graphic Kepresentation of the Influence of a Narrow Gap 158 .... 278 Graphic Representation of the relation of Flux to Mag- netomotive Force . . . . . . . . . . 159 .... 280 Application to Dynamos 160 .... 282 Bar and Yoke 161 .... 283 Magnetic Resistance of Joints 162 .... 285 Calculation of the Equivalent Air-Gap . . . . 163 .... 287 Influence of Compression on the Magnetic Resistance of a Joint 164 .... 289 Experiments with Rough Joints . . ... . . 165 .... 2'Jl CHAPTER XI. MOLECULAR THEORY. SECTION. PAGE. Molecular Theories : Poissou and^ Weber 166 .... 291 Experimental Evidence in Favour of Weber's Theory from the Facts of Saturation, &c 167 295 Constraint of the Molecular Magnets in Weber's Theory 168 .... 297 Maxwell's Modification of Weber's Hypothesis .. ..169 .... 298 Hypothesis of Frictional Resistance to the Deflection of the Molecules 170 .... 298 The Constraint of the Molecules due to their Mutual Action as Magnets .. 171 299 Imaginary Molecular Groups. A Single Pair . . . . 172 .... 301 Group of Four Members 173 307 Continuous Distribution in Cubical Order . . . . 174 .... 310 Agreement of the Theory with known Facts about Sus- ceptibility 175 .... 313 Retentiveness and Residual Magnetism 176 .... 314 Experiments on Residual Magnetism in Iron . . 177 . * . 316 Retentiveness of Nickel 178 -- 323 CONTENTS. Xlii. SECTION. PAGE. Amount of Ketentiveness possible under the Molecular Theory 179 .... 323 Hysteresis and the Dissipation of Energy . . . . 180 .... 326 Eotation in a Magnetic Field. Disappearance of Hysteresis when the Field is strong .. .. 181 326 Reduction of Hysteresis by Vibration and other Dis- turbances 182 .... 329 The Molecular Theory and the Effects of Temperature 183 333 Time-Lag in Magnetisation . . . . . . . . 18 1 .... 334 Effects of Permanent Mechanical Strain. . .. ..185 .... 335 Effects of Eepetition of Magnetic Processes.. .. 186 .... 337 Effects of Elastic Strain 187 .... 343 Hysteresis in Changes of Molecular Configuration, apart from the Existence of Magnetisation . . . . 188 .... 347 Experimental Study of Molecular Groups by means of Models 189 .... 348 Ampere's Hypothesis as to the Nature of the Magnetic Molecules 190 .... 352 CHAPTER XII. PRACTICAL MAGNETIC TESTING. SECTION. PAGE. Practical Magnetic Tests 191 355 The Ballistic Method 192 356 Form of Specimens for Ballistic Te?ts 193 360 Use of Double Bars and Yokes 194 ... 362 Permeability Briage 195 .... 366 Apparatus using a Yoke with a Gap . . . . . . 196 .... 372 Du Bois' Magnetic Balance 197 .... 374 The Author's Magnetic Balance 198 375 Hysteresis Tester 199 .... 378 INDEX 385 LIST OF ILLUSTRATIONS. Fio. PAGE. 1 Force due to Magnetic Poles . . . . . 4 2 Lines of Force due to Two Poles 5 3 Magnetic Field Bound a Bar Magnet 5 4 Lines of Magnetisation in a Magnetised Bing . . . . 10 fi Disturbance of an Originally Uniform Magnetic Field by the Introduction of a Soft Iron Sphere 17 8 Disturbance of an Originally Uniform Magnetic Field by the Introduction of a Sphere of Strongly Diamagnetic Material 17 7-8 Uniformly Magnetised Ellipsoids 25 9-10 Distribution of Free Magnetism in a Uniformly Magnetised Ellipsoid 26 11 Short Ellipsoid of Infinitely Permeable Material in an Originally Uniform Field . . 29 12-13 Deflection of a Magnetometer Needle 38 14 " One-Pole " Method of using the Magnetometer .. ..40 15 Mirror Magnetometer 41 16 Arrangement for Examining Magnetic Quality by means of the Magnetometer . . . . . . . . . . . . 43 17 Liquid Bheostat 45 18 Diagram of Connections in Magnetometric Experiments . . 45 19 Magnetic Force Due to a Circular Coil 49 20 Curve of Magnetisation in Annealed Wrought Iron. . . . 53 21 Curve Distorted by using a Compensating Coil . . . . 57 22 Earth Coil for use in Ballistic Measurements . . . . 61 23 Diagram of Connections for Ballistic Method . . . . 64 24-25 Bings for Ballistic Tests . . , 67 26 Yoke and Bar for Ballistic Tests .. ... .. .. 68 27 Hopkinson's Yoke and Bar 69 28 Yoke with Double Bars 70 29 Curve of Magnetisation of a Wrought-Iron Bing . . . . 72 80 Induced and Besidual Magnetism in a Wrought-Iron King (Bowland) 75 81 Magnetisation of a Soft Iron Wire 76 32 Magnetisation of Soft Iron Bods of Various Lengths . . 78 33 Magnetisation of a Wrought-Iron Bar in a Yoke (Hopki*on) 80 34 Cyclic Magnetisation of Soft Iron Wire 81 35-36 Cyclic Magnetisation of Pianoforte Steel, Annealed and Glass-Hard 84 37 Magnetisation of Cast-Iron (Hopkinson) 85 vJ. LIST OF ILLUSTRATIONS. FIG. PAGE. 38 Cyclic Magnetisation of Nickel Wire 87 39 Cyclic Magnetisation of Cobalt 89 40 Curves of Magnetic Susceptibility in Soft and Hard Iron 90 41 Curves of Permeability in Nickel . . . . . . . . 91 42 Curves of Permeability in Cobalt 92 43 Illustration of Hysteresis in the Magnetisation of a Soft Iron King 95 44 Hysteresis in the Kemoval and Ke-application of Magnetic Force in Soft Iron 96 45 Influence of Previous Magnetisation 98 46-49 Work Done in Magnetising 100-102 50 Graded Cyclic Magnetisation of Soft Iron 106 51 Curve of Energy Dissipated in Reversals of Magnetism in Soft Iron 107 52 Cyclic Reversals in Steel 109 53 Heating Effect of Reversals in Iron and Steel. . . . 110 54-55 Magnetisation of Soft Iron with and without Vibration 115-116 56 Effects of Tapping at Points in the Magnetising Process 117 56A Magnetic Curve-Tracer 118 56s General Arrangement of Curve-Tracer 119 56c Cyclic Process recorded by Magnetic Curve-Tracer . . 120 56o Cyclic Process with Subordinate Loops . . . . 120 56s Cyclic Process at Various Speeds 121 56F Cyclic Processes in Iron and Steel 122 56a Cyclic Curves with Graded Limits of Magnetising Current 123 57 Magnetic Lag in Very Weak Fields 129 58-59 Influence of Time in the Magnetisation of Soft Iron by Weak Forces 130 60 Effects of Steps in the Magnetising Process . . . . 131 61 Diagram Showing Lagging in a Step 132 62 Influence of Time in the Performance of a Small Cyclic Process 133 63 Curve of Permeability in Strong Fields (Bidwell) . . 138 64-65 The Isthmus Method of testing the Effects of Strong Fields 140 66 Curves of Permeability of Cast and Wrought-Iron in very S-rong Fields 143 67 Application of the Isthmus Method . . . . . . 144 68 Concentration of Magnetic Force by Cones . . . . 146 69 Form of Cones giving Maximum Concentration . . . 149 70 Form of Cones giving most Uniform Field . . . . 149 7 L Sections of Cones and Bobbins 151 72 Curves of Permeability of Wrought Iron, Steel, Cast Iron, Nickel, Cobalt, and Manganese Steel in very Strong Fields 155 73-74 Electromagnet and Turning Bobbin for the Isthmus Method 157 75 Optical Method of Measuring Magnetism in Strong Fields (DuBois) ... 160 LIST OF ILLUSTRATIONS. Xvii. Fio. PAGE. 76 Magnetisation Curve of Iron, Nickel, and Cobalt . . 163 77-78 Magnetisation Curves of Iron at Various Temperatures (Hopkinson) 171 79 Eelation of Permeability to Temperature in Iron, under a Weak Magnetising Force ( Hopkinson) .. .. 172 80-81 The same under Stronger Forces 173 82-83 Magnetisation of Mild Stoel at Various Temperatures (Hopkinson) 174 84-85 Magnetisation of liard Steel at Various Temperatures (Hopkinson) 175 86-87 Magnetisation of Nickel at Various Temperatures (Hop- kinson) 176-177 88 Effects of Heating to 100C. on the Magnetic Susceptibility of Soft and Hard Iron 179 89 Effect of Heating and Cooling a Steel Bar Magnet . . 183 90-94 Hopkinson's Experiments with Nickel Steel . . 186-189 94A Effects of Temperature on the Permeability of Iron (Morris) 191 94s Record of the Cooling of Iron (Roberts Austen) . . 192 94o Effects of Baking on the Hysteresis of Sheet Iron (Roget) 194 94D Effects of Baking on the Permeability of Sheet Iron (Roget) 196 95 Magnetisation of Annealed Nickel under Various Amounts of Longitudinal Pull 200 96 The same for Hard-Drawn Nickel 201 97 Apparatus for Testing Metals under Compression . . 203 98 Curves of Induced Magnetism of Nickel under Longitudinal Compression.. .. .. .. .. .. .. 204 99 Curves of Residual Magnetism of Nickel under Longi- tudinal Compression . . . . . . . . . . 205 100 Curves of Permeability of Nickel under Compression . . 206 101 Curves of Induced and Residual Magnetism of Annealed Nickel under Compression 207 102 Effects of Loading and Unloading Nickel Wire in Various Constant Fields 208 103-104 Curve of Magnetisation of Annealed Iron under Longi- tudinal Pull .. .. 210-211 105-107 Curve of Magnetisation of Hard Iron under Longitudinal Pull 213-215 108-111 Effects of Applying and Removing Loads on Magnetised Iron Wires . . . . . . . . . . . . 218-221 112 Effect of Compressive Stress in Cobalt . . . . . . 223 113 Magnetisation Curves of Iron, showing Residual Effects of Previous Loads . . . . . . . . . . 229 114 Effects of Twist in Iron 232 115 Development of Aeolotropy by Twist 233 116 Production of Longitudinal Magnetisation by Twisting a Circularly Magnetised Rod 235 117 Curves of Circular Magnetisation produced by Twisting Longitudinally Magnetised Iron 237 118-119 The same in Steel 238-239 LIST OF ILLUSTRATIONS. Fio. PAGE. 120 Magnetisation of Nickel under Torsion (Nagaoka) . . 242 121 Magnetisation of Nickel under combined Pull and Torsion 243 122-124 Effects of Cyclic Twisting in Magnetised Nickel (Nagaoka) 246-248 125 Apparatus for determining the Change of Length caused by Magnetisation (Bidwell) 250 126-1 27 Curves showing Changes of Length due to Magnetisation in Iron, Nickel, and Cobalt (Bidwell; 252 128 The same for Iron under Longitudinal Pull . . . . 253 129 Apparatus for Measuring Magnetic Tractive Force (Bosan- quet) 256 130 S. P. Thompson's Permeameter 261 131 Example of an Imperfect Magnetic Circuit . . . . 273 132 Graphic Treatment of an Air Gap in the Magnetic Circuit 279 133 Graphic Treatment of a Composite Circuit . . . . 281 134 Influence of a Smooth Joint on the Magnetic Eesistance of an Iron Bar . . , 288 135 Effects of Successive Cuts in a Bar 292 136 The Three Stages of the Magnetising Process . . . . 300 137-140 Deflection of a Pair of Magnetic Molecules by Application of an External Field 301-304 141-143 Deflection of a Group of Four Magnetic Molecules . . 307-308 144 Curve of the Eesultant Moment of the Group . . . . 309 145-147 Deflection of a Multiform Group 310-312 148 Curves of Induced and Residual Magnetism in Iron, in the Soft State, and Hardened by Stretching . . . . 317 149-151 Proportion of Eesidual to Induced Magnetism in Iron 318-322 15lA Hysteresis in Alternating and Eotating Fields (Baily) . . 328 152-153 Influence of an Alternating Electric Current in Iron Wire during Magnetisation (Gerosa and Finzi) . . . . 331-332 154 Eepetition of Magnetic Cycles in Iron 311 155 Cyclic Force in Iron previously Demagnetised by Reversals 342 156 Repetition of Magnetic Cycles in Steel 344 157 Effects of Eepeated Loading on an Iron Wire in a Weak Field 346 158 Pivoted Magnet used in Construction of Model to Illustrate the Molecular Theory 348 158A General Arrangement of Model . . . . . . . . 350 159 Curve of Cyclic Process applied to a Group of Pivoted Magnets 351 160 Arrangement for Ballistic Tests 357 161 Cyclic Processes by Ballistic Method 360 162-3 Double Bars and Yokes . . 362 164 Method of Correcting for Yokes 365 165 General View of Permeability Bridge 366 166 Details of Permeability Bridge 368 167 Example of Curve by Permeability Bridge . . . . 371 168-9 Koepsel's Apparatus 372-373 170-171 Du Bois' Magnetic Balance 374-375 172 ^ The Author's Magnetic Balance 377 173 Hysteresis Tester . . . . 380 CHAPTER L INTRODUCTORY. 1. Introductory. Though all substances show some mag- netic quality, there are three that form a group distinct from all others in this respect. In other metals and non-metals a feeble magnetisation may be induced with difficulty ; iron, nickel and cobalt take magnetism readily, and take it in amounts that are relatively enormous. In other substances we have no evidence that there is such a thing as permanent magnetism, but these three can retain magnetism strongly. Their capability of being magnetised, which is more or less shared by alloys in which one or other of them is contained (and also by the magnetic oxide of iron), is so conspicuously great, in comparison with that of any other substance, that they may properly be said to stand apart as the magnetic family of metals. Our purpose is to give some account of the properties that entitle them to this name. Before proceeding to speak of experiments and their results, it may be well to recall the various conventions according to which magnetic quantities are expressed. Most of this intro- ductory matter is, of course, familiar to the student, but parts of it, perhaps, are less familiar, and some confusion is apt to be felt on account of the variety of ways which one may follow in stating facts about magnetic quality. The magnetisation of an iron bar, for example, maybe specified by its magnetic moment, by its intensity of magnetisation, or by its magnetic induction ; and its readiness to be magnetised may be measured either by what is called its magnetic permeability, or by another not quite identical quantity called its magnetic suscepti- bility. The student is liable to feel that there is an embarras 2 MAGNETISM IN IRON. de rickesse in magnetic ideas and phraseology. The various lights in which the magnetism of a piece and its magnetic quality may be regarded are, of course, consistent with one another, and are related in a simple enough manner. Some forms of expression have the advantage that they fit in best with modern conceptions of the magnetic state; others survive because they are more convenient in special cases. The magnetic circuit of a dynamo is most simply treated by using one set of terms ; another set of terms come readier to hand when we have to speak about the properties of a magnetised steel bar. The student will, therefore, do well to master the meaning of all the magnetic terms in common use, and should accustom himself to look at magnetic phenomena from various points of view. 2. Magnetic Poles, Axis, and Moment. An old and still useful way of looking at the matter is to think of the action of a magnet as due to the existence of two quantities of hypothetical magnetic substance, or " free magnetism," equal in amount and opposite in kind, which are distributed in the neighbourhood of the two ends. These hypothetical positive and negative substances have the property that two portions of like kind repel each other, and two portions of unlike kind attract each other, with a force which is proportional to the product of the amounts of the substances, and inversely proportional to the square of the distance between them. In an ordinary bar magnet the free magnetism is distributed partly over the surface at and near the ends of the bar, and partly throughout the interior of the bar, especially near the ends. The action of the magnet upon anything at a considerable distance from it is much the same as it would be if the free magnetism were concen- trated at two points, near the ends, which are called the poles. Strictly speaking, there are no precise poles in a magnet that is to say, there are no two points at which we might imagine the positive and negative free magnetism to be gathered, and find the magnetic action on external things to be quite un- changed. It is only when the bar is very thin and uniformly magnetised ( 7, below) that we come near to realising the idea of two definite centres of force at the ends of the bar where the positive and negative free magnetism is concentrated. The idea of poles in a magnet has therefore to be employed with MAGNETIC FIELD AND MAGNETIC FORCE. 3 much caution, but it is too useful to be altogether aban- doned. The strength of a pole is the whole amount of magnetism which is to be taken as gathered there. Unit pole, or unit quantity of free magnetism, is that quantity which repels or attracts another quantity equal to itself with unit force when the two are placed at unit distance from each other. It is now a universal practice to express magnetic quantities in terms of the centimetre-gramme-second system of units. We may, therefore, define the unit pole as that which acts on another pole of equal strength with a force of one dyne when the two are placed one centimetre apart. The axis of a magnet is the line joining its poles. The moment of a magnet is its pole-strength multiplied by the distance between the poles. According to this conception of a magnet, the magnetic action of the bar is due to the free magnetism at the poles ; the middle portion of it is neutral, and merely serves to hold apart the ends, in which the free magnetism resides. 3. Magnetic Field and Magnetic Force. For many purposes this conception of poles is a very serviceable one. It is especially serviceable when we have to treat of the influence which the magnet exerts throughout the space in its neighbourhood, or throughout what is called the magnetic field. To examine the magnetic field, we may think of the force which the magnet N S (Fig. 1) will exert on an imaginary particle of magnetic sub- stance, P, placed anywhere in its neighbourhood. The two poles of the magnet will exert two forces, F 1 and F 2 , which are proportional to and : one pole will tend to pull the particle towards it, the other pole will tend to push the particle from it. These forces will have for their resultant a single force, R, which is the whole force exerted by the magnet upon the particle. The direction of this resultant is definite at any point in the field, but its amount will depend on the amount of magnetic substance in the particle. Suppose, now, that we take a particle in which the amount of magnetic sub- stance is one unit (as defined in 2), and observe the force exerted upon it when it is placed anywhere in the field, we now find a force which is definite (at any one point of the B2 MAGNETISM IN IRON. field) both in magnitude and direction. This force measmns the intensity of the field at the point in question, and is called the magnetic force at that point. Instead of one magnet only there may be any number of magnets, the poles of which con- tribute to the production of magnetic force at any point of the field in which the magnets lie. We may still think of each pole as exerting its own component of force on the imaginary par- ticle of unit strength, and then combine all these componenta to find a single resultant which measures the magnetic force. Electric currents also give rise to magnetic force in their neighbourhood, so that, in considering the value of the mag- netic force at any place, we have to take their action into Fia. L account as well as the action of the poles of neighbouring magnets. But whatever currents or magnets contribute to the production of the magnetic field, the magnetic force at any point of space has a definite direction and value, which may be expressed by stating the mechanical force which would be felt by a unit magnetic pole when placed there. The direction of the magnetic force is the direction in which the unit particle will tend to move, and the value of the magnetic force is the value in dynes of the mechanical force which tends to move the particle. 4. Lines of Magnetic Force. If we allow the particle to move so that the direction it takes is, at every instant, the OF THE UNIVERSITY ] OF LINES OF MAGNETIC PORCH. direction in which the magnetic force acts upon it, and if we mark the course it takes through space, we shall trace out what is called a line, of magnetic force. In general these lines are curved, for the direction of the magnetic force varies as FIQ. 2. we pass from point to point through the field. If the magnetic field is produced by a single pair of opposite poles, the lines of force start from the positive pole and spread in curves, which bend round through space, and all Fio. 3, converge on the negative pole (Fig. 2). The well-known curves in which iron filings group themselves when scattered near a magnet represent approximately the forms taken by the lines of force. In the field produced by an actual bar magnet (Fig. 3) the lines do not converge as in Fig. 2 to a single pair 6 MAGNETISM IN IRON. of points, for the positive and negative quantities of free mag netism are each distributed over a considerable part of the length of the bar. Where the lines come close to one another the magnetic force is intense : where they lie far apart the field is weak. If we pass along lines of force from one place to another in the magnetic field, we shall find that the in- tensity of magnetic force at each place is proportional to the number of lines of force which cross an imaginary sur- face of unit area, placed there and set so that it stands at right angles to the direction of the lines. We can make the number of lines which cut such a surface not only propor- tional, but numerically equal to the magnetic force, through- out the whole field, by adhering to a proper convention as to the whole number of lines to be drawn. The convention is that the number of lines of force which start from any pole of strength m is 4:irm. Consider a sphere of radius r in centi- metres enclosing a magnetic pole of strength m. According to the convention, the number of lines of force which radiate from the pole and cut the surface of the sphere is 4:irm. But the area of surface of the sphere is in square centimetres 47rr 2 . The number of lines of force per square centimetre at the surface of the sphere is therefore or , and this is also 4 TT r 2 r 2 the measure of the magnetic force there, for the force is due to a pole ?7i at a distance r. 5. Uniform Magnetic Field. In a uniform field that is to say, a field in which the magnetic force has the same direction and the same intensity at all points the lines of force are straight, parallel, and equally spaced. The magnetic field due to the earth's action as a magnet is sensibly uniform throughout any small space, such as that of a room. Good approximations to a uniform field can be obtained by suitable arrangements of magnets, or of conductors carrying electric currents. Thus, if we take a long uniform solenoid or helix of wire, wound so that the diameter is constant and the number of turns is the same in each unit of the length, and pass a current through it, a magnetic field will be produced which is very nearly uniform throughout the whole space within the solenoid, except close to the ends. The value of the magnetic force in this field due to the current is CONTINUITY OP THE MAGNETIC STATE. 7 , where C is the current in absolute electro-magnetic units,* and n is the number of turns in the winding per centi- metre of the length of the solenoid. Reducing this to practical units, the magnetic force within the solenoid is 1*257 times the number of ampere-turns per centimetre of the lengtn. Again, a nearly uniform field may be produced by taking two similar magnets with flat ends and placing them in line with their flat ends parallel, so that the north pole of one nearly touches the south pole of the other. In the narrow gap between the ends facing one another there is a strong mag- netic field, through which the lines of force pass almost straight across from one face to the other. The field is very nearly uniform except at the edges. 6. Continuity of the Magnetic State. We have seen that the magnetism of a magnetised bar may be described by refer- ence to its ends, where the imaginary positive and negative magnetic substance is accumulated, the middle parts being in- active. From another point of view the magnetisation extends throughout the whole substance. We may think of every por- tion of the magnet as polarised; that is to say, every particle or elementary piece of the bar may be regarded as a separate magnet. Throughout the middle portion of the length these elementary pieces are grouped so that each pole of one touches the opposite pole of its next neighbour, and the result is that the middle portion of the bar shows no positive or negative magnetism ; but at the ends the poles of the elementary pieces are no longer neutralised, and the poles of the pieces there become the poles of the bar. This is the modern view of the matter, and is in many ways an advance on the simple polar view. It is borne out by the fact, experimentally observed, that when a magnet is cut up into pieces, however small, each piece is a separate magnet. 7. Intensity of Magnetisation. From this point of view we are to regard the magnetic state as existing continuously throughout the bar. If this state is uniform from end to end * The absolute electro-magnetic unit of current in the C.-G.-S. system is equal to 10 amperes. 8 MAGNETISM IN IRON of a bar, the metal is said to be uniformly magnetised. If we could cut up such a bar by cross-sections into short lengths with- out disturbing the uniformity of the magnetisation, we should find every part to be a magnet with the same pole-strength as the original bar. If we could split it by longitudinal sections we should find the pole-strength of each part to be proportional to the area of cross-section in that part. In other words, if we could cut up the bar in any manner (always without altering the magnetic state of the metal) we should find that the pieces were separate magnets of which the moments were proportional to the volumes of the pieces. The magnetic moment of each piece will be the same fraction of the magnetic moment of the uncut bar as the volume of the piece is of the volume of the uncut bar. The magnetic state which existed throughout the bar before it was cut, and exists throughout each piece after cutting, may be specified if we state the moment per cubic centimetre of the metal. This quantity is called the intensity of magnetisa- tion, and is usually denoted by I. 8. Relation of I to Pole-Strength. Let M be the moment of a uniformly magnetised straight bar ; let I be the length of the bar in centimetres, s its area of cross-section in square centi- metres, and m its pole-strength. Then M = m The volume of the bar is si; hence I, which is M divided by the volume, is , or . Si 8 We might, therefore, have defined I as the pole-strength per square centimetre of sectional area. It is useful to remember that I has also this meaning, but the essential idea implied in the phrase " intensity of magnetisation " is better conveyed by the definition of I given above. We are to think of I as the measure of a polarised state which has a true existence every- where in the substance of the metal, though it manifests itself only at the ends, so far as external action is concerned. 9. Ring Magnet. The usefulness of this idea will be at once apparent if we consider what happens when a uniformly mag- LINES OF MAGNETISATION, 9 netised rod is bent round into a ring until the ends meet. There are now no poles : those that existed in the rod have met and have neutralised each other ; there is now no magnetic moment, and the ideas of poles and moment will no longer serve as means of stating the magnetic state of the ring. But the ring is still magnetised : if we were to cut it in pieces we should find the pieces to be magnets. The magnetic state expressed by the quantity I still exists within the metal : there is a definite " intensity of magnetisation " throughout. If we were to cut a narrow gap through the ring we should find on one side of the gap a positive pole, and on the other side a negative pole, and the strength of each would be I s. 10. Lines of Magnetisation. Suppose such a gap or crevasse to be cut, the number of lines of force which cross the gap is 4 TT I s (by 4), and hence the magnetic force within the gap (which is the number of lines of force per square centimetre) is 4 TT \ ; so far, that is to say, as the magnetic force there is due to the magnetism of the ring. Of course there may be additional magnetic force within the gap due to other magnets or to electric currents in the neighbour- hood ; but for the present we may confine our attention to the force that exists there on account of the magnetisation of the ring itself alone. The same lines 4 TT I s which cross the gap may be conceived as extending continuously round the ring through the substance of the metal. Each line forms a closed curve : a short part of it is in the gap, the greater part is in the metal. We may call the parts of the lines which lie within the metal lines of magnetisation. The name " lines of force," which is applicable to the lines in the gap, is inappropriate to those parts of the lines which lie within the metal, because the lines within the metal do not form a measure of the magnetic force there. 11. Lines of Magnetisation (continued). Fig. 4 illustrates the supposed case of a narrow gap or crevasse, A B, cut across the substance of a magnetised ring at any place in its circumference. Within the metal we have the lines of magnetisation which are shown by dotted lines in the figure. The number of these, per square centimetre of cross-section, is 4 TT I. These lines are con- 10 MAGNETISM IN IRON. tinuous closed curves, and pass across the gap, forming lines of force there. If we measure the magnetic force within the crevasse, we shall find it equal to this quantity, 4 TT I, together with whatever other magnetic force may act there in con- sequence of electric currents or magnets in the neighbourhood. That part of the magnetic force within the crevasse which is represented by 4 TT I, is directly due to the breach which we have made in the continuity of the magnetised ring. It may be regarded as existing there in consequence of the fact that lines of magnetisation within the metal are necessarily con- tinuous with lines of force outside the metal. Fia. 4. Take another way of looking at the matter. We may think of this force within the crevasse A B as due to free magnetism on the surfaces A and B. When we cut the crevasse in the magnetised ring, we bring into existence a positive pole which is distributed over the surface at A, and a negative pole which is distributed over the surface at B. The strength of each of these poles is I s, and the surface-density of free magnetism that is to say, the amount of free magnetism per square centi- metre of surface is I. By a well-known proposition in the MAGNETIC FORCE WITHIN THE METAL. 11 theory of attraction, a plate on which the surface-density is I attracts a unit particle placed close to it with a force equal to 2 TT I (except near the edge, where the force is less). Let a unit positive magnetic pole, then, be placed in the crevasse. The plate of free magnetism on A repels it with the force 2 TT I ; the plate of free magnetism on B attracts it with an equal force. The whole force at a point in the crevasse, due to the magnet- isation of the ring, is the joint force exerted by the two plates; in other words, it is 4 TT I. Suppose now that the uniformly magnetised magnetic ring is stretched out to form a straight bar. If we imagine a crevasse to be cut across it at any part of its length, we shall still find in the crevasse the lines 4 TT \ per square centimetre due to the continuous magnetisation of the bar, in addition to what- ever lines of force may exist there in consequence of electric circuits or free magnetism in the neighbourhood (excluding, of course, the free magnetism on the faces of the crevasse, to which the lines 4 TT I are directly due). The whole field within the imaginary crevasse may therefore be thought of as made up of two components, namely, (1) the lines of magnetisation, the number of which is 4 ir \ per square centimetre ; and (2) the magnetic force due to external causes, namely, that which is due to electric currents and free magnetism in the neigh- bourhood. Amongst the causes of this magnetic force is to be included the free magnetism at the ends of the bar itself, as well as the poles of any other magnets which may be near enough to produce any sensible effect. 12. Magnetic Force within the Metal. The magnetic force due to external causes that is, to magnets or electric cur- rents in the neighbourhood which has just been described as constituting one part of the magnetic force which we should measure in a crevasse, is to be thought of as acting also within the uncut substance of the metal itself. It consti- tutes the whole magnetic force there. We shall denote the magnetic force by H. It must be borne in mind that in reckoning the value of H at any point within the substance of a piece of magnetised metal, account is to be taken not merely of the forces due to electric currents and to ter- restrial magnetism and to the poles of other magnets, but 12 MAGNETISM IN IRON. also of the forces which are contributed by the poles of the piece itself. 13. Magnetic Induction. The whole group of lines which cross the crevasse is to be conceived as existing within the metal before the crevasse was cut, partly as lines of magnetisation and partly as lines of force. The whole group of lines which cross the imaginary crevasse consists (per square centimetre) of the resultant of 4 TT I and H. This resultant is called the magnetic induction within the metal, and is denoted by B. The quan- tities 4 TT I and B are vectors, having direction as well as mag- nitude, and are to be compounded as forces or velocities are compounded. If H and I happen to have the same direction, B is numerically equal to the sum of 4 TT I and H. In any case the equation B = 4 TT I + H is true when understood in the vector sense, that B is the resultant of 4 TT I and H. In most of the cases that are of prac- tical interest H has either the same direction as B or it has the opposite direction, so that the above equation holds good in the numerical sense when the proper sign ( + or - ) is given to H, according as it assists or opposes the magnetisation. 14. Distinction between Magnetic Induction and Mag- netic Force within the Metal. The lines of magnetic induc- tion (B) within the bar are continuous with the lines of magnetic force in the space outside that is to say, every Line of Force outside is completed, so that it forms a closed curve, by a Line of Induction inside. For many purposes B is the most important quantity by which the magnetisation of a magnet may be specified. In a dynamo, for instance, it is the value of B in the armature core that determines the strength of the magnetic circuit. The analysis of B into two components, H and 47r|, is no doubt highly artificial, but it is of service when we have to deal with the relations which exist between the magnetism of a magnet and the influences which are affecting its magnetism from outside. The student will find it useful to picture to himself the state of a magnet at any point of its substance by thinking of two groups of lines as passing through the metal, namely, 4 TT | and H, which combine PARTICULAR CASES. 13 to form a resultant group B. To obtain B directly we have only to imagine a narrow crevasse cut across the magnet : B is measured by the force a unit pole would experience if placed in such a crevasse ; in other words, it is the number of lines which cross the crevasse per square centimetre of cross-section. If, on the other hand, we wish to isolate the magnetic force H that acts at any point within the metal, we may imagine a hole drilled through the magnet from end to end in the direc- tion of magnetisation, and passing through the point at which H is to be measured. The force which a unit pole would expe- rience if placed in the hole at that point is H. That this is so will be evident when it fa remembered that there is no free magnetism on the sides of the hole, because it is supposed to be drilled in the direction of magnetisation, and the force within it is, therefore, due solely to the outside influences which give rise to the magnetic force H, as denned in 12, namely, the free magnetism at the ends of the magnet and any other magnets or currents that are near. It is only at points inside the metal that we need distinguish the magnetic force H from the magnetic induction B. Outside, at points in non-magnetisable space, the magnetic induction is identical with the magnetic force. There is no discontinuity in the lines of ind uction where they pass into the metal or out of it. 15. Particular Oases. The following illustrations may help to make these definitions intelligible. Take a ring electro-magnet consisting of an iron core, wound with a solenoid of n turns per centimetre, and let a current, C, flow in the solenoid. The mag- netic force within the solenoid, due to this current, is approxi- mately equal to 4 TT C n at all points. If there are no neighbour- ing magnets or other sources of magnetic force, this is the value of H which acts on the metal of the ring. Next, let the ring be cut and straightened into a bar, with the solenoid still ov it, through which the current C flows. The magnetic force du& to the current is still sensibly equal to 4 TT C ft (except near the ends). But we now have another term to consider in reckoning H. The free magnetism residing at the ends of the bar pro- duces magnetic force at all points in the interior, as well as at points in the space outside, and H is the resultant of 14 MAGNETISM IN IRON. this force, together with the force 47rCn due to the cur rent. The force due to the free magnetism at the ends is opposite in direction to that due to the current j hence H at any point within the metal is less than 4 TT C n by an amount which depends on the distance of the point considered from the ends of the bar. The longer the bar is the more nearly will H be identical with 4 TT C T&, and if the bar is very long, so that the ends are too far removed to have any material influence, we may take the magnetic force on central portions as sensibly equal to 4 TT C n. Again, in a permanent bar-magnet there is at any point a certain magnetic force, H, due to the free magnetism at the ends, and opposite in direction to the lines of magnetisation within the metal. We may call this the self-demagnetising force exerted by the bar, since its tendency is to reduce the bar's magnetisation. Again, a long piece of straight iron wire stretched in the direction of the lines of force of the earth's magnetic field is acted on by a magnetic force, H, equal to the force of the earth's field. If the wire is hung vertically it is convenient to treat the earth's field as consisting of a horizontal and a vertical com- ponent. The former is a magnetic force which acts across the wire ; the latter is in this case much the more important of the two, for it constitutes the whole longitudinal part of the mag- netic force H, and, as we shall presently see, it is upon this almost wholly that the magnetisation of the wire depends. 16. Magnetic Permeability. In general, when a substance is placed in a magnetic field it becomes magnetised. The connection between the magnetism it acquires and the mag- netic force which acts upon it may be expressed in two ways. One of these ways is to compare the magnetic induction B which is produced in the metal with the magnetic force H to which that induction is due. For many purposes this is the most convenient way. To fix our ideas let* us think of a very long uniform rod placed in a uniform field of magnetic force, with the direction of its length parallel to that of the lines of force. When the rod becomes magnetised its ends disturb the field of force, but we can get rid of any trouble about the ends by thinking of thti MAGNETIC PERMEABILITY. 15 rod as indefinitely long, or so long that the influence which the ends have on the value of the magnetic force is negligible. Let the uniform magnetic field exert a certain force, H, on the rod. This produces within the rod a certain induction, B, the value of which might be measured by cutting a narrow crevasse acroos the rod at any place, and measuring the number of lines per square centimetre which cross the crevasse. If the rod is of iron, nickel, or cobalt, it will be found that the number of lines of induction B per square centimetre within the rod is much greater than the number of lines per square centimetre in the field. This fact may be expressed by saying that the material of the rod is more permeable with respect to lines of magnetic induction than is the space or medium surrounding it. In Faraday's expressive language, the material of rod has greater conductivity for the lines of induction than the surrounding space or medium has. We may think of the lines as crowding by preference into the rod, finding an easier path through it than through the surrounding medium. The quality in virtue of which the material of the rod con- ducts the lines better than empty space conducts them, is called Its magnetic permeability. This phrase was introduced by Lord Kelvin in his mathematical development of the subject, as a synonym for Faraday's " Conducting power of a magnetic medium for lines of force." In the case we have supposed, of an indefinitely long rod, the magnetic force at any point within the metal has the same value as the magnetic force at any neighbouring point in the space outside, since the force is not disturbed by the magnetisation of the rod. In such a case we might define the permeability as the number (per square centimetre) of lines of induction B in the rod to the number (per square centimetre) of lines of force in the space outside. But if we wish a definition which will be of more general application applying to short rods as well as to long ones, and to other forms of magnet we have to bear in mind that the surrounding field is generally disturbed by the magnetisation of the piece. What has to bo compared is the induction at any place in the metal with tha magnetic force which is in operation there ; in other words, we may define the permeability as the ratio of the induction 16 MAGNETISM IN IRON. B at any point of the metal to the magnetic force H which acts within the metal at that point. The permeability is usually denoted by ft ; so that we have In this definition it is to be understood that B, the magnetic induction, has been produced by subjecting the material to a magnetic force, H. 17. Permeability of Paramagnetic and Diamagnetic Sub- stances. A paramagnetic substance is one in which the per- meability is greater than that of empty space. In other words, when such a substance is placed in a magnetic field it will become magnetised in such a way that B is greater than H. The lines of force of the surrounding field will converge more or less towards it, preferring it to the neighbouring space as a magnetic "conductor." Iron, nickel, and cobalt are para- magnets with exceedingly great permeability. In a diamagnetic substance, on the other hand, the per- meability is less than that of empty space. When such a substance is placed in a magnetic field, the lines of force more or less avoid it as a bad "conductor," preferring the space outside. No substance is more than slightly diamagnetic. Even in bismuth, which is the most highly diamagnetic substance known, the magnetic permeability is very little less than unity : its value is about 0'999S2. The permeability of air is sensibly the same as that of empty space. Hence, when a magnetic field is formed in air, the lines cf induction are indistinguishable from the lines of force. It is only when the lines pass into a substance which is either para- magnetic or diamagnetic that the distinction between magnetic force and magnetic induction must be maintained. 18. Illustrations of Permeability. By way of illustrating the behaviour of paramagnetic and diamagnetic substances when placed in a magnetic field, Fig. 5 and Fig. 6 have been copied from one of Lord Kelvin's Papers.* In Fig. 5 a magnetic field which was originally uniform has been disturbed * Reprint of Paper on " Electrostatics and Magnetism," pp. 489 and 491. ILLUSTRATIONS OP PERMEABILITY. 17 by having a sphere of exceedingly permeable material placed in it. Before the sphere was placed in the field the lines of force were straight, parallel, and equally spaced. The effect of introducing the sphere is to make them converge upon it in the FIG. 5. Disturbance of an originally uniform magnetic field by the intro duction of a soft iron sphere. FIG. 6. Disturbance of an originally uniform magnetic field by the intro- duction of a sphere of strongly diamagnetic material. manner which has been exactly represented in the figure from which Fig. 5 is copied. Outside the sphere the lines may be called indifferently lines of induction or lines of force ( 14). The lines inside, which have been added in this copy, are continuous with them, and are lines of induction. The mag- C 18 MAGNETISM IN IRON. netic induction within the sphere is uniform. Fig. 5 may be taken to represent what happens when a homogeneous spherical ball of soft iron is placed in an originally uniform magnetic field. Fig. 6 shows in the same way how an originally uniform field of force is disturbed by the introduction of a sphere of diamag- netic material. The material here is a purely imaginary one, with permeability barely one-half that of the surrounding medium, and is far more highly diamagnetic than any actual substance. The student will not fail to notice that the convergence or divergence of the lines of induction, illustrated by these typical cases, depends on whether the permeability of the body is greater or is less than the permeability of the medium in which it is placed. If the surrounding medium were itself a paramagnetic substance, the case shown in Fig. 6 might be realised by choosing for the material of the spherical ball a substance whose permeability was about half (more exactly 0'48 times) that of the substance surrounding it. We shall return to these figures later, in speaking of the influence which the form of the body that is placed in a magnetic field exercises on the amount of magnetic induction within the body. 19. Magnetic Susceptibility. When a substance is mag- netised by subjecting it to the action of magnetic force, the relation of the induction B to the force H measures, as we have seen, the permeability of the substance. But instead of expressing the magnetisability of the substance by stating the relation of the induction B to the force H, we may state it in a different way by giving the relation of the intensity of mag- netisation I to the force H. The ratio of the intensity of magnetisation to the magnetic force producing it is called the magnetic susceptibility of the substance, and is usually denoted by K ; thus . K= F 20. Connection of the Ideas of Permeability and Sus- ceptibility. We have seen ( 13) that CONNECTION OF IDEAS OP PERMEABILITY, ETC. 19 and by definition of the susceptibity K, I = K H J Hence B = 4?rK But by definition of the permeability ju, B = /* H ; Hence /A and K = 4:TT In a substance such as air, in which the permeability Is unity, the magnetic susceptibility is zero. In a paramagnetic sub* stance, in which p, is greater than 1, the susceptibility is positive. In a diamagnetic substance, in which the permeability is less than 1, the susceptibility is negative. In other words, a paramagnetic substance when subjected to magnetic force acquires a magnetisation I, which is in the same direction as the force, and so makes B greater than H. A dia- magnetic, on the other hand, acquires a magnetisation I, which is opposite to the force, and so makes B less than H. 21. A word of caution is, perhaps, desirable here as to the application of the equations which have just been given. It has been assumed that the material to which the magnetic force H has been applied, has no magnetism except what the force itself induces. If other forces had acted before, leaving residual D magnetisation, the ratio would not be a true measure of H the permeability, nor would the ratio . be a true measure of H the susceptibility. Again, it has been assumed that the material is magnetically isotropic that is to say, that a lump of it is equally capable of taking magnetisation in all directions. If this were not so, if the magnetic properties of the substance were different in different directions (as would, for instance, be the case to some extent in a piece of iron cut from a rolled plate), it would be necessary, if we wished to specify fully the relation of the magnetisation to the magnetic force, to resolve the force c2 20 MAGNETISM IN IRON. into components along axes chosen in the directions which give greatest susceptibility and least susceptibility, find the component magnetisation in each of those directions by multiplying each component force by the value which the susceptibility has in that direction, and then compound these components of magnetisation to find the resultant value of I. In such a case the direction of the resultant magnetisation will not in general coincide with that of the resultant magnetic force, and the equation B 4 TT | + H will be true only when interpreted in its vector sense. But in the cases of magnetisation in iron which have ordi- narily to be dealt with, it is not necessary to take account of this consideration, for the material is either sufficiently nearly isotropic, or the direction of the applied magnetic force coin- cides with an axis of greatest or least magnetic susceptibility, and the effect is that I and B have the same direction as H. 22. Influence of the Form of Bodies on the Magnetisation induced in them. When a body is placed in a magnetic field the degree to which it becomes magnetised depends not only on the original strength of the field and on the permeability of the substance, it depends also (often in very great measure) on the form of the body. This is because the body, in becoming magnetised, generally disturbs the field, causing the magnetic force at any point within or near the body to be different from the force that existed there before the body was introduced. The free magnetism which is developed by the body's magneti- sation contributes to produce magnetic force, and so affects the resultant value of the force at any point, inside the body or outside, that is not too far off' to be sensibly affected. With iron and other very susceptible materials this disturbance of the field is often so great that the original value of the mag- netic force is not even a rough approximation to the value the force assumes when modified by the magnetisation of the body. The intensity of magnetisation at any point within the body depends on the actual value which the magnetic force assumes at that point, and this in its turn depends partly upon the magnetisation of the body as a whole. When we wish to examine the magnetic susceptibility or per- meability of a substance, we require to know the actual value INFLUENCE OF FORM ON MAGNETISATION. 21 of the magnetic force within it, for the purpose of comparing that with the intensity of magnetisation, or with the magnetic induction there. The permeability is measured by the propor- tion which the induction B bears to the strength which the magnetic force H actually has at the same place, not to the strength which it may have had there before the body was in- troduced, nor to the strength which it may still have in external parts of the field. We have, therefore, to take account of what may be called the reaction of the magnetised body upon the magnetising field. In very many cases the reaction of the body upon the field is too complex to allow a mathematical examination of it to be practicable. With bodies of irregular form it is out of the question to calculate beforehand what will be the magnetic force and the magnetic induction at internal points, having given the original strength of the external field and the per- meability of the substance. The problem is determinate, but too difficult to attack. Even so apparently simple a case as that of a short cylindrical iron rod with flat ends, placed lengthwise in an originally uniform field, presents difficulties so formidable that no exact solution has been given. The difficulty in the case of such a rod is aggravated by the fact that even though the rod be perfectly homogeneous to begin with, the suscepti- bility or the permeability is not uniform throughout when the rod becomes magnetised. This is because the magnetisation is not uniform, and, as we shall see later, the permeability of iron depends to a considerable extent on the intensity of magnetisa- tion. The reaction of the rod upon the original field tends to reduce the magnetic force at internal points, but this effect is unequal at different parts of the length. It is least at the middle of the length; hence the magnetic force, and conse- quently the induction also, is greatest there and is less near the ends. 23. Long Rod placed Lengthwise in a Uniform Field. When the rod is long in comparison with its breadth and thick- ness the effect of its free magnetism in reducing the magnetic force is less than when the rod is short, especially in the middle region of the length, because the ends, in which the free mag 22 MAGNETISM IN moN. netism chiefly resides, are too far off to have much influence. The amount of magnetic induction is consequently greater in a long rod than in a short one of the same breadth and thickness, the original strength of the field and the permeability of the substance being the same in both cases. When a very long rod is placed lengthwise in a uniform field the influence of the ends becomes almost insensible, and the actual magnetic force at points within the rod is then almost the same as at points outside, except near the ends. The magnetisation will be practically uniform throughout the middle region, but will fall off towards the ends. When the substance of the rod is very permeable, the rod must be very long relatively to its transverse dimensions before we may neglect its reaction upon the magnetic field, and before we may treat the magnetic force at internal points near the middle as sensibly equal to the force at external points, and the magnetisation as nearly uniform. When the substance is less permeable a shorter length will give an equally good approach to uniform force and uniform magnetisation. 24. Analogy of Induced Magnetisation to Electric Con- duction. The concentration of magnetic induction which takes place when a permeable body is placed in a magnetic field is analogous to the concentration of electric flow which may be brought about by immersing a piece of copper in a tube full of mercury, through which an electric current is passing. Let the tube be wide and long, and let the current in it be uni- formly distributed over the whole cross-section : we have in this the analogue of a uniform magnetic field. Suppose a short piece of copper wire to be inserted and held lengthwise anywhere near the axis of the tube. The lines of electric flow, which before were straight and parallel, converge more or less towards the piece of copper, preferring to crowd into it because its conductivity is much greater than that of the surround- ing medium. The whole current is divided between the copper and the mercury around it, the copper taking a share that is greater than the proportion which its cross-section bears to that of the whole conducting tube. The current enters and leaves the copper not at the ends merely, but also along the sides, especially near the ends. If the piece of copper is short, there can be no ANALOGY OP MAGNETISATION TO CONDUCTION. 23 more than a slight convergence of the flow into it. For instance, to take an extreme case, a little disc of thin copper plate placed in the mercury, so that it faces in the direction of the flow, has little more conduction through it than through an equal area of the surrounding liquid. In other words, the disc produces but a slight disturbance of the distribution of flow in the tube. On the other hand, a long thin copper wire set lengthwise will gather much of the flow into itself, and if the wire be very long its share of the whole will be greater than the amount taken by an equal section of the mercury in the proportion in which the conductivity of copper is greater than that of mercury. Substitute magnetic permeability for electric conductivity, and magnetic induction for electric flow, and we have a nearly perfect analogue of what happens when an iron rod or wire is placed in a magnetic field. There is, however, this important difference, which makes the magnetic case less simple than the other. The electric conductivity of the copper is a constant quantity, independent of the strength of current in the metal; whereas the permea- bility of iron depends on the actual intensity of magnetisation, and consequently varies (in general) to some extent throughout the piece. 25. Cases in which the Magnetisation is Uniform : Ellipsoid. In certain special cases it happens that when a magnetisable body is placed in a uniform magnetic field, the magnetic force at all points inside the body is uniform, though its value there is not the same as at external points. A very important instance in which this is true occurs when the form of the body is that of an ellipsoid, the material being homo- geneous, so that the permeability has the same value through- out. In such a case it may be shown that the effect of an originally uniform external field is to produce a strictly uniform magnetisation.* Let the ellipsoidal body be made of a paramagnetic material, such as iron, and let it be placed in a uniform field : then the originally straight and parallel lines of the field become bent, so that they converge on it, as the lines converge on the sphere * See Maxwell's " Electricity," Vol. II., 437-43a 24 MAGNETISM IN IRON. in Fig 5. The reaction of the body on the field is such that the magnetic force at outside points near the body is no longer uniform. But at internal points the effect of the reaction is different. The force becomes uniform there, with a value, however, which is less than the value it had in the undis- turbed field. This uniform internal force implies uniform induc- tion and uniform intensity of magnetisation that is to say, each of the quantities H and I and B is uniform throughout the whole of the body ; but it must be borne in mind that H differs, and often differs greatly, from the value which the force had originally, and still has in distant parts of the field. The amount of this difference will depend on the shortness of the ellipsoid and the intensity of its magnetisation. For brevity we shall use H' to designate what may be called the external force that is, the original value which the force had before the field was disturbed, or, what is the same thing, the value which the force still has at distant external points; and we shall keep H to mean, as usual, the actual magnetic force at points within the metal. 26. Magnetisation of an Ellipsoid (continued). The case of an ellipsoid subjected to the action of an originally uniform field is of so much practical interest that it is worth while to state here some of the results of calculation which are applicable to it. Suppose the ellipsoid to be set with one of its axes pointing in the direction of the magnetic force. Let c be half the length of this axis, and a and b half the lengths of the other axes, which point in directions that are perpendicular to the direction of the force. It will suffice to take the case of an ellipsoid of revolution, in which a = b The original external force being H' and the force actually operative being H, we have where JN is a number depending on the relation of the length of the ellipsoid to its transverse dimensions. We may express JV in terms of the eccentricity e. When the ellipsoid is of the prolate or elongated form, Fig. 7 (the polar diameter 2 c or C C' greater than the equatorial diameter 2 a or A A'), / 2~ -i = When p is exceedingly large, the factor iL approximates to 3. Hence, in a sphere of very permeable material, the number of lines of induction through the sphere (per square centimetre of section) is nearly three times the number of lines in the undisturbed field. This is the case in the sphere of Fig. 6 (the proportion of the closeness of the lines inside to that of the lines outside at a distance from the sphere being J3 to 1, as seen on the plane of the diagram). The student should APPLICATION TO THE CASE OF A SHORT ELLIPSOID. 29 note that when the permeability of the sphere is great, its exact value has very little influence on the number of lines of induction that pass through the sphere, and hence a spherical ball would be a very bad form of body to select if we wished by measuring the induction to determine the permeability of the material. A small error in the form of the sphere would, in fact, have more influence in altering the amount of the induction than a large difference in the value of /A or of K ; so that, as Prof. Chrystal has well put it, the experimenter would be testing the accuracy of his instrument- maker rather than the magnetic susceptibility of his material. * 30. The same objection would apply, though in a slightly less degree, to a short ellipsoid. By way of illustrating this Fio. 11. Short ellipsoid of infinitely permeable material in a uniform field. further, Fig. 11 has been drawn to show in a general manner the induction through an ellipsoid, and the distortion which it produces in an originally uniform field, when the axes have the proportion of 4 to 1, the material being assumed to have indefinitely great permeability. With this proportion between the axes, jy, by the formula (1) of 26, is 0*946, and for every line of force (per square centimetre) in the undisturbed field there are 13 '3 lines of induction (per square centimetre) within the ellipsoid. The space between the lines within the body is therefore narrower than the space between the lines in any distant part of the field in the proportion of 1 to J13'3. The permeability might vary widely without materially affecting * Article " Magnetism," Encyc. JBritannica, Ninth Edition. 30 MAGNETISM IN IROX. the amount of induction, and the figure may be accepted as representing very nearly what would happen if the ellipsoid were of soft iron.* 31. Application to the Case of a Long Cylindrical Rod of Circular Section Magnetised Transversely in a Uniform Field. This case, of which an example is furnished by a long wire stretched in the earth's field in a direction perpendicular to the lines of force, is deducible from the general case of the ellipsoid by making one of the axes infinite.! This gives JV=27r, so that H = H'-27r|. Hence, M, = _ ! _ , and ^-=^L. H 27TK + I* H' /* + ! Thus, when p is very large, as it is in soft iron, the trans- verse induction B across the wire approximates to a value which is twice that of the external field. This is a very small induction compared with that which the same wire would take longitudinally if it were set lengthwise instead of cross- wise in the field (compare 15 above). If we assume K to be 20, the proportion of the induction in the two cases is about 1 to 127. It follows from this that when we hang a wire vertically in the earth's field, the transverse magnetisation due to the hori- zontal component of the earth's field is so small that account * Generally, to find the proportion of the induction B within an ellipsoid to the force H' in the undisturbed field, we have : ~( When the permeability of the substance is very great, the expression within brackets approximates to ^, giving B=-^r H'. In the case con- sidered in the text, is 13'3. t And using a formula (not quoted in 26) which refers to magnetisa- tion in the direction of an equatorial axis. See Maxwell, loc. cit. THIN DISC AND LONG ELLIPSOID. 31 need not in general be taken of it, and the same thing is true of the transverse magnetisation of a wire laid horizontally in the earth's field. 32. Case of a Thin Disc Magnetised in the Direction of the Thickness by a Uniform Field. We may find the true mag- netic force within a disc or large thin plate magnetised nor- mally in a uniform field from the fact that the lines of induction B within the disc are continuous with the lines of force H' in external space, and if the disc is very wide in comparison with its thickness, the lines go straight through it without sensible distortion. Thus H'=B = 47r| + H, so that H = H'-47r|, H I _- = , and the induction within the disc is the same what- H' /A ever be the permeability of the material. The same result may be derived from equation (3) of 26, by making a inde- finitely great in comparison with c. This gives e = \ and 33. Long Ellipsoid : Influence of the Length on the Mag- netising Force. Returning now to the general case of a long ellipsoid of revolution placed longitudinally in a uniform mag- netising field, it is interesting to notice to what extent the uniform magnetisation of the ellipsoid itself affects the magnetic force, when we assume various values as the ratio of length (2 c) to transverse diameter (2 a). In the formula B-H we may write , for I (by 13), and if the material is very permeable, so that B is large compared with H, this will be p very nearly equal to simply. Hence in an ellipsoid made of 4 7T very permeable material, such as iron, N H = H' - ^ B, very nearly. The following values of .ZVand also of j have been calcu- lated by means of the expressions in 26 for ellipsoids in which OF THE t i *i iv/CDClTV MAGNETISM IN [RON. the ratio of length to breadth is f>0, 100, 200, 300, 400, and 500 respectively. Since H = H'--flT I, Ratio of Length to N V Breadth () 47T 50 0-01817* 0-001446 100 0-00540 0-000430 200 0-00157 0-000125 300 0-00075 0-000060 400 0-00045 0-000037 500 0-00030 0-000024 K- + 1. The proportion which the resultant force H bears to the original force H' in the undisturbed field, HI By the help of the above table it is easy to find this propor- tion, for an assigned ratio of length to breadth, when the susceptibility of the material is known. As an example, we may take K = 200 as a representative value of the susceptibility in soft iron when subjected to a moderately strong magnetic force. Suppose that the ellipsoid is 100 diameters long, then H 1 1 H' 0-0054x200 + 1 2-08* In other words, the magnetic force actually operative within the metal as reduced by the magnetism of the piece itself is in that case rather less than one half the force due to external causes. 3 34. Residual Magnetism and Retentiveness. When a piece of any one of the strongly magnetisable metals iron, steel, nickel, or cobalt is magnetised by applying magnetic force, and the externally-applied force is then withdrawn, it is found that the magnetisation does not wholly disappear. What * The approximate formula (2) of 26 gives 0'01812. For the longer ellipsoids the values of N calculated from it may be taken as correct. SELF-DEMAGNETISING FORCE. 33 remains is usually called the residual magnetism, and metals which retain residual magnetism when the external magnetic force is withdrawn are said to possess retentiveness. We shall see later that this retention of residual magnetism, when the externally applied magnetising force is withdrawn, is only one instance of a general tendency which these metals exhibit to resist any change in their magnetic state. 35. Self-Demagnetising Force. In connection with the subject of retentiveness it is of the first importance to notice that though the externally applied magnetic force be withdrawn from a magnetised piece, there is in general some magnetic force in action. This force is due to the residual magnetism itself, and its tendency is to reduce the residual magnetisa- tion. In a bar magnet, for instance, the residual magnetism at and near the ends of the bar produces a magnetic force acting in the direction of the length and tending to demagnetise the bar. In a ring magnet uniformly magnetised we get rid of this self-demagnetising force by having the ends, so to speak, brought together. In an exceedingly long bar the self- demagnetising force becomes insignificant because the ends are far removed from most parts of the bar. The residual mag netism in a ring or a very long rod will therefore be greater, other things being equal, than in a short rod. Indeed, so much is this the case that, in dealing with soft annealed iron, we shall find almost no residual magnetism if we experiment with rods the length of which is only 10 or 20 times their diameter, because in these rods the self-demagnetising force is sufficient to remove the residual magnetism almost completely, whereas a rod 400 or 500 diameters long will be found to retain a very large proportion of its induced magnetism when the inducing force is withdrawn. Hence the term residual magnetism has one meaning when it is used to describe the magnetism that remains when magnetic force is completely withdrawn without any reverse force being applied, an experiment which can be made if we use an exceedingly long rod or a ring magnet ; and it has another and quite different meaning when it is used to describe the magnetism which a bar or other short piece will retain in opposition to the demagnetising force which it exercises upon itself. D 34 MAGNETISM IN IRON. 36. Self-Demagnetising Force in Ellipsoids. In the case of an ellipsoid, uniformly magnetised, the self-demagnetising force is uniform throughout the body, and its value is yi, where N has the same meaning as in 26, and I is the residual intensity of magnetisation. To get an idea of what this may amount to in actual cases, we may take 1,000 C.-G.-S. units as a residual value of I which is commonly enough found in the magnetisation of iron. When an ellipsoid is 200 times as long as it is broad the value of Nia 0-00157 (by 32), and a residual intensity (I) of 1,000 would therefore produce a self -demagnetising force of 1-57. The experimental results which will be given later will show that a force of this magnitude is by no means insignificant, and that it would, in fact, be sufficient to remove a large part of the residual magnetisnVxJt is only when the length is as much as 400 or 500 times the transverse diameter that the self-demagnetising force in a material so susceptible as iron becomes nearly negligible. The factor N is called by Prof. H. du Bois the tan we may write 0, 'which is equal to , 8 being the deflection as measured on the scale, and D the distance of the scale from the mirror expressed in scale divisions. Fig. 16 illustrates an arrangement for examining the mag- netic quality of long thin rods or wires by the " one-pole " variety of the magnetometric method. The specimen is slipped into a tube, A, which is clamped in a vertical position behind the magnetometer B, the distance being adjusted by trial to make the deflection conveniently large. Over the tube a magnetising solenoid is wound, extending a little way above and below the wire core, so that the magnetising force inside may be sensibly uniform, except in so far as it is affected by the ends of the specimen itself. (When only one wire is to be tested, the magnetising solenoid may conveniently enough be wound on the wire itself, instead of on a tube.) Owing to the vertical position of the specimen, it is exposed to the vertical component of the earth's magnetic force. For many purposes it is desirable to eliminate this, so that the only force acting along the wire may be that due to the magnetising solenoid. To secure this a second solenoid is wound upon the tube, and through it a constant current is kept up, the strength of which is adjusted (by a method to be described later) until the mag- netic force it produces within the tube just balances the earth's vertical force. In the sketch, the single gravity Daniell cell C and the resistance box D give the means of maintaining and regulating this constant current. In circuit with the main solenoid and behind the specimen is a coil, E, consisting of a few turns of wire wound on a wooden frame which can slide towards or from the magneto- meter, its axis passing through the magnetometer at right angles to the undeflected direction of the needle. This " com- pensating coil," as we shall call it, serves to neutralise the direct action of the magnetising solenoid upon the magneto- meter. Its position is adjusted thus : Before putting the speci- men to be magnetised into the magnetising solenoid, pass a fairly strong current through the solenoid and the compensat- ing coil, and push the coil backwards or forwards until the magnetometer shows no deflection. The adjustment remains correct for all currents, and its effect is that when the specimen DETAILS OP MAGNETOMETRIC METHOD. 43 44 MAGNETISM IX IRON. is put in no deduction has to be made from the observed deflection on account of the magnetising solenoid. We may of course allow for the effect of the solenoid without using a compensating coil, by observing what deflection the solenoid itself produces with a given strength of current when the specimen is removed, and then making a proportional deduction for other currents. The compensating coil, however, has a great advantage over this in point of practical convenience, and has other uses besides, of which examples will be given later. In each part of the connections the leading wires are twisted together a very necessary precaution to prevent their acting on the magnetometer. In examining the permeability of a specimen, a weak mag- netising current is first applied, and this is increased step by step or continuously, observations of the current strength being taken along with observations of the magnetometric deflection. A storage battery forms the most convenient source of current ; if that is not available, a battery of gravity Daniell cells will do well. To observe the current strength, any good form of galvanometer or ampere-meter may be kept in circuit with the magnetising solenoid. A plan which is as good as any is to use a low-resistance mirror galvanometer, strongly controlled by a fixed permanent magnet, and test its sensibility by passing a current through it from a gravity Daniell cell ; the strength of the current in amperes may be taken as - , where . Iv R is the total resistance of the circuit in B.A. units. Care must be taken to set up the galvanometer far enough away from the magnetometer to prevent one from acting on the other. In many magnetic experiments it is desirable to have the means of altering the magnetising current continuously instead of by steps, between zero and its highest value. This is con- veniently effected by using the liquid rheostat, or potential slide, shown in Fig. 17. A tall glass jar of fairly uniform bore, two inches or so in diameter, is filled with dilute solution of sulphate of zinc. Three blocks of amalgamated zinc, cr, b, and c, are fitted in the jar, one lying at the bottom, another fired at the top, and the third hung between them so that it may be raised or lowered by the cord d which passes DETAILS OF MAGNETOMETRIC METHOD. 45 over a pulley above to the little winch at e. The blocks are connected to three terminals at /, insulated wires being FlG. 17. Liquid rheostat used for the purpose of continuously altering the strength of the iiiagnetising current. FIG. 18. led up through the liquid from the middle and lowei blocks. The battery is connected to a and c, so that the liquid 46 MAGNETISM IN IRON. column forms a shunt to it, and a part of its E.M.F. is taken ofl to produce current in the magnetising solenoid by connecting the ends of the solenoid to one of the fixed and one of the mov- ing blocks, say a and b. Thus, when b is raised into contact with a no current passes through the solenoid, and when b is gradually lowered the current increases, reaching its highest value when b touches c. With this slide it is easy to adjust the current to any intermediate value, and to keep it constant for as long as may be wished. Fig. 18 is a general diagram of the connections. The letters A, B, C, D and E refer to the same parts as in Fig. 16. F is a revolving commutator, G a galvanometer for measuring the magnetising current, and H is the slide described above. 42. Demagnetising by Reversals. The liquid slide gives a handy means of performing a process which is resorted to when we wish to rid the specimen of any initial magnetism it may possess, or to wipe out the residual effects of previous operations. The process of "demagnetising by reversals" consists in applying a numerous series of magnetic forces alternating in direction, and gradually diminishing to zero. A commutator or rapid reversing key is inserted either between the battery and the slide or between the slide and the mag- netising solenoid. Working it rapidly with one hand, and turning the winch-handle of Fig. 17 very slowly with the other, the operator applies a long series of alternating magnetising currents, each a very little weaker than the one before it, and the result is, when the process is carefully conducted, to remove all trace of residual magnetism, provided the strongest current of the series is at least as strong as the current by which the piece had been previously magnetised. 43. Adjustment of the Current Required to Balance the Vertical Component of the Earth's Field. The operation of demagnetising by reversals will not be completely successful unless the earth's vertical force is very exactly balanced, other- wise there will be a one-sidedness in the alternate opposite magnetic forces, which will show itself by leaving a persistent residue of magnetism in one direction or the other, the direc- tion depending on whether the constant current which is applied TO FIRD DIRECTING FORCE AT MAGNETOMETER. 47 to balance the earth's force is too strong or too weak. This affords an. excellent criterion by which we may adjust the current. It has to be strengthened or weakened until, when the process of demagnetising by reversals is performed, the de- magnetisation is complete. The more susceptible the material within the solenoid is, the more sensitive is the test, and it is well to keep at hand, for the purpose of adjusting the current in this way, a core of soft annealed iron, which may be slipped into the solenoid when the test is to be made. In order to increase the sensibility further, when a fine adjustment is re- quired, the solenoid should be set a good deal closer to the magnetometer than it is set when we are afterwards measuring the magnetism of a wire or rod within it. 44. To Find the Directing Force at the Magnetometer. In measuring magnetism by the magnetometric method, we must know the force F : which directs the needle when it hangs in the undeflected position. Even when no special directing magnets are used, it is not safe to assume that Fj is identical in value with the horizontal component of terrestrial magnetism, for the earth's field is often seriously altered within a room by the magnetic influence of iron pipes, beams, and so forth. So long as these disturbing bodies are not liable to be moved about, or to have their temperature much altered, their effect in modifying the magnetic field though it may be con- siderable will be nearly constant, and in that case an occa- sional measurement of Fj will suffice. If there are iron heating pipes or stoves in the neighbourhood, the utmost care is neces- sary to see that F x does not vary. Fixed masses of iron at the atmospheric temperature are not a very objectionable feature in a magnetic laboratory ; but it is difficult to exaggerate the nuisance that may be caused by an iron stove or steam-pipe liable to quick changes of temperature. We may make an entirely independent measurement of F x , following the well-known method which is used in measuring the horizontal component of the earth's field,* and taking care to * Full directions for the determination of the horizontal component ol the earth's field will be found in Prof. A. Gray's " Absolute Measurements in Electricity and Magnetism." 48 MAGNETISM IN IRON. swing the deflecting magnet in th<3 place where the magneto- meter is to stand. But in general all that is required is to go through as much of this process as will serve to find the relative values of F l and the horizontal field F at a place where there is no local magnetic disturbance. In most places F is sufficiently well known from the results of recent 'magnetic surveys, so that the absolute value of Fj may be deduced when we know the ratio it bears to F. To compare the two, take a short straight piece of perma- nently magnetised steel wire, and suspend it to hang hori- zontally within a glass vessel by a little cradle and a silk fibre 3in. or 4in. long attached to the cover, so that it is free to swing. Put it where the magnetometer is to stand, and set it swinging torsionally (not in pendulum fashion). This is most easily done by bringing a bar magnet near it, and then drawing that away, keeping the two poles of the bar equally distant from the hang- ing wire. When the swings have subsided so that the motion is no more than 5deg. or so to either side, begin to count them. Note with a watch the instant at which the magnet swings past its middle position towards one side, count 30 or 40 com- plete swings, and again note the time the magnet swings past its middle position towards the same side. Find in this way the time ^ (in seconds) required for one complete swing. Then take the swinging magnet to some place (outside) where there is nothing to interfere with the terrestrial magnetic field, and repeat the counting there to find the time that is required to make one complete swing when the only directing force is the horizontal component F of the earth's field. The directing force is inversely proportional to the square of the period of swinging, hence the directing force at the place where the swings were first counted F = When the magnetometer is furnished with a " compensating coil" ( 41) the following is a good way to find F r Remove the magnetising solenoid and set the compensating coil at a known distance, A (Fig. 19), behind the magnetometer. Pass TEST OF IRON BY THE MAGNETOMETRIC METHOD. 49 a known current, C,* through it and observe the deflection 6 of the magnetometer. A B is the mean radius of the coil, and A is measured to the middle of its width. Let q be the number of turns in the coil ; then the deflecting force which is produced at by the current in the coil is or (KB 3 and, since this is equal to F x tan 0, we have B 3 tan FIG. 19. 45. Example of a Test of Iron by the Magnetometric Method. Before proceeding to describe the ballistic method of measuring magnetisation, it may be useful to illustrate the magnetometric method by giving the particulars of an actual experiment on a piece of wrought-iron wire. The diameter of the wire (d) was 0-077 cm. The length of the specimen was 30 -5 cms., or 400 diameters. It was annealed or softened before the test by drawing it through a lamp flame so slowly that each part of the length, in succes- sion, was heated to bright redness and then cooled slowly as it passed away from the flame. The " one-pole" arrangement (40) was adopted. A preliminary trial showed that the effective " poles " lay very near the ends of the wire. The upper one was set at a distance (0 Q) of 10 cms. behind the magnetometer the distance Q' to the lower pole was 31 cms. * Here, as elsewhere, the current is expressed in absolute electro- magnetic (C.-G.-S.) units. If its value is known in amperes we must divide the number of amperes by 10 to find C, 50 MAGNETISM IN IRON. The directing force at the magnetometer Fj was 0-299 in C.-G.-S. units. The deflections were read in millimetres, and the scale was set at a distance of 1 metre from the magneto- meter. Hence one scale division of deflection corresponds to a value of -^Vrr for 6 or tan 0. Substituting these values in the expression of 40, , 4.QQ 2 . FJ tan = we have I for one scale division of magnetometer deflection 4 x io 2 x 0-299 __ ^ Lvy =3'32 3-1416 x OK)77 2 x 0-9665 x~2000 Again, the magnetising solenoid contained 69 turns per centimetre of its length. Its magnetising force for one ampere of current was, therefore, 47rx69_ 86 . 7 10 The current was measured by a mirror galvanometer, which was found to give a deflection of 575 scale divisions, with a current of 0-235 amperes. This corresponds to 0-000408 amperes per scale division. Hence the magnetising force for one scale division of the galvanometer was 867 x -000408 = 0-0354. After the independent current (in a separate solenoid) which was required to balance the vertical component of the earth's force had been adjusted, the process of demagnetising by reversals was gone through to wipe out any traces of magnetism the wire might have acquired in handling. Readings of the magnetometer and galvanometer were then taken, while the current was slowly increased step by step from zero till the magnetic force reached a value of 22*27 units. Then the turrent was slowly and step by step reduced to zero, the mag- netism retained by the specimen being observed at each stage, and then a negative current was applied, giving a reversed magnetic force, which was slowly increased until the residual MAGNETISATION OF ANNEALED IRON WIRE. 51 magnetism began to become reversed. The results of the experiment are stated in Ta.ble I. Column 1 gives the ob- served galvanometer deflections, and column 2 the magnetising force calculated from them. This is the force produced by the solenoid; in the notation of 25 it is H', and is a little greater than the true magnetic force H, which is diminished by the action of the ends of the specimen when it becomes magnetised (see 47 below). Column 3 gives the observed magnetometer deflections (due to the wire alone), and column 4 gives values of I calculated from them. TABLE I. Magnetisation of Annealed Iron Wire. (1) Magnetising cur- rent (Gal. readings). (2) Magnetising Force. (3) Magnetometer Readings. (4) 1 9 0'32 1 3 24 0-85 4 13 39 1-38 10 33 59 2-18 28 93 79 2-80 89 295 99 3-50 175 581 119 4-21 239 793 139 4-92 279 926 159 5-63 304 1,009 189 6-69 327 1,086 239 8-46 348 1,155 289 10-23 359 1,192 342 12-11 365 1,212 441 15-61 373 1,238 574 20-32 378 1,255 629 22-27 380 1,262 464 16-42 379 1,258 239 8-46 375 1,245 139 4-92 372 1,235 89 3-15 369 1,225 39 1-38 363 1,205 350 1,162 - 11-5 -0-41 342 1,135 - 23 -0-81 329 1,092 - 31 -1-10 318 1,056 - 41 -1-45 295 979 - 51 -1-80 253 840 - 62 -2-20 166 551 - 71 -2-51 70 232 - 81 -2-87 -12 -40 52 MAGNETISM IN IRON. 46. Magnetisation Curve. A convenient way of repre- senting such results graphically is to draw a curve showing the relation of the magnetising force to I or to B. In Fig. 20 a curve showing the relation of the magnetising force of the solenoid to I is drawn from the above table. A B is the ascending limb, got by applying and increasing a magnetising current, the iron being originally in a non-magnetised and per- fectly neutral state. From B to C the magnetising current is being reduced to zero; from C to D an increasing negative current is being applied. This example is thoroughly characteristic of the behaviour of annealed wrought iron. The ascending limb of the curve may be divided, broadly, into three portions. In the first, under feeble magnetic forces, the gradient of the curve is very small, which means that at this stage there is (comparatively) very little magnetic susceptibility.* Later, as the force increases, the curve becomes exceedingly steep, and nearly straight ; this is the region of great susceptibility. Then, lastly, the curve rounds off until the rate of ascent again becomes small, so that the susceptibility diminishes, and any considerable addition to I can then be brought about only by applying a very strong magnetising force. This third stage is a necessary consequence of the well- known phenomenon of magnetic " saturation." We shall see later that the value of I has a definite limit which cannot be exceeded no matter how high the magnetic force be raised. 47. Residual Magnetism and Coercive Force. In the descending limb of the curve it is interesting to notice how little of the magnetism disappears as the magnetic force is withdrawn. Even when the solenoid current is reduced to zero, the residual magnetism C is in this case 1,162 C.-G.-S. units, which is no less than 92 per cent, of the value reached when the current was in action (1,262 units). This residual magnetism is, however, very feebly held. Applying a reverse * The comparatively small susceptibility of iron to feeble forces seems to have been first clearly pointed out by Stoletow (Phil. Mag., Vol. XLV., 1873, p. 40), whose observations on the relation of magnetisation to mag- netic force were confirmed and greatly extended by Rowland (Phil. Mag. t Vol. XLVL, 1873, p. 140 j and Vol. XLVIIL, 1874, p. 321). uoiJESijauBew o jisuajui o o -o ^b * o- o 1 o gooooooo ff>^ From a Paper by the Author, Phil. Trans. Roy. Soc., 1885 p. 564 EXPERIMENTS ON THE EFFECTS OF VIBRATION. 115 A glance at these figures will show the enormous increase of susceptibility brought about by tapping. A force of 0'96 in the solenoid, with tapping, brings B up to 9,540; but another experiment on the same piece of wire showed that without tapping the value of B under the same force was only 550. In Fig. 54 curves are drawn, with a very open scale of H, to illus- trate the portions of this experiment which deal with feeble mag- netic forces. The full line P refers to the application of mag- netic force, and the dotted line above it to the removal of the ,000 9,000 8,000 7,000 6,000 5,000 4,000 3.000 2,000 1,000 01 0-2 0-3 0-4 0-5 0'6 07 0'8 0'9 I'O I'l T2 1'3 Magnetising Force due to Solenoid (C.Q.S.). Fio. 54. Magnetisation of Soft Iron Wire ; P, with vibration, O Q, without vibration. force, both with tapping ; while the line Q refers to the appli- cation of magnetic force without tapping. The magnetic force plotted here is that due to the solenoid alone, but it is impor- tant to notice that this is by no means the true total force in the experiment made with vibration. Though the wire is 400 diameters long, it cannot be treated as sensibly endless. The reaction of the ends becomes very important on account of the excessively great susceptibility. The real field is much less than the field due to the solenoid how much less may be judged from the line A, which is drawn (in the manner J2 116 MAGNETISM IN IRON. described in 48) on the supposition that the wire may fairly be treated as an ellipsoid 400 times as long as it is broad. On this supposition the true magnetic force is to be found by measuring the horizontal distance of any point in the curves from the line A. Even neglecting this correction of the magnetic force the ratio of B to the (solenoid's) force is not less than 20,000 in the initial part of the curve ; and after allowing for the influence of the ends of the specimen by measuring the magnetic force from the line A the permeability is found to have the enormous value of about 80,000. The permeability is greatest at or near the beginning of the magnetising process ; the 14,000 12,000 10,000 8,000 6,000 4,OOC 2,000 as ... ,*' '"'*' ..^ ^ '/ f ,.- ^ I/a II / / | i II i 1 S ' 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Magnetising Force due to Solenoid. FIG. 55. Magnetisation of Very Soft Annealed Iron Wire. Without tapping, ; with tapping, ; continuation, without tapping, after reaching (with tapping) the point a, concavity, which is a feature in the early part of curves deter- mined without tapping, has nearly, if not quite, disappeared. The complete experiment is shown in Fig. 55. The curves shown by full lines were obtained by applying and removing a mag- netising force of nearly 17 units without vibration. The curves shown thus refer to the same process performed with vibration. Finally, after magnetising again to the point a with vibration, the application of magnetic force was continued without vibration, and the results of this are shown by the dotted curve It is interesting to notice how the effects of hysteresis immediately re-assert themselves when, after tapping, we continue the magnetising process with the specimen at rest. EXPERIMENTS ON THE EFFECTS OF VIBRATION. 117 In another experiment, with the same piece of wire, the magnetic force was raised to a certain value, without vibra- tion, while B was determined ballistically; then the wire was smartly tapped, and the change which B underwent through the tapping was measured by slipping off the induction coil; then the coil was replaced, and the force was raised by steps to a higher value; then the wire was again tapped, and so on. The wire had an initial magnetism (B) of 170, which rose to 190 when a force of 0'32 was applied with- out tapping; then, while this force continued to act, tapping brought up the value of B at a bound to 6,620. Againj under a force of 1*61 tapping changed B from 7,120 to 14000 12000 10000 B 8000 GOOO 4000 2000 1-1 . =* < = == = ! *~"~T . y- { i * .3 ! I Z 3 4 5 6 7 8 9 10 II 12 13 (4 15 16 17 Magnetising Force due CO Solenoid FIG. 56. Magnetisation of Very Soft Annealed Iron Wire. Effects of tapping shown thus, . 11,600, and under a force of 3-4 it changed B from 11,940 to 12,960. On coming down the effects were equally well marked. When the force had been reduced from a fairly high value to 0-33, tapping brought B down from 11,260 to 6,880, and finally when the force was the residual value of B, amounting to 6,880, was reduced by tapping to 320. The forces whose values are stated here are those due to the solenoid without allowing for the reaction of the specimen itself upon the mag- netising field. The complete results of this experiment are shown in Fig. 56, where the full lines show those parts of the process which were performed without tapping; and the changes Of magnetic state brought about by tapping, while the external field was kept constant, are shown thus : . 118 MAGNETISM IN IRON. In experiments of the same class with hard iron or with steel vibration produces effects of the same general kind ; but its influence in destroying hysteresis is far less complete than in soft iron. In a piece of iron wire of the same quality as the last, but not annealed, where a residual magnetism (B) amount- ing to 7,000 was left after applying a force of 17, the residue fell to 2,500 when the specimen was smartly tapped. Magnetic hysteresis exhibits itself in other changes of mag- netism as well as in the changes that are brought about by varying the magnetic force. It is a prominent feature in the effects of stress upon magnetic quality, but the consideration of it in this aspect will be more conveniently reserved for a later chapter. FIG. 56A. Magnetic Curve-Tracer. The effects of temperature on hysteresis will be referred to in Chapter VIII. 85a. Magnetic Curve-Tracer. For the purpose of exhibit- ing the behaviour of iron or steel during a cyclic process of magnetisation, the author has devised an instrument known as the magnetic curve-tracer,* which causes a spot of light to trace upon a screen the form assumed by the B H curve while the iron magnetising process is actually going on. By making the process happen fast enough the movement of the spot of light may be made to show a continuously luminous curve. The * See The Electrician, May 26, 1893. MAGNETIC CUE.VB TRACER. 119 mirror and other moving parts of the apparatus are sufficiently free from inertia to allow a cycle of magnetisation to b d QZD repeated several times in a second. The mirror receives two components of angular motion a vertical component, which is 120 MAGNETISM IN IRON. proportional to the magnetisation of the iron, and a horizontal component, which is proportional to the magnetising force. The apparatus is shown in Fig. 56A, but its working will be more readily understood by reference to Fig. 56s, which shows the principal parts diagrammatically. E is the mirror, which is mounted on a single needle point in such a way that it has two degrees of freedom for deflection. Fia. 56c. Cyclic process of magnetisation automatically Fia. 56D. Cyclic Process with subordinate recorded by the Magnetic loops. Curve Tracer. It receives azimuthal movement, causing the spot of light to travel horizontally from the wire B B, which is tightly stretched in a narrow gap in a magnet C, and is connected by a thread to the frame which carries the mirror. The magnet C, which may conveniently be made by cutting a longitudinal slot in a piece of iron pipe, is magnetised by a longitudinally wound coil, through which a constant current passes. The lines of force accordingly jump across the slot in which the wire B B is strung, forming a MAGNETIC CURVE TRACER. 121 constant field there. The variable magnetising current which is to act on the iron under examination is caused to pass through the wire B B, and hence any variation in the current produces corresponding horizontal movements of the spot of light reflected from the mirror. At the same time the mirror receives vertical movement through another thread, which connects it to the wire A A stretched in a gap in the magnet under examination. This magnet is made up of two rods D D connected at the back by a yoke, and terminating in pole pieces, between which is the narrow gap containing the stretched wire A A. A constant current is kept up in the wire A A, and it therefore sags up or down proportionally to the variations of magnetism in the rods D D. These rods are surrounded by FIG. 56E. magnetising coils, and the current which magnetises them passes also through the wire B B, which, as has just been said, is stretched in a constant magnetic field, The wire B B consequently sags out or in, giving horizontal deflection to the mirror, by amounts which are proportional to the magnetising force in the coils of D D. Hence, to describe a magnetising curve for the rods D D it is only necessary to apply a gradually- increasing current to the coils of D D, when the mirror takes vertical movement proportional to the magnetism and horizontal movement proportional to the magnetising force ; 122 MAGNETISM IN IRON. and by reducing the current to zero, re applying it, reversing It, and so on, all the characteristics of the magnetising process are rendered obvious at a glance. The magnetising current must be varied gradually, not by sudden steps, and for this purpose a liquid resistance and liquid commutator are useful. With a liquid commutator the apparatus may readily be arranged so that a complete cycle of magnetisation the usual cycle of double reversal can be gone through in one-tenth or even one-twentieth of a second ; and this allows the spot 56F. Cyclic Curves in Iron and Steel. of light to trace a curve which appears as a continuously luminous line. For high-speed working such as this the metal of the magnetic circuit D D must be laminated. For some purposes, however, it seems best to trace the curve more slowly, following with a pencil the movement of the spot of light, and so obtaining a permanent record, or recording the movement of the spot on a photographic plate. The curves shown in Figs. 56c and 56D are reproduced from photographs of magnetic cycles taken by means of this instrument, using a sensitive plate to record the movements of MAGNETIC CURVE TRACER. 123 the spot of light, and using laminated iron as the material under examination. When solid rods of soft iron are used to form the magnet, the influence of time in the performance of the cycle becomes very marked. In that case even a com- paratively slow increase of current is followed, after it ceases, by a continued creeping up of the magnetism, and the spot of light goes on rising for some seconds. In great part, at least, this effect is to be attributed to Foucault currents in the iron. It follows that a cyclic process, in solid rods, takes very different forms when gone through at different rates. Fig. 56E illustrates this by giving a set of magnetic curve-tracer records for a pair of soft iron rods Jin. in diameter. The curve a is Fia. 660 obtained by going very slowly round the cycle and shows the hysteresis loop in its normal state, undisturbed by Foucault currents. The curves b and c show how much disturbance is produced when the period is 3 seconds and 0-43 second respectively.* Figs. 56p and 56a are further examples of curves given by the magnetic curve-tracer. In these the curve is traced by going slowly round the cycle, and marking successive posi- tions reached by the spot of light. In 56o the magnetising current was progressively raised from 1 to 3 amperes. * An account of these and other investigations made by aid of the magnetic curve tracer will be found in a paper by MISR Klaassen and the author on "The Magnetic Qualities of Iron," Phil. Trans., 1894, p. 1024. In this connection reference should be made to a research by J. Hopldnson and E. Wilson on " The Propagation of Magnetisation in Iron as Affected by the Electric Currents in the Iron," Phil. Trans., 1895, Vol. 186, p. 93. CHAPTER VI. MAGNETISM IN WEAK FIELDS. 86. Permeability with respect to Small Magnetic Forces. The instances which have been set forth in earlier chapters may suffice to give a general notion of the behaviour of iron and the other magnetic metals when exposed to magnetic fields of moderate strength. It remains to give some account of experiments dealing with the two extremes of very weak and very strong magnetisation. The effects of weak fields will be taken up first. A glance at the curves of B and H or of I and H for any of the examples which have been already given will serve to show that the initial permeability that is to say, the per- meability at the beginning of the process of magnetisation is so comparatively small that special means are required to examine its value. The arrangements for measuring this early magnetism, whether they are ballistic or magnetometric, must be much more sensitive than those that serve when we have to deal with later portions of the curve. So small, indeed, is the permeability under very feeble forces, compared with the permeability found later, that without special appliances one might readily fall into th3 error of supposing it to be initially zero. Experiments made by Baur, Lord Rayleigh, and others are conclusive, however, in showing that this is not the case. They show that the initial permeability has a finite value which is applicable, without sensible change, so long as the magnetising force remains very small. In other words, the magnetisation curve starts with a definite gradient, and its very early portion is nearly straight. Lord Rayleigh has carried his investigation of the action of weak forces further, PERMEABILITY UNDER SMALL MAGNETIC FORCES. 125 showing that the permeability has a finite value with respect to any small cyclic change of magnetic force when that is frequently repeated, whether the piece be otherwise mag- netised or not a value which is sensibly constant when the range of change is varied, provided the range be kept very small, and which is approximately independent of the mean condition as to force and magnetisation, provided the magnetic state does not approach saturation. Baur's experiments were made ballistically with a ring of soft iron, the cross-section of which had a diameter of a little over two centimetres. Reduced to C.-G.-S. measure, his results for one trial are as follows : * H 1 K 0-0158 0-263 16-5 0-0308 0-547 17-6 0-0708 7-633 23-0 0-1319 3-815 28-9 0-230 9-156 39-8 0-384 22-487 58-6 When these values of the susceptibility K are plotted in rela- tion to H, they are seen to lie on what is practically a straight line. By producing the straight line backwards to cut the axis, the value of K corresponding to H = is found to be 14'5. This is, therefore, the susceptibility with respect to indefinitely feeble forces ; the corresponding initial permeability, /z, is 182. Moreover, with respect to forces which are still feeble though not indefinitely small, the susceptibility and permeability may be expressed by the equations /c = 14-5 + 110 H,f ft= 183 + 1382 H, which apply with much accuracy within the limits of H used In the experiment. With any considerably higher force, however, these formulas would not apply. It follows that the relation * C. Baur, Inaugural Dissertation, Zurich, 1879. Wied. Annalen, XI., 1880, p 399. t Baur gives *=15 + 100 H, but the constants given in the text seem to the writer to agree better with the numerical results of the tests. 126 MAGNETISM IN IRON. of magnetisation to magnetic force for feeble forces may be expressed thus : 1 = 14-5 H + 110 H 2 , B = 183 H + 1382 H 2 . These particular numerical constants are, of course, to be taken as applying to the specimen of soft iron tested by Baur ; but similar parabolic formulas may be constructed with different constants for any specimen of any of the magnetic metals. In other words, the curve of I and H or of B and H is sensibly a parabola in its earliest stages, starting, however, with a finite inclination to the axis of H. For excessively feeble forces it is virtually an inclined straight line, the term involving H 2 being then negligible. 87. Lord Rayleigh's Experiments. The inference drawn by Baur as to the value of K when H is zero depends on the legitimacy of extending the straight line connecting K and H backward beyond the region of actual experiment to cut the axis of K. It has been entirely confirmed by the experiments of Lord Rayleigh,* who has examined the action of much feebler magnetic forces, and has found that the proportionality of mag- netic induction to magnetic force continues to hold good when the force is excessively reduced. In his experiments a bar or wire of iron was tested magneto- metrically with one end very near the magnetometer, and with a compensating coil adjusted to balance the magnetism which a feeble magnetising current induced in the bar. The specimen under examination being a piece of Swedish iron wire (not annealed), the compensating coil was adjusted so that there was no movement of the magnetometer needle when a magnetising current was made or broken, the strength being such as to give a field of 0'04 C.-G.-S. Then the strength of the current was gradually reduced till the mag- netic force fell to about 0'00004, and it was found that the compensation remained perfect. In other words, within these limits the induced magnetism was proportional to the inducing force : K and p were constant. " In view of this," says Lord Rayleigh, "neither theory nor observation give us any reason * Phil. Mag., March, 1887, MAGNETIC VISCOSITY UNDER SMALL FORCES. 127 for thinking that the proportionality would fail for still smaller forces." Quite similar results were obtained with other speci- mens of unannealed iron and of steel. The range through which K and //, are sensibly constant is much less in annealed than in hard iron. Within this range of force there is no re- tentiveness -, the magnetising process begins like the straining of a solid body with an elastic stage within which there is no " permanent set." When the magnetising force was increased above 0-04 the compensation failed to remain exact, and the deviations followed the parabolic law stated above. The formulas agreed well with the results of experiment for values of H ranging up to 1*2 C.-G.-S. unit. (In comparing these with the formulas given in the last paragraph, it must be remembered that these refer to hard iron, the others to annealed iron : the initial susceptibility is less here, and the deviation from the initial value is very much less rapid.) With another specimen of hard-drawn iron wire the initial value of p was 87. Lord Kayleigh has also examined the effect of alternately applying and removing a small amount of magnetic force, when the piece is kept more or less strongly magnetised by means of a constant force. So long as the constant force is moderately small, and the mean magnetisation consequently not very strong, the susceptibility with regard to alternate applications and removals of a small part of the force is not materially different from the initial susceptibility of the same piece when unmagnetised. But as the mean magnetisation is raised, the susceptibility with respect to small changes of force becomes reduced. In a piece of hard iron a steady force of 29 C.-G.-S. had the effect of reducing the susceptibility with respect to small alternations by about 40 per cent, of its original value \ and in a piece of annealed iron the reduction due to the same steady force was more than 80 per cent. 88. Magnetic Viscosity under Small Forces. Allusion has already been made ( 50) to the fact that after any change has taken place in the magnetic force acting on a piece of soft annealed wrought iron, some time elapses before the correspond- 128 MAGNETISM IN IRON. ing change of magnetic state is complete.* This magnetic viscosity is most noticeable when we have to deal with feeble forces or with small changes of force, and when the specimens tested are of considerable size. In such cases the time-lag in magnetisation may be so great that the ballistic method, which, of course, omits to take note of slow continuous changes, is not properly applicable. In describing the experiments which were referred to in the last paragraph, Lord Eayleigh remarked that when small magnetic forces were applied to hard iron or steel it was possible to adjust the compensating coil, so that neither at the moment of closing the magnetising circuit nor afterward was there any deflection which means that, so far as the magnetometer can decide, these metals take their full magnetism at once. With annealed wrought iron, however, the effects were more complicated. "When the coil was so placed as to reduce as much as possible the instantaneous effect, there ensued a drift of the magnetometer needle in such a direction as to indicate a continued increase of magnetisation. Precisely opposite effects followed the withdrawal of the magnetising force. The settling down of the iron into a ne\? magnetic state is thus shown to be far from instantaneous." Following Lord Rayleigh's plan of balancing the instantaneous effect by means of a compensating coil, and then observing the drift, the writer examined this time-lag in the magnetisation of a thick wire of annealed wrought-iron 0*404 cm. in diameter and 39*6 cms. long.f The wire was demagnetised by reversals to begin with, and feeble magnetising forces were used, not at first exceeding O'l C.-G.-S. So long as the force was less than this it was found that one adjustment of the compensating coil served to balance the instantaneous effect of making or break- ing or reversing the current. When the compensation was correct the magnetometer needle began to drift slowly over as soon as the magnetising force was either applied or removed ; and * Phil. Trans., 1885, p. 569. " When the magnetising current was applied to long wires of soft iron, either gradually or with more or less sudden ness, there was a distinct creeping up of the magnetometer deflection after the current had attained a steady value. This action was sometimes so considerable as to oblige me to wait for some minutes before taking the magnetometer reading." t Proc. Roy. Soc., June 20, 1889. MAGNETIC VISCOSITY UNDER SMALL FORCES. 129 by observing the drift and adding that to the amount neutralised by the compensating coil, the total magnetism after any time was readily deduced. A force of 0-044 C.-G.-S. was applied, the instantaneous effect of which was to produce a value of I equal to 0'44 ; in five seconds this crept up to 0'58, and in 60 seconds to 0'67. Then the magnetising current was broken ; the instan- taneous effect on I was to remove 0'44, leaving 0*27 ; in five seconds this residue fell to 0-09, and before 60 seconds it had completely disappeared. Next a magnetising force of 0'084 was applied. The value of I reached at once was 0'85 ; in five seconds it crept up to 1-20, and in 60 seconds to 1-40. On breaking the current, I fell at once to 0'55, after five seconds to 005 ' Force H. FIQ. 57. 0'23, and after 60 seconds to 0*07. Possibly this small residue, or part of it, was permanent. These results are shown in Fig. 57. Precisely similar results were obtained by reversing feeble magnetic forces, the initial gradient of the lines being the same when the force was reversed as when it was applied and removed. If we measure the initial susceptibility by the imme- diate effect of applying or reversing H it is 10 ; if we measure it by the effect after one minute it is about 15. Fig. 58 shows the results of another experiment, in which successive forces were applied, ranging up to about 0*34 C.-G.-S., the compensating coil being adjusted for each force to give an instantaneous balance, so that the effect of the subsequent creeping up might be observed. Before applying each force the specimen was completely demagnetised. The three curves, 130 MAGNETISM IN IRON. Fig. 58, show the amounts of magnetism taken (a) at once, (6) after five seconds, and (c) after one minute. In noting the y < 7 .1 Magnetising Force H. FIG. 58. Effects of applying Feeble Magnetising Forces to a Soft Iron Rod. 081 20 40 Time in Seconds . 60 Fia. 59. Growth of Magnetism after applying Feeble Magnetising Forces. gradual growth of magnetism after each force was applied, readings of the magnetometer were taken every five seconds, TIME-LAO IN MAGNETISATION. 131 and the two curves of Fig. 59 have been drawn from these, to show the time rate at which the process of creeping up went on under the action of magnetising torces equal to 0'035 and 0*081 respectively. 89. Further Experiments on Time-Lag in Magnetisation. Similar differences between the immediate and ultimate action of magnetic force on soft iron present themselves when we examine the effects of small increments of the magnetic force at any stage in the process of magnetisation. In another ex- periment, which was made with the same specimen of annealed 0'4 tr5 Magnetising force H. Fia. 60. Effects of Steps in the Magnetisation of a Soft Iron Rod. wrought iron, the magnetising force was applied in a series of small steps each step being produced by a rapid but not quite sudden augmentation of the magnetising current. The imme- diate effect of each step was balanced by means of the compen- sating coil, and after each step a pause of one minute was made during which the gradual growth of magnetism was observed. The results are shown in the full lines of Fig. 60 ; the dotted line has been added to show that the points reached after the pauses of one minute lie in a continuous curve. As the experiment was continued into higher parts of the magne- tisation curve, the compensating coil had to be pushed a little K2 OF THE UNIVERSITY 132 MAGNETISM IN IRON. nearer the magnetometer to procure a perfect balance : in other words, the immediate effect of the step became somewhat greater. At the beginning, the instantaneous value of I d H was about 10; but when the experiment of Fig. 60 was ex tended until the force produced by the magnetising solenoid was 3 C.-G.-S. or so, and I was about 320, the instantaneous value of rose to 13. In that region of the curve, the d H creeping-up of magnetism after a very small step-up of the cur- rent was enormous ; in the course of one minute it amounted 1. H. Fid. 61. Effects of a sudden small increase of Force in the steep part of the Magnetisation Curve. to six or seven times the immediate effect of the step. Fig. 61 illustrates the kind of action which is observed when a small increment of magnetising force is made to take place quickly after a pause anywhere in the steep part of the magnetising process, the metal dealt with being soft wrought iron. The dotted line is the normal slope of the magnetisation curve when the process of magnetising is performed slowly. A very small increment of H rapidly performed after a pause at P produces an immediate effect, P Q, which is followed by the slow creeping up Q R. It is only when the step is a very small one that P Q correctly represents the immediate effect, TIME-LAG IN MAGNETISATION. 133 Very Interesting results are obtained in examining how the time-rate of creeping up after a step is affected by the length of the pause (under constant force) which preceded the step. When the preceding pause is long the creeping up which fol- lows a step goes on much more slowly than when the preceding pause is short.* In an experiment with the same specimen of soft iron the effects of two equal small steps were compared, both made at the same part of the magnetisation curve, one after the magnetising force had been kept constant for three minutes, and the other after it had been kept constant for an hour. The immediate effects were the same ; but the subsequent creeping up, which was observed during no less than ten minutes, went on so much faster in the former case that it amounted in ten minutes to 531 scale divisions of the magnetometer, as against 320 scale divisions in the latter. The effects of an alternate small step up and step down, per- formed at any stage in the process of magnetisation, are quite like those that have been shown in Fig. 57. After the steps have been repeated often enough to bring about a cyclic set of changes, the instantaneous value of -TYI becomes ap- d M proximately the same as at the initial part of the curve namely, about 10 in the particular specimen examined unless the whole magnetisation approaches saturation, in which case the value of is distinctly less. The diagram (Fig. 62) re- d H presents in a general way the change of magnetism which takes place when any very small periodic variation of magnetic con- dition is made to occur in a soft iron bar, about a mean condi- *loc. cit., p. 280. 134 MAGNETISM IN IRON. tion 0. If the changes of force occur fast and without pauses the cycle is shown by the lines a a' and a' a. They enclose no area, and there is no dissipation of energy. If, on the other hand, the changes of force occur gradually and very slowly the cycle is shown by the lines c c' and c' c. They also enclose no area ; and again there is no dissipation of energy. But if the changes of force take place quickly, with pauses at the extreme values, the cycle is b' c' b c, and an amount of energy is dissi- pated which is to be measured by the area of that parallelo< gram. In most actual cases in which the force varies periodically it does so not suddenly with pauses at the extreme values, but in such a manner that a loop will be formed instead of the parallelogram. When the frequency of the alternations is very great, the loop will flatten itself into the straight line a a' ; when the frequency is very small it will again flatten itself into the straight line b b'. With any frequency lying between these extremes there will be dissipation of energy, and when the limits and mode of variation of the force ara specified, there must be some particular frequency which will make the amount of energy dissipated in the cycle a maximum. In hard iron and in steel the phenomenon of time-lag in mag- netisation occurs, but so slightly as to be scarcely observable. A piece of the same wire as had been used in the above experi- ments was hardened, after being annealed, by stretching it a little beyond the limit of elasticity. Scarcely a trace of creeping could be detected when a feeble magnetic force was applied to the wire in this hardened state, but it was possible to pro- duce a measurable amount of creeping by first applying a moderately strong magnetising force, and then making a small step up after a pause. The initial instantaneous value of . for a small step was 5 3. d H The whole phenomenon depends much on the size of the specimen that is tested. In the experiments which have been described the iron was a rod four millimetres in diameter. Smaller rods showed much less magnetic " creeping," and when a bundle of fine annealed iron wire was substituted for the rod, nearly all trace of creeping disappeared. The cause of this difference is at present obscure. MOLECULAR ACCOMMODATION. 135 90. Molecular Accommodation. Closely related to the experiments which have been detailed in this chapter are results recently published by H. Tomlinson.* Examining the action of feeble magnetic forces, in the region within which the relation of B to H may be expressed ( 86) in the form. he has discussed the influence of temperature and other con- ditions on the constants a and b. The constant a is of course the initial permeability, and it is on the value of b that the dissipation of energy depends. Some of the more interesting of Tomlinson's results may be briefly stated in his own words : " The internal friction of iron, nickel, and cobalt in any com- plete cycle may be decreased by repetition of the cycle ; the molecules are said to be ' accommodated ' by this process. " The molecular ' accommodation ' of freshly annealed iron can be largely aided by repeatedly raising the metal to 100C , and then allowing it to cool. " The ' accommodation ' of the molecules of iron, nickel, and cobalt is disturbed by very slight mechanical shocks, by small change of temperature, or by magnetisation beyond certain limits ; under such influences the internal friction may for a time, or even permanently, be considerably increased. " The values of a and b for iron are temporarily increased when the temperature is raised from 0C. to 100C." * Proc. Roy. Soc. Dec. 5, 1889. CHAPTER VII. MAGNETISM IN STRONG FIELDS. 91. Magnetisation in Strong Fields. We pass now to speak of the opposite extreme of the magnetising process. In study- ing the relation of magnetism to magnetising force by any of the methods which have been described in earlier chapters, it is scarcely practicable to raise the force H beyond a few hun- dreds of C.-G.-S. units at the most. Formidable difficulties present themselves, one of which is the heating effect of the magnetising coil. Special methods have therefore to be resorted to when we wish to examine the behaviour of iron or other magnetic metal in very strong fields. It is true that the most important parts of the magnetising process lie within the range of those forces which may easily be produced by means of a magnetising coil. Within that range the permeability or the susceptibility passes through its great changes, increasing quickly from a small finite initial value to a maximum ten or fifteen times as great, and decreasing almost as quickly to a value smaller than the first. Within that range, too, the residual magnetism apparently reaches the full value it is capable of reaching. It is within that range that the most prominent features in the influence of vibration, of temperature, and of stress, manifest themselves. And it is pro- bably true that whatever knowledge of magnetic quality is wanted for application to the practical ends of electrical engi- neering can be obtained by experiments within that range. But still the action of stronger fields is of very great interest, especially in relation to the molecular theory of magnetism pro- pounded by Weber. According to Weber's theory the molecules of iron or any other magnetisable metal are always magnets. These point anyhow in the unmagnetised piece, so that the sum of their moments, resolved in any direction, amounts to eero, and the piece, therefore, has no magnetism as a whole. But when a magnetising force acts the molecular magnets tend MAGNETISATION IN STRONG FIELDS. 137 to turn so that their axes may point more nearly in the direcv ion in which the force acte; and thus the piece, as a whole, becons a magnet. The intensity of magnetisation I is the sum (per um\ of volume) tit the moments of the molecular magnets resolved in the direction of the magnetising force. We shall discuss this theory more fully in a later chapter. Meanwhile, one obvious deduction from it may be pointed out. When all the molecular magnets are turned round to face exactly in the direction in which the force acts, no further magnetisation in that direction will be possible, however much the force may be increased. In other words, the theory points to this that the intensity of mag- netisation I has a saturation value which cannot be exceeded, though it points to no limit to the value which B, the magnetic induction, may reach. In experiments made with moderately strong magnetising forces both B and I are increasing slowly at the last ; and it is impossible to infer, from the results of such experiments, whether B or I or either of them is approaching a finite limit. The curves of permeability or of susceptibility in relation to B or to I (such as have been given in Figs. 40, 41, and 42) do not help us to a conclusion ; we cannot produce a curve of this kind beyond the region of experiment until it cuts the axis of B or of I, because (as Figs. 41 and 42 show) the curve bends out when the magnetising force is sufficiently increased. This characteristic of the curve of K and I or of /x and B was first pointed out by Fromme,* and has been commented on by a number of other experimenters. In some of the writer's ex- periments it appeared when B exceeded about 15,000.1 Figures given by Bosanquet| for experiments with iron and steel rings, in one of which the induction was pushed as high as 19,300, show when plotted a similar inflexion in the curve of p. and B, occurring when B is about 15,000. The same feature is well shown in Fig. 63, which is copied from a Paper by Bidwell, describing experiments with soft wrought iron, in which the * Fromme, Gott. Nahr., 1875, p. 500. Wied. Ann. XIII., p. 695, 1881 ; see also J. Haubner, Wien. Am., October 21, 1880 ; Wied. Beiblatter, V., 1881, p. 205. t Phil. Trans., 1885, Part II., p. 567. $ Bosanquet, Phil. Mag., February and May, 1885. Bidwell,Proc. Roy. Soc., Vol. XL., 1886, p. 486. 138 MAGNETISM IN IRON. induction was raised to 19,820, with the result of reducing /A to 33-9. To produce this the force H was 585, and the resulting magnetisation I was 1,530. These numbers give some idea of the extent to which experience has shown it is practicable to go in experiments of the ordinary class, using the magnetising 2,000 1,000 5,000 10,000 B 15,000 20,000 Fio. 63. Permeability of Wrought Iron when Strongly Magnetised. force of a current in a coil.* To answer the question whether there is any finite limit to I or to B, we have to go far beyond this range. 92. The Isthmus Method. This name has been given to a method introduced in 1887 by the writer and Mr. W. Low,t which has allowed the magnetisation of iron to be raised to greatly higher values, with the result of showing that, while B has apparently no limit, there is a finite limit to I, as Weber's molecular theory predicts. In the air-space between the pole-pieces of a strong electro- magnet, we have a magnetic field of much greater intensity than any that can easily be produced by the direct action of the electric current. If a small test-piece of the metal which is to be magnetised be placed across this space, so that it forms an isthmus between the two pole-pieces, it will become strongly magnetised. In becoming magnetised, however, it disturbs this field, and the force acting on it may be very * In recent experiments by du Bois, described in 107 infra, a coil was used to produce magnetic forces which ranged up to 1,300 C.-G.-S. tProc. Roy. Soc., March 24, 1887; Phil. Trans., 1889, A, p. 221. THE ISTHMUS METHOD. 139 different from the force which existed in the empty space. If it is a short cylinder extending lengthways from pole-piece to pole-piece, its magnetism will be very unequal. At the ends the induction will have the same value as it has in the pole- pieces themselves ; at the middle it will be stronger, owing to the convergence of lines of induction from neighbouring parts of the pole-pieces, which find their way into the test-piece through its sides. Evidently we may increase the induc- tion in the middle by furnishing the specimen with spreading ends, which will present an easier path along which the lines of induction may converge. Moreover, when the test-piece takes the form of a bobbin, with a short, narrow, central neck, from each end of which a cone extends, spreading over the face of the pole-piece, it becomes possible (by giving a proper form to the cone) to secure that the central neck will be uniformly magnetised, and that the magnetic force which acts on it will have the same value as the magnetic force in the immediately surrounding air-space. The magnetic force and the magnetic induction within the neck then admit of being measured, and the permeability, susceptibility, and intensity of magnetisation under exceedingly strong forces are readily deduced. 93. Early Experiments, using the Isthmus Method. Figs. 64 and 65 show two forms of bobbin which were used in the first application of the isthmus method. The dimensions are marked in millimetres. The central neck was wound with an induction coil consisting of a single layer of fine wire, and its magnetism was measured by the ballistic method. With bobbins of the shape shown in Fig. 64, the induction was measured by suddenly slipping the bobbin out from its place between the pole pieces while the electro-magnet was excited. An objection to this is that it takes no direct account of the resi- dual induction ; it shows only the magnetism that is lost when the bobbin is withdrawn from the field. The residue is small, and it may be separately measured and allowed for ; but a better arrangement is shown in Fig. 65, where the bobbin may be turned suddenly round so that its magnetism is reversed ; half the ballistic effect of this reversal of course measures the magnetic induction. To measure the field in the air-space immediately surrounding the neck, a second induction coil was 140 MAGNETISM IN IRON. wound over the first, but at a little distance from it, so that a narrow ring of non-magnetic space about l'3mm. wide was FIG. 64. FIG. 65. included between the two. The magnetic force in this space was calculated from the observed difference in the ballistic O'HH! ISTHMUS METHOD. effects of the inner and outer coil. The knowledge of it allowed a proper correction to be made, by which the whole induction within the inner coil was reduced to allow for those lines of in- duction which lay within it but not within the iron. With the bobbins shown in Figs. 64 and 65 the outside field that is to say, the magnetic force in this narrow ring of space surrounding the neck was probably a very little stronger than the mean force within the metal of the neck itself. Still, the outside field was so nearly equal to H that the quantity B outside field approximated closely to the value of I, and the quantity. B approximated closely to the value of outside field the permeability, p. The results in Table VIII. were obtained with a bobbin of soft Swedish wrought iron in the annealed state. TABLE VIII. Swedish Wrought Iron in Strong Fields. Outside field (=H nearly). B B - outside field B 47T (=1 nearly). outside field (= A* nearly). 6,690 27,960 1700 418 8,900 29,730 1660 334 9,510 30,820 1700 3-24 10,000 31,210 1690 312 10,360 31,630 1700 305 10,810 31,720 1670 2-94 10,880 32,060 1690 295 11,200 32,360 1690 2-90 These figures show that in the very strong fields with which this experiment deals, the quantity in the third column, which is approximately equal to the intensity of magnetisation I, becomes practically constant. Such variations as occur in the numbers are irregular and come from errors of observation. The iron is here in a condition of true saturation ; I has reached a value which refuses to undergo any sensible increase, though the strength of the field be doubled; but the field itself may be increased without limit, and consequently there is no sign of any limit to the value of B. 142 MAGNETISM IN IRON. Table IX. gives the results of a similar experiment made with a bobbin of annealed Lowmoor wrought iron, and with a wider range of magnetic forces. The apparent decrease of I in TABLE IX. Lowmoor Wrought Iron in Strong Fields. Outside field B - outside field B ( = H nearly). B 47T ( = 1 nearly). outside field (=/x nearly). 3,630 24,700 1680 6-80 6,680 27,610 1670 4-13 7,800 28,870 1680 370 8,810 29,350 1630 3-33 9,500 30,200 1650 3-18 9,780 30,680 1660 314 10,360 30,830 1630 2-98 10,840 31,370 1630 2-89 11,180 31,560 1620 2-82 TABLE X. Cast Iron in Strong Fields. Outside field ( = H nearly). B B = outside field B ATT (=1 nearly). outside field (= /A nearly). 3,900 19,660 1250 5-04 6,400 21,930 1240 3-42 7,710 22,830 1200 2-96 8,080 23,520 1230 2-91 9,210 24,580 1220 2-67 9,700 24,900 1210 2-57 10,610 25,600 1190 2-46 the strongest field, which is shown by the last numbers in the third column, is due to the fact that the outside field was rather greater tha i the true magnetic force within the metal. When the bobbin is so shaped that this source of error is avoided, the apparent decrease disappears, and I is then found to be as nearly constant as casual errors of observation allow it to be. A noticeable feature in these results is the reduction of the permeability that is brought about by continuing to increase the magnetising force after a state of saturation has been reached. With wrought iron such as was used here the initial value of /A for exceedingly small forces is nearly 200 j and the maxi- THE ISTHMUS METHOD. 143 mum of /i, reached generally with a magnetising force of two or three units, may be as much as 3,000. Here, with a magnetis- ing force of 10,000 units or so, p has fallen to less than 3. Table X. gives the results of a similar experiment with cast iron. In it, as in the two last cases, saturation has been reached even with the lowest value of H within the range of the observations. The saturation value of I in this cast iron is about 1,240 a value distinctly less than that found in wrought iron. Fig. 66 exhibits in the form of curves of permeability the results given in Tables IX. and X. These are in effect an 8 2 O I- CD 1 * a * B FIG. 66. Curves of Permeability for Wrought Iron and Cast Iron very Strongly Magnetised. extension into regions of strong force of curves of the type shown before in Figs. 41 and 42 and in Fig. 63. 94. Later Experiments, using the Isthmus Method. In subsequent experiments* the induction in iron was forced to much higher values by using a larger electro-magnet and by turning down the neck of the bobbin. The extent to which concentration of induction in the neck may be carried depends on the proportion which the sectional area of the neck bears to that of the pole from which the lines converge. In the follow- * Ewing and Low, PM. Trans., CLXXX., 1889, A, p. 221 ; Rep. Brit, gsoc., 1887, p. 586. 144 MAGNETISM IN IRON. Ing experiment the section of the neck was reduced until it was finally only yj^ that of either pole. The magnet an exceptionally powerful one, belonging to the Physical Laboratory of Edinburgh University was excited with 64,000 ampere- turns, and its force was concentrated from poles about 10 cms. Fia. 67. Pole-pieces and Bobbin used in the Isthmus Method. square upon a neck or isthmus 2'66 mm. in diameter and 3-5 mm. long. Fig. 67 is a full-size sketch of the poles with the bobbin in its place after its neck had been reduced to the smallest diameter. The dimensions are entered in millimetres. The bobbin c was the same bobbin of annealed Lowmoor wrought iron as had been used in the earlier experi- THE ISTHMUS METHOD. 145 ments, a pair of separate conical pieces bb being interposed to connect its ends with the pole-faces a a. With each reduction in the size of the neck a higher value of B was reached; finally, when its diameter was 0-266 mm., the induction B was 45,350, and the force in the space immediately surrounding the neck was 24,500. From other experiments we may infer that this was, as nearly as possible, equal to the actual magnetic force within the metal : hence the result may be written thus : H B I p 24,500 45,350 1,660 1-85 No attempt was made to reduce the neck further, and this is the highest induction that has hitherto been recorded in any experiment. There is no reason to doubt, however, that higher values of H and of B might be obtained by using an electro-magnet of greater size and power. 95. Theory of the Isthmus Method : Form of Cone to give Maximum Concentration.* Consider an imaginary section through the middle of the neck, at right angles to the axis of the bobbin. It is clear that there is no discontinuity between the magnetic force, at points in this plane, inside and outside the metal, for there is no free magnetism on the surface of the neck at the middle of its length. We have to consider the con- ditions which will make the magnetic force as nearly uniform as possible over this medial section in order that the force just outside the neck, which we are able to measure, may be fairly representative of the force within the substance of the neck itself. The magnetic force in the space between the pole-pieces is made up of two parts : (1) the electro-magnetic force directly produced there by the current in the magnet coils; and (2) the force due to free magnetism, distributed for the most part over the pole-faces. The first of these forms a comparatively small part of the whole; and its value is sensibly uniform at such small distances from the axis as those with which we are now con- cerned. In considering the conditions which will secure the greatest strength or the greatest uniformity in the field at the * Parts of this and the succeeding paragraphs are taken from the Paper cited (Phil. Trans., 1889, A, p. 221). L 146 MAGNETISM IN IRON. neck, we need only deal with that part of the force which is produced by free magnetism. The free magnetism of the pole-faces may be treated as made up of a series of co-axial circular rings in planes normal to the axis of the bobbin. Calling M the whole free magnetism of one of these rings (Fig. 68) and r its radius, the magnetic force F due to it at a point in the axis at a distance x from the plane ~\i[ x of the ring is where I = + ^ This force will be a d F maximum when - = 0, that is, when ax which occurs when x = ~ ; tan 0= J^ > # = 5 4 44' Hence V 2 a series of co-axial rings will be most advantageously disposed for producing force at a point on the axis if they lie on a cone having its vertex at the point in question, with a semi-vertical angle of 54 44'. The greatest force will be produced when the pole-pieces are themselves saturated, so that I reaches its limiting value in all parts of the metal. In that case the distribution of density from ring to ring is uniform. The surface density of free magnetism at any point of a sloping pole-face is lsin#, where is the slope of the face to the axis of magnetisation. The THE ISTHMUS METHOD. 147 whole quantity in each ring is I multiplied by the area of the ring projected upon a plane normal to the axis a quantity which is independent of the slope of the cone. We have, therefore, the same series of attracting rings to deal with whatever be the slope of the convergent faces, and whether that slope be uniform or not. Given, then, a certain diameter for the neck of the bobbin to be magnetised, the greatest magnetic force will be produced at the middle of the axis of the neck when the pole-pieces are saturated and when we make the expanding ends and pole-faces in the form of cones, with a semi-angle of 54 44', and with their vertices at the middle of the neck. This determines what may be called the cones of maximum concentrative power. In practice cones intended to produce as great a concentration as possible should have a somewhat greater semi-angle say 60 or so because of the defective saturation of the pole-pieces. 96. Greatest Magnetising Force producible by Means of Cones. With a cone of any semi-angle 6, magnetised to a uniform intensity I , the surface density of free magnetism is | sin 0, and the force at the vertex due to a ring at an axial distance x, of radius r, and of length dl, measured along the slope, is 27rrdl.\ Q smO.^, or 2 TT I sin2 $ cos 0-. The whole force at the vertex is 2 TT sin 2 6 cos a being the radius of the neck on which the cone converges, and b the radius of the base to which it spreads. Hence (treating I as uniform), with a pair of truncated cones, joined by a neck at the middle of which they have their common vertex, the whole force there is F = 47rl sin 2 0cos<91og A, e a which, for convenience of calculation, may be written F = 28-935 I sin 2 cos 6 Iog 10 . a 148 MAGNETISM IN IRON. Applying this to the cones of maximum concentrative power (95), in which sin 6= ^/f and cos = -L- . V 3 F ma , = 11-137 I log 10 -, a and the greatest value of the force will be obtained when 1 has the saturation value (of say 1,700 C.-G.-S. units for soft wrought iron), in which case F = 18930 lo ma , an expression which measures the greatest possible force which the isthmus method of magnetisation can apply at a point in the axis of the bobbin (over and above the small force which is directly produced by the magnet coils). It is not practicable to produce quite so large a force, because the magnet poles cannot be fully saturated. 97. Form of Cone to give Most Uniform Field. The cone of maximum concentrative power is not the form best suited for producing a uniform magnetic force throughout the neck. It makes the field rather stronger at places near the axis than on the axis itself. To make the field as nearly uniform as possible in and close to the neck we must slope the cone at .72 "p such an angle that - =0, a condition which secures that dx* 72 Tji J2 "p 1 - and - shall also be zero. This condition is satisfied dy* dz* 9x 15 a* A when T'-^- =0 ' which makes x = r j$} tan 0=^/1 5 0=39 14'. In other words, the best approximation to a uniform field (the pole-pieces being saturated) is reached when the pole-faces are cones converging upon the middle of the neck, with a semi- vertical angle of 39 14'. When the cones have this form, and the neck is very narrow in comparison with the base, the field is so nearly uniform that the magnetic force in a narrow ring of space round the neck and close to it may be taken to repre- THE ISTHMUS METHOD. 149 sent, without sensible error, the force within the neck itself, and there is no practical variation of the force in the neck from end to end, or from side to centre. With cones of this form the concentration of force upon the neck is less than in the former case. Using the same notation as before the force is 15,240 Iog 10 *, a in the event of the poles being of wrought iron and fully saturated. , Fia. 69. FIG. 70 The difference between the two cases is illustrated by Figs. 69 and 70, where curves are drawn to show the force exerted at various points on the axis by a single pair of rings, forming parts of conical pole-faces which have a common vertex. In Fig. 69 the rings are parts of cones of maximum concentrative power; in Fig. 70 they are parts of cones shaped to produce the best possible approximation to a uniform field. The rings are taken equal in both cases, so that the height to which the curves rise in the middle will serve for comparison of the forces : the flat- 150 MAGNETISM IN IRON. ness of the curve in Fig. 70 shows the superiority of that form of cone in respect to uniformity of field. With actual conical pole-pieces, the force produced in the neck is, of course, made up of the sum of the forces due to pairs of rings like these dis- tributed over the whole conical surface. 98. Further Experiments with Wrought Iron. In the following experiments bobbins were used of a shape suited to give a fair approximation to a uniform field, and hence the outside field close to the neck is taken as the measure of H : TABLE XL Lowmoor Wrought Iron. H B 1 A* 3,080 24,130 1,680 7'83 6,450 28,300 1,740 4-39 10,450 32,250 1,730 3-09 13,600 35,200 1,720 2-59 16,390 36,810 1,630 2-25 18,760 39,900 1,680 2-13 18,980 40,730 1,730 215 TABLE XII. Sivedish Iron, " L s Lancash." Brand. H B 1 A* 1,490 22,650 1,680 15-20 3,600 24,650 1,680 6-85 6,070 27,130 1,680 4-47 8,600 30,270 1,720 3-52 18,310 38,960 1,640 2-13 19,450 40,820 1,700 210 19,880 41,140 1,700 2-07 TABLE *XIII.Fine Swedish Iron, ( L J Brand. H B . A* 5,310 25,670 1,620 4-83 17,680 38,080 1,620 215 19,240 39,540 1,620 2-06 OAST IRON AND STEEL IN VERY STRONG FIELDS. 151 In this last iron, which is described as the finest and most ex- pensive iron used in commerce, made by the Walloon process, the saturation value of I seems to be specifically rather less than in other brands. The saturation value usually found in wrought iron may be stated to be, in round numbers, 1,700. The state of saturation is practically reached, in soft metal, with a force of, say, 2,000 C.-G.-S. units; from this force upwards no material change can be observed in I, though the force be increased ten-fold. 99. Cast Iron and Steel in very Strong Fields. In cast iron the highest value to which B was pushed in these Fio. 71. Experiments on Vickers' Tool Steel. experiments was 31,760, with the result of reducing the per- meability to 1*9. The saturation value of I in the sample tested was 1,240, and saturation was practically complete under a force of 4,000. In hard steel the state of complete saturation is not so easily reached. The following test, which was made with a sample of Yickers' tool steel possessing much coercive force, exemplifies this. The test piece formed the central part of a bobbin with wrought- iron cones, built up in the manner shown in Fig. 71. By re- moving one of the cones, a loose coil on the neck could be 152 MAGNETISM IN IRON. slipped off to determine the residual magnetism, which in this case formed a considerable part of the whole. (The residual induction in the neck was about 8,000.) It may be doubted whether saturation was complete even in the strongest field. TABLE XIV. Victors' Tool Steel. H B 1 V- 6,210 25,480 1,530 4-10 9,970 29,650 1,570 2-97 12,120 31,620 1,550 2-60 14,660 34,550 1,580 2-36 15,530 35,820 1,610 2-31 There appear, however, to be specific differences in the satu- ration values of I in different steels. In the following Table a summary of the results of experiments with other steels is given, showing in each case the highest force applied and the highest induction reached, along with (approximate) corresponding values of I and /*. TABLE XV. Steel of Various Qualities. Outside field B- outside field B Description of Steel. (=H nearly). B 47T (=| nearly). Outside field (=A* nearly). 1. Bessemer steel, contain- ing about 0'4 per cent, of carbon 17610 39,880 1,770 2'27 2. Siemens-Martin steel, containing about 0'5 per cent, of carbon 18,000 38,860 1,660 2'16 3. Crucible steel for making chisels, containing about 0'6 per cent, of carbon . . . 4. Finer quality of crucible steel for chisels, con- taining about 0'8 per cent of carbon .. 19,470 18330 38,010 38,190 1,480 1,580 1-95 2-08 5. Crucible steel, containing 1 cer cent, of carbon . . . 6. Whitworth fluid - com- pressed steel 19,620 18,700 37,690 38,710 1,440 1,590 1-92 2-07 NICKEL AND COBALT IN STRONG FIELDS. 153 100. Hadfield's Manganese Steel in Strong Fields. Kefer- ence has been made in 70 to the remarkable absence of magnetic susceptibility shown by this steel, which contains about 12 per cent, of manganese and 1 per cent, or less of carbon. In fields of ordinary strength this alloy has a sensibly constant permeability of about 1 '3, as Hopkinson's experiments have shown.* Application of very strong fields, by means of the isthmus method, shows that the permeability, even under very great forces, remains constant as nearly as may be judged. One might expect that a material which resists magnetisation so strongly would show much coercive force ; the reverse, how- ever, is the case. Even the strongest force is unable to pro- duce more than a trace of residual magnetism. The following is one of several experiments which agree in showing that the permeability of manganese steel, under any force up to 10,000 C.-G.-S. units, is practically constant with a value of about 1*4. This permeability is so low that when the field is weak, the metal takes up scarcely any magnetism ; on the other hand, since the permeability retains the same value in very strong fields, a respectably high intensity of magnetisation may be produced by applying a sufficiently strong force. The variations of p in Table XVI. are irregular, and are no greater than may be ascribed to errors of observation. TABLE XVI. Hadfield's Manganese Steel. H B 1 /* 1,930 2,620 55 1-36 2,380 3,430 84 1-44 3,350 4,400 84 1-31 6,920 7,310 111 1-24 6,620 8,970 187 1-35 7,890 10,290 191 1-30 8,390 11,690 263 1-39 9,810 14,790 396 1-51 101. Nickel and Cobalt in Strong Fields. With nickel and cobalt a state of complete saturation is reached without * Phil. Trans., 1885, p. 462. 154 MAGNETISM IN IRON. difficulty, as the following observations show. In the two specimens of nickel tested (Tables XVII. and XVIII.) the saturation values of I were about 400 and 515 respectively ; the difference is perhaps due to differences in the amount of iron present : neither specimen was pure. The saturation value of I in cobalt (Table XIX.) appears to be 1,300, which is a little greater than the value in cast iron. TABLE XVII. Hard-drawn Nickel (with 0'56 per cent. of Iron). H B 1 /* 2,220 7,100 390 3-20 4,440 9,210 380 2-09 7,940 12,970 400 1-63 14,660 19,640 400 1-34 16,000 21,070 400 1-32 TABLE XVIII. Annealed Nickel (with 0'75 per cent, of Iron). H B 1 A* 3,450 9,850 510 2-86 6,420 12,860 510 2-00 8,630 15,260 530 1-77 11,220 17,200 480 1-53 12,780 19,310 520 1-51 13,020 19,800 540 1-52 TABLE XIX. Cobalt (with 1-66 per cent, of Iron). H B 1 /* 1,350 16,000 1,260 12-73 4,040 18,870 1,280 4-98 8,930 23,890 1,290 2-82 14,990 30,210 1,310 2-10 CONCLUSIONS FROM ISTHMUS EXPERIMENTS. 155 102. Summary of Conclusions from Isthmus Experi- ments. To sum up the results which have been arrived at by means of the isthmus method, the concluding paragraph of the Paper from which these figures are taken may be quoted.* Under sufficiently strong magnetising forces the intensity of magnetisation, I, reaches a constant or very nearly constant value in wrought iron, cast iron, most steels, nickel, and cobalt. The magnetic force at which I may be said to become practi- cally constant is less than 2,000 C.-G.-S. units for wrought iron of o" IN" ^ "N 2000 ^ \ ^ woo \ ', 1 \ 1 ^ 1- - \ * 1- 1 \ \ } \ 500 FIG. 92. Steel with 25 per cent. Nickel. Magnetising Force 64. warmed until the temperature rose to 5SOC. At that tem- perature it became again non-magnetisable, and remained so on cooling down to the ordinary temperature of the air. Within a range of about 600 degrees this steel is capable of existing, quite stably, in either state. Figs. 91 and 92 show the 188 MAGNETISM TN IRON. induction B (produced by reversals of magnetic forces equal to 6*7 and 64 respectively) in terms of the temperature. In the non-magnetisable state the permeability is only 1*4; in the magnetisable state the permeability resembles (but falls rather short of) that of hard nickel. The curve of magnetisation (at 13C.) is copied in Fig. 93. Hopkinson has also shown that other physical properties of this alloy change along with its magnetic properties. The electrical conductivity is markedly different in the two states : at 0C., for instance, the specific resistance is only 0*00052 if the substance has been brought into its magnetisable state by applying a freezing mixture, but is 0*00072 if it has been brought into the non-magnetisable state by previous heating above 600C. /r/1/1/5 ir -*-- 41000 3.000 onnn o -d o ^ -* ~^~~ , 1 ^ ^ ^ / 1000 y / *^ Magi tf/V's/ nq / 'orct 10 20 30 40 50 60 ID 80 90 100 110' 120 130 140 Fia. 93. Steel with 25 per cent. Nickel. Curve of B and H. Equally pronounced differences are found with regard to extensibility and strength. In the non-magnetisable state this metal is comparatively soft ; wires show an elongation of 30 per cent, or more before rupture, and break with a load of about 50 tons per square inch. In the magnetisable state it is much harder ; there is only 7 or 8 per cent, of extension, and the strength is as much as 85 tons per square inch, or even more. " If," says Hopkinson, " this material could be produced at a lower cost these facts would have a very important bearing. As a mild steel the non-magnetisable material is very fine, having so high a breaking stress for so great an elongation at rupture. Suppose it were used for any purpose for which a mild steel is suitable on account of this considerable elongation at rupture: NICKEL-IRON ALLOTS. 189 if exposed to a sharp frost its properties would be completely changed it would become essentially a hard steel until it had actually been heated to a temperature of 600 C." It is interesting to notice that specimens of the non-magnetisable metal when broken in the testing machine pass into the mag- netisable state ; the change occurs along with the mechanical hardening which the metal suffers in being drawn out. This remarkable power of assuming one or other of two widely different physical states is less noticeable when the per- centage of nickel in the alloy is further increased. Two other nickel- iron alloys, containing respectively 30 per cent, and 50 tOO 150 200 250 U FIG. 94. Steel with 33 per cent. Nickel. Magnetising Force I'O. 33 per cent, of nickel, Hopkinson found to be much more permeable, and to show very much less hysteresis with respect to temperature in changing between the magnetisable and non-magnetisable states, and to change at a comparatively low temperature. Fig. 94 shows the results of magnetising the 33 per cent, sample with a force H of I'O. The curves, which correspond to rising and falling temperatures, are not far apart, and the change takes place at temperatures lying near 200C. In the 30 per cent, sample the critical temperatures are lower (about 140C. in heating and 125C. in cooling). Finally, a sample containing 73 per cent, of nickel showed no material 190 MAGNETISM IN IRON. difference between the critical points for heating and cooling ; its critical temperature was 600C. These observations suggest the idea that a substance such as manganese steel, which is nearly non-magnetic in all conditions of temperature in which it has hitherto been tested, would become magnetic if the temperature were sufficiently lowered. And it is even possible that other metals than iron, nickel, and cobalt are non-magnetic only because all our dealings with them are at temperatures above a "critical point." This conjecture, however, is not borne out by experiment, so far as observations at low temperature have yet been made. Even at the very low temperature of liquid air there is no development of magnetic quality in metals which are non-magnetic under ordinary conditions. 119a. Researches on Effects of Temperature by Dr. Morris. A very complete investigation of the immediate effects of heating on the magnetic qualities of certain specimens of iron has been made by Dr. D. K. Morris,* who has examined both the permeability and the hysteresis over a range of temperature extending considerably beyond the critical point. The specimens were in the form of rings, electrically heated by means of a non-inductive coil of platinum wire. Under small magnetising forces (H < 0-5 C.G.S.) the permeability was found to rise with rising temperature, at first slowing, and, then, in the neighbourhood of 300C. quite rapidly. It remained nearly constant between 400 and 500 and then rose with very great rapidity as the temperature approached 750 9 , reaching a value of nearly 13,000. After this it fell off with equal rapidity as the critical point was reached. The critical point was at 795 s 780 and 770 in three specimens examined by Dr. Morris. Changes of a generally similar kind were observed in the fermeability with respect to stronger forces. In all cases the general rise in permeability, with rising temperature, is subject to several set-backs at temperatures below the critical point. These are illustrated in Fig. 94A, which is copied from one of the curves in Dr. Morris' paper. It shows the changes which * Morris, Phil. Mag., September, 1897. CRITICAL POINTS IN IRON. 191 are observed in the maximum permeability as the Iron is heated. The curve passes at least three maximums before the critical point is reached. Even above the chief critical point some susceptibility to magnetisation is still found : between 800 and 1,000C. there is another maximum, and after falling to a value of only about 2'3, about 750C., the permeability again begins to increase very appreciably as the temperature continues to rise. It is clear that these irregular changes of magnetic quality which begin as low as 250C. or even lower, and go on to 1000C. or higher, and of which the great drop at the chief critical Fia. 94A. Effects of Temperature on the Permeability of Iron (Morris). point is only a particular case, are associated with changes in crystalline structure of which we have independent evidence. Sir W. Roberts Austen has examined the rate of cooling of iron, from a bright red heat, and has found corresponding irregu- larities, due to the evolution of heat within the substance of the metal at a series of stages in the cooling process. Fig. 94s is a record of one of his results,* the co-ordinates representing * Fifth Report of the Alloys Research Committee, Proc., Inst. Mech. Eng., February, 1899 192 MAGNETISM IN IRON. temperature and time. As the iron cools a series of more or less sudden evolutions of heat occur due to some internal convulsion. The lowest of these occurs at obout 260C., the highest (in the dia- gram) at about 900. On comparing the two curves, Fig. 94s and Fig. 94A, we can readily trace a connection be- tween the changes of structure which the cooling curve exhibits and the changes of magnetic quality, not only at the great mag- netic critical point (say 770C.), but also at the earlier and later points of arrest. With regard to hy- steresis, Dr. Morris' ex- periments show that with constant limits of magnetic induction the area enclosed within cyclic curves of B and H becomes enormously reduced as the tempera- ture approaches the chief critical point : in other words the hysteresis tends in great part to disappear. He gives the following figures for a AGEING OF IRON. 193 specimen of iron, previously annealed at a temperature of 1150C., and then taken through cvcles of magnetisation between the limits B= 4550: Temperature. C. Hysteresis in Ergs per cub. cm. per Cycle (B=4550). Temperature. C. Hysteresis in Ergs per cub. cm. per Cycle (B=4550). 18 137i 249 352 457 554 613 555 508 475 379 335 634 695 730 748 764 264 178 128 109 81 119b. "Ageing" of Iron by Prolonged Exposure to Moderate Temperature. Apart from the immediate change which heating produces in the magnetic quality of iron it brings about a slow deterioration of the metal which shows itself in reduced permeability and increased hysteresis. This action proceeds very gradually if the temperature is compara- tively low. An important practical instance of it is found in transformers. The heat which is generated in the transformer by the currents in the coils and by hysteresis in the core keeps the apparatus at a temperature considerably higher than that of its surroundings. It was observed that the efficiency of transformers generally became reduced after they had been at work for some months, and this was traced to increase of hysteresis in the core.* At first it was conjectured that this increase of hysteresis was a species of " fatigue " due to repeated reversals of magnetisation, resembling the fatigue of an elastic body under repeated reversals of mechanical strain, but it was shown by the author that reversals of magnetism did not in themselves have any such effect.! Mr. W. M. MordeyJ showed conclusively that the augmentation of hysteresis arose simply from prolonged heating. More recently the subject has been investigated by Mr. S. R. Roget, who has examined * Curves illustrating this increase were published in The Electrician by Mr. G. W. Partridge, Dec. 7, 1894. t The Electrician, Dec. 7, 1894, and Jan. 11, 1895. Mordey, Proc. Roy. Soc., June, 1895. 194 MAGNETISM IN IRON. the effect of prolonged exposure to temperatures ranging from 50C. to 700C.* Even so low a temperature as 50C., if con- tinued for some weeks, produces an appreciable effect. When the temperature was 160C. the hysteresis of a specimen of trans- former iron increased so rapidly that in a few hours it doubled, and in a few days it reached nearly three times its original value. But a longer time of heating at such a temperature as that makes the hysteresis pass a maximum and begin to diminish again, though not sufficiently to revert to the value it had before heating. FIG. 94c. Effects of Baking of the Hysteresis of Sheet Iron (Roget). The tables opposite, which are quoted from Mr. Roget'a paper, show how a maximum of hysteresis is passed under continued exposure to a constant temperature, at least in cases where the temperature is not less than 135C. The second table deals with higher temperatures, ranging from 300 to 700C., and there it will be observed that the maximum is reached after a very short time in some cases after a few minutes. In both tables the hysteresis is stated for a cycle with the limits B = 4000. ^ * Koget, Proc. Roy, Soc., May 12, 1898, and Dec, 8 1898, AGEING" OF IRON. 195 g .^ Increase per cent. OCOOO 'VOOOCN -CO -OrH 4^-iO 'ICiOlO O -iOi5 .2* per cent. co AH AH AH S 00 gi \ooo oom o oo o eS a i i r-t **" pt . 0000000 & || O CO ' C^ GO t^* CO 1O 10 CO CM I-H I-H i 1 r- 1 i 1 i 1 i Ir 1 ^ CO CO CO CO CO CO CO ? I 1 S, 4 CO I-H 1 jg U1 O O O O ?OGO J^. -* i 1 * -rtl .2* o h o> ft -4< (N (N rH -^ ^0 O d s a> 4J S, HH a d 'm d> (H 0) d HO I D? 3 I I i-H i-H " i 1 i 1 i 1 i-H ? ! 33 > CO | co'S ^ ^co -co '.5* I^ 1 d i s. 10 CO (N CN GN r-H rH rH Si o s a <3 s s | 1 1 K s HH ft ^3 >3 1 CO i i m w2 0000 iO 10 55 w i (MOS-^li IGOGOCO-^COCO P^ H 5 ^ COOiOO -CO -^ '^f -Ttl Tfl .g 53 COOJOSOOt^l>.t^l>.l^t^ d v g x d .2 II OOO5 OO(MCO 1O i 1 CO(MO5 rH(M -TfllOlO -1OCO 'COGOGO 1 d .2 . per cent. 83S 1 j CO W'~ ? 1OO -1OO1O -OO .1OO1O . 1 s- ^d COCOt>. GOO5OS O50i OSOr-H I-H I 1 1 g oooooooooo OS-^HOIOCNOOOOOS 1 II O. 'OrHCO t ^ 1O O O^ CO GO OO CO OO GO -I*-* 2 O p 1 O ^H ^ 1 CO ft O >O >O O O 1O 1O 1O 1O O 1O COCOCO t>.t>.t>.GO CO OOCiOS ?;" g o teresis. 6 a HH i 1 . 11 . CO . CO ... . O C3 OOOOOOOOOO g 1 l ^ i-H i-H . j MH ^d CD CO CO CO CO CO "cS o bb a rt fc^ I a J OQ . I-H i-H i-H (N (N (N ! H 8 ^ - ~ J * ~ "rjj r-( CO 02 196 MAGNETISM IN IRON. These changes of hysteresis are associated with changes of permeability in the early portion of the magnetisation curve. The figures 94c and 94o illustrate this by showing the hysteresis cycle and also the early stage of the B-H curve for a specimen : first in its initial state, then after heating at 200C. for 19 hours, and finally after heating at the same 1,000 '5 1-0 1-5 2-0 2'5 8'5 FIG. 94D. Effects of Baking on the Permeability of Sheet Iron (Roget). temperature for four days, by which time the maximum of hysteresis had been passed. It is a characteristic of these changes that they occur Irregularly, and they are much more conspicuous in some specimens of iron than in others. Specimens, especially of sheet steel, will sometimes be found in which prolonged heating is almost without effect, but the conditions which secure this very desirable result are not fully understood. CHAF.TER IS. EFFECTS OF STRESS. 120, Effects of Stress : Introductory. No part of our subject is more interesting than that which deals with the effects of mechanical stress in altering the susceptibility, the retentiveness, and other qualities of the three magnetic metals. The matter is not, at least as yet, one of practical moment, for it has at present no direct bearing on any of the applications of magnetism ; but its importance on the theoretical side is not easily overrated. The effects of stress form a fascinating subject of inquiry to the physical student, and are likely to play a con- siderable part in revealing the molecular structure which makes magnetisation possible. The subiect is a large one, and the results that have been already obtained are too intricate to permit more than a very general account of them to be given here. It will be most convenient to state the salient facts, without much regard to the historical order of their discovery. The first inquirer in this field appears to have been Matteucci,* who noticed an increase of magnetism in a magnetised iron bar when the bar was pulled lengthwise. Villari f made the important discovery that the character of this effect became reversed when the bar was sufficiently strongly magnetised : let the iron bar be weakly magnetised, and the effect of pull is to increase the magnetism ; but let the bar be strongly magnetised, and the effect of pull is to reduce the magnetism. This "Villari reversal" (as it is now called) of the mag- netic effects of stress in iron was rediscovered by Lord Kelvin in the course of an inquiry which may be said to have * Comptes Rendus, 1847 ; Ann. de Chemie et de Physique, 1858. f Pogg. Ann., 1868. 198 MAGNETISM IN IRON. laid the foundation of exacb knowledge in this subject.* Kelvin studied the effects of longitudinal stress by loading and unloading if on wire and steel wire in magnetic fields of various strengths ; he extended the same method of investigation to nickel and cobalt. He found by experiment with a steel gun- barrel under hydraulic pressure that the effects of transverse stress were opposite in kind to those of longitudinal stress. Com- paring the results of longitudinal and transverse pull, he pointed out that the effect of a simple pulling or pushing stress was to develop a difference of magnetic susceptibility in directions lying along and across the line of pull or push ; and he applied this consideration to the case of torsional strain, deducing results which were verified by experiment, and discussing earlier experiments by Wiedemann, who, it may be added, has made the relations of torsion and magnetisation the subject of much detailed study. t The work of Kelvin has been followed up and extended by others, particularly in the direction of inves- tigating the forms which the magnetisation curve (the curve of I and H) assumes when the piece under test is subjected to various kinds and degrees of stress ; and also of investigating, by continuous magnetometric observations, the manner in which a loaded piece gradually acquires or loses magnetism when the loads are varied, a constant magnetising force being kept in action. The effects of hysteresis, which present themselves at every turn in experiments on this subject, do much to compli- cate the results : and it is only by following both methods of inquiry that is to say, by examining the consequences of changing the magnetic force while the state of stress is kept constant, and also those of changing the stress while the mag- netic force is kept constant that we can obtain a tolerably clear connected view of the phenomena. 121. Effects of Longitudinal Pull on the Susceptibility and Retentiveness of Nickel. It is most convenient to begin with nickel, because the effects of stress are for the * Lord Kelvin " Effects of Stress on Magnetisation," forming Parts VI. and VII. of his great series of Papers on the " Electro-Dynamic Qua- lities of Metals " (Phil. Trans., 1875, 1878 ; Eeprint of Papers, Vol. II., pp.332 407). t See Wiedemann's Elektricitat, Vol. III., 762, et seq. EFFECTS OF PULL IN NICKEL. 199 most part much greater in it than in the other metals, and are also simpler in one very material respect. There is nothing in nickel that corresponds to the Villari reversal in iron. If we apply pull to a magnetised rod or wire of nickel, we find as Kelvin first showed* that pull diminishes the magnetism, and relaxation of pull increases the magnetism; and this effect is still observed, however strongly or weakly the piece be magnetised. If we magnetise nickel while it is kept in a state of longi- tudinal tension by means of a constant load, we find an enor- mous reduction in its susceptibility. This is well shown by the curves of Fig. 95, which show the magnetisation of a long piece of annealed nickel wire under various amounts of longi- tudinal pull.f The wire was O'OGScm. in diameter, and 374 diameters long ; its section was 0'363 sq. mm., so that each kilogramme of load produced a stress of 275 kilogrammes per sq. mm. The curves drawn in full lines show the relation of I to H when there was no load, and also when the load was 2 and 12 kilogrammes, corresponding to 5*5 and 33 kilos, per sq. mm. respectively. The effect of tensile stress in depressing the magnetisation curve is very marked. With no load the maximum susceptibility is fully 15, with 2 kilos, it is only about 8, and with. 12 kilos, the resistance to magnetisation has become so great that the maximum of susceptibility has not been reached even by raising H to 100 C.-G.-S. Great as the effects of stress are upon the magnetic suscepti- bility, they are even greater on the retentiveness. In the same figure (95), three other curves have been drawn in broken lines, thus : , to show the residual magnetism that was found on withdrawing H at each of a series of stages during the process of magnetising under each load. The presence of load reduces the residual magnetism even more than it reduces the total induced magnetism. The residual value of I, after applying a force, H, of 100, is nearly 300 when there is no stress; under 2 kilos, it is reduced to 150; and under 12 * Reprint of Papers, Vol. II., p. 382. t This and a number of the succeeding figures are taken from two papers, on the " Magnetic Qualities of Nickel " (Phil. Trans., 1888, pp. 325 and 333), in one of which the author had the collaboration of Mr. Q. C. Cowan. 202 MAGNETISM IN IRON. kilos, it is only 16. The proportion of residual to total induced magnetism Las a maximum o 076 under no load ; but under 2 kilos, it is reduced to 0'61, and under 12 kilos, to O19. The amounts of magnetism which disappear when H is removed, under various loads, form a greater proportion of the whole the more the load is increased, although (owing to the re- duction in the total magnetism) the absolute amount that disappears when a strong force is removed is greater for a small load than it is for no load, and then less again for a large load.* The presence of a small amount of load may, therefore, be said to increase the susceptibility of nickel with respect to that part of the magnetism which comes and goes when H is alternately applied and removed, provided H is strong; when H is weak the effect of any load is only to reduce this susceptibilty. Fig. 96 gives the results of a similar experiment in which the same piece of nickel wire, after being hardened, how- ever, by a slight amount of stretching beyond its limit of elasticity, was magnetised under a succession of pulling loads, ranging up to 18 kilos., or about 50 kilos, per sq. mm. With no load the maximum susceptibility of this hardened wire was about 8. Under the highest load the susceptibility was prac- tically constant within the range of H used (up to 100 C.-G.-S.), and its value was only about 0'5 (permeability about 6 -3). In this condition of stress the residual magnetism is almost nil. The dotted lines in this figure show the effect of gradually removing the strongest value of H which had been reached in the process of magnetising; they illustrate well how the residual magnetism becomes smaller, not only abso- lutely, but as a fraction of the whole magnetism, when heavier loads are used. 122. Effects of Longitudinal Push on the Susceptibility and Retentiveness of Nickel. The reduction of susceptibility and retentiveness in nickel by longitudinal tensile stress is asso- ciated with an equally striking augmentation of susceptibility * This fact has been noticed independently and commented on in a recent Paper by H. Tomlinson (Phil. Mag., May, 18GO). EFFECTS OF PUSH IN NICKEL. 203 and retentiveness by longitudinal compressive stress. Fig. 97 shows an arrangement by which nickel rods have been tested,* under compression, within a yoke of wrought iron, by means of the method described in 58, the total magnetisation being determined ballistically by reversing H, and the residual mag- netisation by deducting the ballistic effect got by removing H from half the ballistic effect got by reversing H. The influ- ence of a number of loads was examined, ranging up to 19 '8 kilos, per sq. mm. Every addition of load produced a decided increase of susceptibility, and caused an increasing fraction of Fia. 97. Arrangement for Testing the Magnetisation of Metals under Compression. the whole magnetism to be retained on the withdrawal of the magnetising force, until finally, under the heaviest load, the magnetisation curve rose with remarkable steepness, and the maximum proportion of residual to total induced magnetism reached the astonishingly great value of 0'96. In this group of experiments the nickel rod was in a hard (unannealed) state. The results of the observations are shown in Figs. 98 and 99. Fig. 98 gives the induced magnetism I in terms of H, under each amount of longitudinal compressive stress ; and Fig. 89 * Phil. Trans., 1888, A, p. 333. 204 MAGNEXltiM IN IKON. 7 BFFECTS OF STRESS IN NICKEL. 205 206 MAGNETISM IN IRON. gives the residual magnetism, which was observed in the usual way by withdrawing H at a number of stages during the taking of each magnetisation curve. Especially to be noted is the sharpness with which the curve of induced magnetism, under the heaviest stresses, bends over when H is about 20. The approach towards saturation is extremely rapid, and the change from a highly susceptible state to an insusceptible because nearly saturated state is remarkably abrupt. Fig. 100 shows the result of the same experiment in a different way : the permeability //, is plotted there in relation woo 2GQO 3000 4-300 Maantfic Induction B. FIQ. 100. Permeability of Nickel in the Lard state. to B for three conditions of stress which are specified on the curves. Fig. 101 records a corresponding set of observations made on a nickel rod in the annealed state, under compressive stresses ranging up to 6 '8 kilos, per square mm. The curves of p and B which relate to this experiment have already been shown in Fig. 41, 75. 123. Effects of Cyclic Variation of Longitudinal Stress on the Magnetism of Nickel. As might be anticipated from the curves that have been given above, a magnetised nickel wire subjected to cyclic variations of pull by loading and unloading EFFECTS OF STRESS IN NICKEL. 207 208 MAGNETISM IN IRON. it with suspended weights suffers much reduction of its mag- netism when the weights are put on, and much increase of its magnetism when the weights are taken off. This happens whether the magnetism be induced or residual. Iu Fig. 102 a number of curves are drawn to show the observed effect (upon I) of applying and removing loads while the magnetising force specified in the right-hand margin of the figure remained continuously in action. The dotted curves in the same figure show how the residual magnetism iro Ruidual MarllS e a Load in Kilos. Fio. 102. Effects of Loading and Unloading Nickel Wire in Various Constant Fields. which was left after the action of the strongest force (116 C.-G.-S.) was affected by loading and unloading. In this experiment each kilogramme of load corresponds to a stress of 2 '7 5 kilos per square mm. When these curves are compared with corresponding curves for iron, which will be given later, it will be seen that there is comparatively little hysteresis of magnetism with respect to stress in these. There is, however, some hysteresis; the curve for the process of loading invariably lies above the curve for the process of unloading, even when the cyclic variations of stress EFFECTS OF PULL IN IRON. 209 are repeated often enough to make the magnetic changes become strictly cyclic. With hardened nickel wire, tested under a wider range of stresses, there is even less hysteresis than here.* 124. Effects of Longitudinal Pull in Iron. Turning now to iron, we find that much more complex variations of mag- netic quality are produced by longitudinal stress. We have to distinguish between two cases, that of soft annealed iron, and that of iron which has beeri hardened by a mechanical operation such as stretching, which has given it a permanent set. With hardened metal the effects of stress are in general much greater than with annealed metal. Both cases have thia in common, that the presence of any moderate amount of longi- tudinal pull increases the susceptibility when the magnetisation is weak, but reduces the susceptibility when the magnetisation is strong. We have here the phenomenon of the Villari reversal to which allusion has already been made. But in the case of hard metal, where it is possible to apply a stronger pull with- out permanently altering the characteristics or structure of the piece, it appears that the presence of a sufficiently great amount of stress may be unfavourable to magnetisation, even in the earliest stages of the magnetising process. These, as well as other effects of stress, will be best appreciated by means of a careful study of curves which exhibit the process of mag- netisation in iron wires pulled by various amounts of hanging load. The wires, in the experiments to be described, were of such a size that each kilogramme of load corresponded to a stress of about 2*2 kilogrammes per square mm. 125. Annealed Iron under Pulling Stress. Fig. 103 shows, by curves of I and H, the magnetisation of a wire of soft annealed iron under various amounts of longitudinal pull (no load, 2 kilos, and 6 kilos), f The curve for no load lies at first lowest, and finally highest. Each curve, in fact, lies at first lower, and afterwards higher, than a curve for any greater amount of load. Thus, the presence of load is favourable to magnetisation when I is small, but unfavourable when I is great. And the curves obtained by removing the magnetising force (which are shown to the left in the figure) preserve throughout their whole course the relative places with which they start, * Phil. Trans., 1888, A, p. 331. t Ewing, Phil. Trans., 1885, plate 64. 210 MAGNETISM IN IRON. tne differences between them becoming only accentuated as the magnetising force is reduced to zero. Thus, the presence of pulling load is unfavourable to the residual magnetism left coo 1100 1000 soc x' ^-*~- ,.'*" | - - ^uro ^_. _ -"^ .. * kilo ^, ~~~*\^--~~ 6 kilo ^/^^^' />-'' ^ / \ /' v^ a -9 IQ U U (3 i* /-X ' 7 j / / * 7 / Kag. Force H. 800 too ll 1 5 Fio. 103. Magnetisation of Annealed Iron under various amounts of Longi- tudinal Pull. i IV) i Intensity of May. /. i 1 ' i\ 200 100 I 1 J I EFFECTS OF PULL IN SOFT IRON. 211 after a strong field has been applied; though, as another experiment has shown, it is favourable to the residual mag- netism that is left after magnetisation by a weak field. Its GOO H-IT9 too] FIG. 104. Magnetisation of Annealed Iron under Various Amounts of Longitudinal Pull. P2 212 MAGNETISM IN IRON. influence on the residual magnetism is, in fact, of the same kind as its influence on the induced magnetism; both suffer reversal when the magnetisation is sufficiently increased. The curves of residual magnetism (which are not drawn in the figure) cross each other in the same manner as the curves of induced magnetism. The results of this experiment are shown in a differ- ent manner in Fig. 104. A series of curves are drawn there, each relating to a particular value of the force H, to show the relation of the value of I reached by applying that force, to the amount of load which was present when the force was applied. This figure shows very clearly that, except under the strongest magnetising force that was applied in the experiment, the pre- sence of a very small amount of pulling load increases the sus- ceptibility ; and further, that except in the weakest fields, the presence of a fairly large amount of pulling load reduces the sus- ceptibility. Except at very low and again at high magnetisations, there is maximum of a susceptibility occurring with a particular load; and the value of this load becomes smaller as the magnetisa- tion is increased. This maximum disappears in the lowest fields, no doubt only because the load is insufficiently great to show it. 126. Hardened Iron under Pulling Stress. Figs. 105 and 106 show the effects of various amounts of longitudinal pull on iron wire which had been previously hardened by stretching beyond the elastic limit. Fig. 105 gives the induced magnet- ism, and Fig. 106 gives the residual magnetism, both in relation to H, the process of magnetising being performed, as in previous examples, while a constant load hung from the wire. The first thing to observe here is the immense effect which a moderate amount of pull has in augmenting the susceptibility with respect to feeble magnetising forces. On the other hand, when a condition approaching saturation is reached, the presence of load is unfavourable to magnetisation ; in other words, we have, as before, the Villari reversal. But it is now to be noticed that even in the weakest fields the susceptibility is increased only when the amount of the load is moderate : to apply stress beyond a certain amount is prejudicial, whether the magnetisa- tion be strong or weak. This is shown by the fact that the curve for 14*8 kilos lies below the curves for 5 and 10 kilos thoughout its whole course. EFFECTS OF PULL IN HARD 213 The same remarks apply to the residual magnetism (shown (n Fig. 106). The influence of stress on it is even greater. Fig. 107 shows, in the same way as Fig. 104, the results of s> \ 1 1 2 i J \ ^ !\ I a r J n I 1 1 55 n \ j 1 A 1 1 \ 5 ^ -II ^ \ \ \ ^p ^ I \ , \ \ c >0^ i i \ \ \ V , x \ ^^ V, \ V ^ ^ v \ 'S x \ V^v ', 3 Fia. 105. Magnetisation of Hardened Iron under various amounts of Longitudinal Pull. 214 MAGNETISM IN IRON. Fio. 106. Residual Magnetisation of Hardened Iron under varioui amounts of Longitudinal Pull. ES9' 1ZOO 1)90 1100 1050 000 $50 900 B50 800 750 700 50 ^ 600 I % 550 4-SO 400 '350 300. 250 MO 'ISO iob 60 7 7 7 7 7 7 7 \ \ \ N H-20-M H-n-li H'H-37 H-8 62 H'S-li ; e 10 LoaoU in/ Kilos, FIG. 107.: Magnetisation of Hardened Iron under various amounts of Longitudinal Pull. 216 MAGNETISM IN IRON. another experiment of the same kind, in which a piece of the same iron wire, also hardened by stretching, was magnetised under a series of loads which in this case ranged up to about 19 kilos. This figure shows very clearly that a moderate amount of load is more favourable to magnetisation than either less load or more ; the exact amount which is most favourable depends on the degree of magnetisation, being less in strong fields than in weak ones. It varies, in this example, from about 10 to 5 kilos, for the range of magnetic forces with which the experiment deals. The effects of pulling stress on the susceptibility of steel are generally similar to the effects in iron. 127. Effects of Applying Longitudinal Pull to Magnetised Iron. In the experiments described above the pull was applied before magnetisation began, and was then left constant. It remains to describe what is observed when the pull is varied while the magnetising force is kept constant. If there were no hysteresis, we should obtain in this way curves similar to those of Figs. 104 or 107. In consequence of hysteresis the changes of magnetism that are actually produced by changing the load, though maintaining a general similarity to these curves, differ from them in two important respects. In the first place, the initial effects which are observed when we first begin to change the stress are in general very great, and are to be distinguished from the effects obtained after a cycle of stress changes has been repeated once or twice. These initial effects of applying stress resemble those that are produced by vibration, although the process of loading may be conducted in such a way that no actual vibration takes place. They proceed, as the molecular theory to be discussed later indicates, from a condition of mole- cular instability ; and they do not disappear when the stress is removed. Thus, when we begin for the first time to load an iron wire, to which a weak or moderately strong magnetising force has been applied, we find that the first loads are associated with an increase of magnetism, which may be so great as to increase the whole quantity ten-fold. Moreover, if a load has been hanging from the wire while the magnetising force was being applied, we find that on beginning to remove it an increase of induced magnetism takes place. Again, if we are dealing with residual magnetism, the first effect of changing the load after EFFECTS OF VARYING THE PULI> 217 the magnetising force has been removed (whether by way of in- creasing or decreasing the load) is in general to reduce largely the amount of the residue. It is only after applying and removing any load several times that the magnetic effects of the stress-changes become cyclic that is to say, after several repetitions of the operation, the magnetism will be found to alter from one to another of two definite values when the load is put on and when it is taken off. But even then the effects of hysteresis are manifest ; for any intermediate value of the load is found to be associated with very different values of the magnetism during loading and during unloading. These features are well seen when we examine curves drawn to show the changes of magnetism in relation to the changes of load, of which Figs. 108 and 109 are examples.* They refer to an iron wire, hardened by previous stretching beyond its elastic limit, of such a size that each kilo of load corresponds to a stress of about 2 '3 kilos per sq. mm. The cycle of stress consisted in applying and removing 15 kilos. Beginning at the bottom of Fig. 108, at the point marked a, we have the wire, free from any load and previously demagnet- ised by reversals, exposed to a magnetising force of 0*34: C.-G.-S. In this state there was very little magnetisation. Then loads were applied, and the effects of the first application and removal are shown by the dotted lines a b c. The full lines imme- diately above them show the effects of the second application and removal of load, by which time the magnetic changes had become nearly cyclic. It is clear that in the first loading we have to deal with a progressive augmentation of magnetism superposed on cyclic changes of the character shown by subse- quent cycles of loading that is to say, we have an initial effect superposed on the cyclic effect. Next, the wire was demagnetised, and then a stronger field (2-49 C.-G.-S.) was applied, while there was no load. The effects of the first loading in this field were enormous ; they are shown by the dotted line which starts from the point d in the figure. Here, again, a repetition of the process of loading and unloading brought the magnetic changes into a nearly cyclic state, which is shown by the full lines at the top of the figure. * Ewing, PhU. Trans., 1885, plate 63, p. 603. 218 MAGNETISM IN IRON. Next, a stronger field still (18-65 C.-G.-S.) was applied (Fig. 109). The curve for first loading still shows a consider- able permanent augmentation of magnetism j but a cyclic state 1 I I \ Fuld if fir, t loc &ng \wc unl0< dxng \ 243 ffuts Loadin Itdos Fio. 108. Effects of applying Pull to Magnetised Iron. Is reached sooner than in weaker magnetic fields. In still stronger magnetic fields the curves become more and more HYSTERESIS IN EFFECTS OF STRESS. 219 flattened down into a form in which the application of load causes a diminution of magnetism throughout. Finally, to show how the residual magnetism is affected by change of stress, the residue left after applying a field of 2 '49 units and subjecting the wire to loads in that field, was made the subject of the experiment shown by the lines f g Ji in Fig. 108. These curves show how (starting from the point/) the residual magnetism suffered changes due to loading and unloading, which may best be described as a progressive decrease of mag- G 8 10 Load in "kHai FIG. 109. Effects of applying Pull to Strongly Magnetised Iron. netism superposed upon cyclic changes of the same character as those which are shown in previous figures. If we repeat the cycles of load on a piece in which there is only residual mag netism, we find, in fact, cyclic changes of the same general kind as those that are found when a magnetising force is in action. 128. Hysteresis in the Effects of Stress. The hysteresis of magnetism with respect to changes of load, which is clearly exhibited by these curves, is static in character that is to say, it does not depend on the time-rate at which loads are 220 MAGNETISM IN IRON. applied nor on the intervals which are allowed to elapse before readings of the magnetisation are taken. After any condition of load is reached, the magnetism does not change with the lapse of time, except possibly to a very insignificant extent. During each loading, after a cyclic condition has been estab- lished the magnetism is at first increased ; but a maximum is Load in kilos. Fia. 110. Effects of Pull on a Stretched Iron Wire. passed as more load is added, and later additions of load reduce the magnetism. A similar maximum is seen during unloading ; but owing to hysteresis the maximum comes at different loads in the two cases ; each maximum is shifted, through hysteresis, to a later place in the operation than it would otherwise have. EFFECTS OF CYCLES OF STKESS. 221 Another manifestation of hysteresis is seen in the easy gradient with which each curve begins, as the process of loading is changed to that of unloading, or vice versd. In a weak field the initial gradient of each curve is so small that the curve appears to set out tangent to the line of loads. Fig. 110 may be referred to in further illustration of the presence of hysteresis in changes of magnetism caused by Load in kilos. Fio. 111. Influence of Vibration on Effects of Loading and Unloading. changes of load.* It shows the effect of superposing on a principal cycle of pulling stress changes several minor cycles, in each of which hysteresis is very apparent. The order in which the loads were applied was this : 0, 5, 0, 8, 3, 12'6, 9, 12-6, 3, 8, 0. The wire dealt with here was of iron, and had been hardened by stretching : it hung in a constant field the force of which was 0-34 C.-G.-S. 222 MAGNETISM IN IRON. 129. Influence of Vibration on the Effects of Stress. These indications of hysteresis disappear almost entirely if we submit the piece under test to mechanical vibration either during or after the changes of load. As modified by vibration the curves for loading and unloading become nearly coincident. The whole amount of magnetic change is increased. A maxi- mum point is still found, which lies, as regards load, between the two maximums that are observed when the processes are gone through without vibration. Tapping the wire at any stage in the process produces, in general, a large change in its magnetism ; but if loading or unloading is then resumed, without further tapping, the presence of hysteresis is at once conspicuous. Fig. Ill (page 209) illustrates the influence of vibration, by showing the curves got by repeated loading and unloading of an iron wire, suspended in a weak magnetic field, first without vibration, and also with smart vibration before each reading of the magnetometer was taken. 130. Effects of Loading Annealed Iron. On applying loads to an annealed iron wire hanging in a magnetic field, we find at first the same extreme sensitiveness, the result of mole- cular instability. ^Repetition of the loading, if repeated often enough, brings about a cyclic state in which there is much less total change of magnetism than is found in the corre- sponding experiment with hardened metal. As to the character of the change, it depends on the magnitude of the load. With a sufficiently light load, loading produces increase and unload- ing produces decrease of magnetism ; with a moderately heavy load these effects are reversed.* 131. Effects of Longitudinal Stress in Cobalt. Lord Kelvin, testing a cobalt bar hung vertically in the earth's magnetic field, found that pulling decreased and relaxing the pull increased the induced magnetism. The effects of * For examples of the curves got by loading and unloading annealed iron see Phil. Trans., 1885, plates 62 and 64. Many of the effects of stress, both in annealed and in hardened metal, will be found exhibited there, by means of curves, more completely than it is possible to exhibit them here. A few examples of the effects of compressive stress on the curves of I and H for iron will be found in a paper in the Phil. Mag. for September, 1888. The presence of compressive stress lowers the curve, as might be antici- pated from the raising of it by tensile stress, shown in Figs. 103 and 105. EFFECTS OF STRESS IN COBALT. 223 longitudinal pressure on the magnetisation of cobalt have been examined by Mr. C. Chree,* who found a reversal of effect, as the magnetisation was increased, resembling the Villari reversal in iron, but opposite to it in character. In iron, as we have already seen, after the first effects of stress are past, pressure will reduce magnetism in weak fields, but will increase it in strong fields. In cobalt the reverse happens ; pressure increases magnetism in weak fields, but reduces magnetism in strong fields. This may be shown either by magnetising when the pressure is on, and again when it is off, or by applying and removing pressure while a constant magnetising force is in ^ so ^ &300 1 200 , / / 10 20 30 40 50 -.60 70 BO 90 100 110 120 130 14-0 iSt Magnetic Force H. FIG. 112. Induced and Eesidual Magnetisation of Cobalt with and without Compressive Stress. action. If the latter plan is followed, we have, of course, to exclude the initial effects, which, as Mr. Chree has pointed out, occur in cobalt as they occur in iron. The first application of pressure in weak fields causes a large increase of induced mag- netism, just as, we may anticipate, the first application or removal of stress of any kind would do ; but repetition of the process soon establishes a cyclic state. The effects of longitudinal pressure in modifying the magneti- sation curve of cobalt are illustrated in Fig. 112 (from an ex- periment by the writer and Mr. W. Low). The full lines are two * Phil. Trans., 1890, A, p. 329 ; Proc. Koy. Soc,, December, 1889. 224 MAGNETISM IN IRON. curves of induced magnetism for a rod of cast cobalt, tested (within a yoke) without stress, and also with a compressiva stress amounting to 16 -2 kilogrammes per square millimetre. The broken lines are the corresponding curves of residual magnetism. The induced curves cross, illustrating the reversal described by Mr. Chree. The residual curves do not cross within the limits of field used here ; but other experiments, made with the same rod but with heavier loads, show a crossing in them also. Curves of the permeability in terms of B, drawn from the data of the same experiment, have already been given in Fig. 42, 76. 132. Relation between the Effects of Stress on Mag- netism, and the Effects of Magnetism in Changing the Dimensions of Magnetic Metals. In his book on "Applications of Mathematics to Physics and Chemistry" (p. 47 et seq.), Prof. J. J. Thomson has discussed this subject, and has pointed out that it is possible, from theoretical considerations, to predict the general character of the effects of stress from a knowledge of the changes of dimension caused by magnetisation. Mr. Shelford Bid well, in a Paper which will be referred to later in more detail,* has shown that an iron rod lengthens when it is magnetised, pro- vided the magnetising force does not exceed a certain limit, but shortens if the force does exceed that limit. Prof. Thomson shows that this reversal of effect is to be anticipated from the Villari reversal which is observed in the effects of longitudinal stress. Again, a nickel rod shortens when magnetised, and con- tinues to shorten under high magnetic forces ; this agrees with the fact that in nickel there is no Villari reversal, and that longitudinal pull diminishes the magnetism, whether that is weak or strong. Again, with cobalt Bidwell has found effects opposite to those found in iron, namely, that weak magnetisa- tion shortens a cobalt rod and strong magnetisation lengthens it. Applying his equations to this result, Prof. Thomson has anticipated what the character of the effects of stress in cobalt should be. Mr. Chree's experiments have verified his conclusions, by showing that the effects of stress in cobalt are the reverse of the effects of stress in iron, tension diminishing weak magnetism but augmenting strong magnetism, f * Phil. Trans., 1888, A, p. 205. t See the introduction to Mr. Chree's Paper, Phil. Trans., 1890, A, p. 329 RESIDUAL EFFECTS OF STRESS. 225 133. Residual Effects of Stress applied before Magnetis- ing. Perhaps the most interesting of all the effects of stress are those that occur in unmagnetised iron. To apply and remove load before beginning to magnetise a piece of iron has been found to affect the magnetic susceptibility, even when the load is well within the elastic limit, and when the piece is per- fectly free from magnetisation during application and removal of the load. We have, in fact, evidence that even in unmag- netised iron the process of loading and unloading causes changes of molecular configuration which are not reversible. These changes exhibit hysteresis with regard to the loads which cause them. They affect more than one physical quality of the metal; in particular, they produce upon the magnetic susceptibility an effect which becomes obvious when the piece is magnetised. These residual effects of past loads may be wiped out by sub- jecting the piece to the operation of demagnetising by reversals. They may also be wholly, or almost wholly, removed by tap- ping the piece smartly and so causing vibration. Hence, in experiments designed to show the differences of susceptibility of iron or steel when subjected to different amounts of load, the piece should be passed through the opera- tion of demagnetising by reversals after the load has been put on. This procedure was, in fact, followed in the experiments that have been described above. The residual effects of stress, occurring in the absence of any actual magnetisation, are of very great interest in their bearing on any theory of the molecular constitution of magnetic metals. One or two experiments by the present writer may be cited to show their general character.* Let an iron wire be subjected to pulling stress, and let the load be removed before beginning to magnetise. Then, pro- vided the load which has been applied lies within the elastic limit, or rs less than some load by which the wire has been previously stretched, we observe no mechanical change of any ordinary kind as the result of applying and removing the load. And if, before beginning to take a curve of magnetisation, we put the wire through the process of demagnetising by reversals, we shall find nothing in the curve to show whether there has 01 has not been any application of load before that. But suppose, Phil. Trans., 1885, Par)- II., pp. 612-619. 226 MAGNETISM IN IRON, after the process of demagnetising has been gone through, we apply and remove some load before beginning to magnetise. Though there has been no immediately obvious mechanical change, the wire has undergone a change of structure which shows itself in the form assumed by the curve of magnetisation. We find the magnetic susceptibility, especially under low forces, much greater in this than in the former case. The whole differ- ence in procedure may be no more than this, that in one case the load is removed before the process of demagnetising is performed; in the other case, the process of demagnetising is performed before the load is removed. So slight a difference in procedure might, perhaps, be expected to have no influence on the form of the curve ; in fact, however, it has a large influence. The curve of magnetisation depends not merely on the load actually pre- sent : it is affected, especially in its early portion, by any changes of load which have taken place since the preceding demagnetisation. For instance, it has been observed that if a curve be taken with (say) a pull of 3 kilos on an iron wire, and if, after complete demagnetisation, the load be raised to 4 kilos and 1 kilo be removed, and a second curve be then taken, the second curve will differ very sensibly from the first, in spite of the fact that the wire may have previously been subjected to many times that amount of load, and was, there- fore, in a mechanically stable state. 134. Experiments showing Residual Effects of Stress. In the following case an iron wire* (previously hardened by permanent strain) was loaded with a weight of 18 '5 kilos, or 42 '5 kilos per sq. mm. This weight was repeatedly applied and removed, then finally removed ; the wire was demagnetised by reversals, and the magnetising process was then gone through, giving the magnetometer readings stated in column I. of Table XXIII. Then the wire was demagnetised : the weight of 18*5 kilos was applied and removed, and then the process of magnetising was again gone through, giving the magneto- meter readings in column II. Finally, the same thing was re- peated, but with this difference, that the wire was briskly tapped after the load had been removed before beginning to magnetise ; the results of this are given in column III. * Loc. cit., p. 614, HYSTERESIS IN MOLECULAR DISPLACEMENTS. 227 TABLE XXIII. Magnetisation of Iron under the influence of previous loads. Magnetometer readings. H I. II. III. After demagnetisation with no load. After the cycle 0-18^-0. After the cycle 0-18J-0 and then vibration. 1-15 5 8 5 2-01 11 19 10 2-87 19 40 17 4-31 44 73 35 575 78-5 110 70 8-62 149 176 150 11-50 212-5 230 214 14-37 267 278 268 17-25 314-5 321 314 20-12 355 358-5 354 23-00 390 394 388 25-87 420 420 422 33-12 472 472 471 Comparing the three columns, it will be clear that in the first and third case the metal is in substantially the same con- dition as to susceptibility. In the third case its susceptibility with respect to low magnetic forces, and even to moderately great forces, has been notably raised, as a consequence of the molecular change brought about through application and re- moval of the load. The same change had occurred in the other two cases, but it had been undone by the demagnetising pro- cess in one, by vibration in the other. Experiments of this kind lead to the conclusion that when we apply and remove stress in iron, even when the magnetic state is perfectly neutral, we cause some kind of molecular displacement in the relation of which to the applied stress there is hysteresis. When any load is applied and removed the changes of molecular configuration lag behind the changes of stress. We accordingly find, if we stop at any intermediate value of the load and examine the susceptibility, that the result is not the same when the stoppage is made during the process of loading, as when it is made, at the same amount of 228 MAGNETISM IN IRON. load, during the process of unloading. Magnetic susceptibility may, of course, be thought of as a physical property of the meta], apart from the existence of any actual magnetisa- tion. During the loading and unloading of an unmagnetised piece the susceptibility changes in a manner that involves hysteresis, just as the magnetism changes when we load and unload a magnetised piece. TABLE XXIV. Magnetisation of Iron under the influence of previous loads. Magnetometer readings. I. ii. III. IV. Galvanometer readings. (To reduce to H multiply by 0-0575.) Demagnetised with no load. ThenO-lS-3. Load =3 kilos. Demagnetised with no load. Then 0-18fc-0-3. Load = 3 kilos. Demagnetised with no load. Loaded to 18J, unloaded to 3 kilos, and tapped before magnetising. Load =3 kilos. Demagnetised with no load. Loaded to 3 kilos and tapped before magnet- ising. Load = 3 kilos. 25 22 13 11 10 50 70 14 36 34 75 139 109 103 100 100 198 176 174 168 125 242 226 227 219 150 276 265 268 259 200 328 323 328 320 250 365 369 365 300 398 398 403 400 350 424 425 429 427 450 461 462 467 466 588 491 494 499 498 274 275 277 276 In Table XXIV. four magnetisations of the same iron wire are exhibited, each under a pulling load of 3 kilos.* In I., the load had been previously raised to 18 J kilos, then reduced to 3 kilos. In II., the condition of load had been reached by ap- plying 3 kilos, after there had been no load. In III. and IV. these differences of procedure were repeated, but the wire was subjected to vibration before the magnetising process began. It will be seen that between I. and II. there is a marked differ- * Owe kilo of load here corresponds to a stress of 2'3 kilos per sq. mr- EXAMPLES OF RESIDUAL EFFECTS. 229 ence, especially in the early portion of the curve ; but in III. and IV. this difference has practically disappeared, the effects of hysteresis being destroyed by vibration. Again, Fig. 113 shows two pairs of curves, two (I. and II.) taken under no load, and two (III. and IV.) taken under a load of 3 kilos. In I., the wire was demagnetised immediately before the curve was taken. In II. it was demagnetised, then loaded with 15 kilos, and then completely unloaded. In III. it was loaded with 10 kilos, and unloaded down to 3 kilos. In IV. it was completely unloaded from 10 kilos, then reloaded up to 3 kilos. Very similar differences in effect have been observed \s- Magnetising Force. FIG. 113. Residual Effects of Previous Loads. when annealed iron (not previously hardened by stretching) has been tested under corresponding varieties of condition in regard to previous stress.* The changes in molecular structure which, as these results show, are going on in iron or steel during the process of ap- plying and removing stress sometimes result in producing a small amount of magnetism in a piece which, after being mag netised, has been brought into an apparently non-magnetic state by the application of a reversed force. There are, in such a case, superposed magnetisations which originally neutralise each * Loc. cit., p. 618. 230 MAGNETISM IN IRON. other so far as external effect is concerned, but the balance ia disturbed through the unequal action of the stress upon them. 135. Other Evidences of Hysteresis in the Effects of Stress. These experiments show that the structure of iron changes, under variation of stress, in a manner that exhibits hysteresis, that is to say, the changes of structure lag behind the changes of stress. We may therefore anticipate that we shall find traces of hysteresis in other physical qualities besides magnetic susceptibility when we examine the variation of those qualities under variations of stress. A remarkable instance is furnished by the thermo- electric quality of iron. Under variations of pull the thermo-electric quality of iron varies in a manner which strikingly resembles those variations of magnetic quality which have been described in this chapter. This is not a secondary effect, resulting from changes of magnetism, for it occurs even when care is taken to keep the iron wholly free from magnetisation during the experi- ment. Curves drawn to represent the relation of thermo-electric quality to load show a very remarkable general resemblance to the curves of Figs. 108-110, which show the relation of magnet- ism to load. There are also interesting points of difference, but a discussion of these would be out of place here. The main point, which was discovered by E. Cohn*, and afterwards, independently, by the writerf, is that there is much hysteresis of thermo-electric quality with respect to stress a result, no doubt, of the irreversible changes of molecular structure to which allusion has just been made. We shall see later, in connection with molecular theories of magnetism, how these irreversible changes probably occur. Further, but slighter, evidence of the occurrence of irrever- sible molecular changes during the loading and unloading of an iron wire is found when we examine the amount of the exten- sion in relation to the load. Though the amount of load be restricted so that it lies well within the so-called limit of elasti- city, it is found that there is no exact proportionality of strain to stress ; and when a cyclic process of loading is repeated often enough to make the elongation and retraction become also * Cohn, Wied. Ann., 1879, VI, p. 385. t Proc. Roy. Soc., 1881, XXXII., p. 399 ; Phil. Trans., 1886, p. 361. EFFECTS OF TORSION. 231 cyclic, it is found that, at any intermediate value of the load, the wire is longer during unloading than during loading. In other words, there is hysteresis in the relation of strain to stress. The amount of this hysteresis is small ; but when means are taken to magnify the extension sufficiently it may be observed without difficulty. The amount of difference in length between the length at the mean load in loading and the length at the mean load in unloading, may be ^J^- of the change of the whole extension. The effect in question has to be distinguished from quasi-plastic changes of length, which depend on the time-rate at which the loads are applied. It has been observed in wires of copper and brass, as well as iron and steel.* One obvious consequence of it is that any process of loading and unloading involves some dissipation of energy. 136. Effects of Torsion on Magnetic Quality. The k fluence of twisting strain on the magnetic quality of metals has engaged the attention of many experimentalists, beginning with Matteucci,t who, in 1847, examined ballistically the change of magnetism undergone by an iron rod when it was twisted back and forth, while a magnetising current was kept up in a surrounding solenoid. Wertheim, E. Becquerel, and Wiede- mann followed on the same lines, | and the subject was taken up by Lord Kelvin in one of the sections of his in- vestigation of the electro-dynamic qualities of metals. || More recently a number of other workers have pursued the matter in great detail. The results of their investigations are much too complicated to admit of anything like full statement here ; we must be content with an account of some of the more conspicuous facts. The general result of early experiments was to show that when a rod of soft iron, exposed to longitudinal magnetising force, was twisted, its magnetism was reduced, by torsion in either direction. In this effect, as in all effects of stress, we have to distinguish between the irreversible initial effect of the * Brit. Assoc. Rep., 1889, p. 502. t Comptcs Rendus, Vol. XXIV., p. 301. t For an abstract of these researches, see "VViedemann's EleJctricitdt, Vol. III., p. 671, et seq. ; see also "Wiedeinann, Phil. Mag., 1886. U Phil. Trans., 1878 j Reprint of Papers, Vol. II., p. 374. 232 MAGNETISM IN IRON. first application (due to molecular instability) and the effect which becomes manifest when a cycle of strain is repeated. The initial effect of torsion will depend on the past history of the piece, but the cyclic effect is, in soft iron, of this character, that twisting, to either side, reduces the induced magnetism, and untwisting increases it. But this effect is very small for small angles of twist. Moreover, as with other effects of stress, the changes of magnetism exhibit hysteresis. This was pointed out in 1878 by Kelvin, who has given curves showing the manner in which the magnetism induced in an iron wire by a constant magnetic field changes as one end of the iron wire is twisted to and fro while the other end is held *NGLE OF TWIST Fia. 114. Effect of Twist on the Magnetism of Iron. fixed. The typical form into which the curves settle after repeated twistings is shown in Fig. 114, which is copied from his Paper. From the form of these curves it is clear that if the effects of hysteresis were eliminated as they no doubt might be, at least in part, by vibrating the wire we should have a single curve resembling a parabola with its vertex at the top of the diagram. Thus in the absence of hysteresis we should find the influence of torsion in reducing the induced magnetism to be indefinitely small for small angles of twist, and to increase initially in proportion to the square of the twist. 137. Effects of Torsion due to Magnetic Aeolotropy. Sir William Thomson has, in fact, pointed out that these EFFECTS OF TORSION. 233 results are to be anticipated from what is known regarding the effects of simple pulling and simple compression on the magnetic susceptibility of iron.* Experiments in which the metal is subjected to longitudinal pull or push and to transverse pull, have shown that a simple pulling stress or a simple pushing stress develops an seolotropic quality in respect of magnetic susceptibility, producing (in iron) greater susceptibility along than across the lines of pull, or less sus- ceptibility along than across the lines of push, provided the magnetisation be not so strong as to pass the Villari critical value. Now in torsional strain, each portion of the twisted rod experiences a simple shearing stress, which may be regarded as made up of a pulling stress in a direction inclined at 45deg. to Fia. 115. the direction of the length, and an equal pushing stress also inclined at 45deg. and at right angles to the pulling stress. Thus, if a b c d (Fig. 115) is a particle anywhere in the front half of the rod, which is twisted in the manner shown by the arrows, the twisting produces a shearing stress in a b c d that is equivalent to a pull on the faces a b and c d, combined with an equal push on the faces d a and b c. The effect is to in- crease the magnetic susceptibility along the direction p p and to reduce it along p' p'. For small stresses these effects are no doubt equal. Hence in the direction of the length of the * Reprint of Papers, Vol. II., p. 374. ' 234 MAGNETISM IN IRON. rod, which is equally inclined to p p and p p, there is, virtually, no change of susceptibility. The effect of torsion is to give a helical quality to the magne- tisation, producing a circular component which is superposed upon the original longitudinal magnetisation. The lines of magnetisation are no longer coincident in direction with the lines of magnetic force; they become in the case considered above right-handed screws. The effect of this on the magni- tude of the longitudinal component is at first indefinitely small, but as the angle of torsion increases the growth of the circular component begins to detract from the longitudinal magnetism, for magnetisation in one direction is prejudicial to magnetisation in other directions, as the molecular theory and the phenomenon of saturation suggest. This consideration of the magnetic aeolotropy produced by the pull and push into which torsional stress may be resolved supplies a key to many of the observed facts about magnetism and torsion. At the same time it fails to explain many of the facts. The influence of seolotropy is, no doubt, always present in the phenomena of torsion, but other considerations of a less obvious kind also enter, and these become in some instances so influential that the effects of seolotropy are entirely masked. This is notably the case with nickel. With soft iron, on the other hand, most of the observed effects of torsion admit of fairly complete explanation in the lines suggested by Lord Kelvin, especially when allowance is made for the complications to be anticipated from hysteresis. 138. Production of Longitudinal Magnetism by Twisting a Circularly Magnetised Wire. From the foregoing account of how a circular component of magnetisation is developed by torsion in a longitudinally magnetised wire or rod, it will be evident that the converse action should occur, namely, that twisting a circularly magnetised rod should make it develop longitudinal magnetism. This fact was observed in 1858 by Wiedemann, who found that an iron wire conducting an electric current, and therefore circularly magnetised, becomes a magnet when twisted.* Following Kelvin, we may ex- * Elektricitat, Vol. III., p. 680. MAGNETISATION DUE TO TWISTING. 235 plain this observation as a consequence of seolotropy by re- solving the magnetising force, whose direction is A (Fig. 116), into components along the lines of pull, Op, and push, Op'. Taking the case of iron, below the Villari critical point, and twisted in the manner shown in the diagram, the susceptibility is greater along the lines of pull, p, than along the lines of push, p'. Hence the resultant magnetisation will be less inclined to Op than to Op' ; in other words, it will take some direction, R, which gives a longitudinal component of magnetisation directed towards the bottom of the rod. This is, in fact, the kind of longitudinal magnetism which is found. FIG. 116. It might, however, be supposed, in view of the Villari re- versal, that under sufficiently strong circular magnetisation the longitudinal component developed by twisting would become reversed. Experiment shows that this does not happen even when a very strong current traverses the wire. The explana- tion appears to lie in the fact that the stresses of pull or push due to torsion act not on the whole intensity of circular magnetisation but on components inclined at 45deg. Hence, though the circular magnetising force be strong enough to bring about saturation, the components of magnetisation on which the pull and push act remain below the Villari critical 236 MAGNETISM IN IRON. value, so that the effect of pull is still to augment and of push to diminish the components on which the pull and push act.* These effects of torsion are found in dealing with residual magnetism as well as with induced. In Wiedemann's experi- ment the same result (namely, the production of longitudinal magnetism by torsion) is noticed though the wire be not twisted until the current has ceased to pass. There is then a strong residual circular magnetism which is affected by torsion, just as might be anticipated from the fact that the residual mag- netism of a bar magnetised in the usual way is affected like induced magnetism by pull and push. 139. Torsional Strain produced by Combining Circular with Longitudinal Magnetisation. A similar explanation applies to another discovery of Wiedemann's, namely, that if an iron wire or rod be both circularly and longitudinally magne- tised, it becomes twisted, though no external mechanical force be used. The superposition of the two magnetisms turns the lines of magnetisation into screws, and the consequent expan- sion along the lines of the screws and contraction across these lines causes the rod to twist. In iron the effect of mag- netising (unless the magnetising force be very strong) is to lengthen the metal in the direction of magnetisation. The direction which the twist is observed to take agrees with this. In nickel, on the other hand, the effect of magnetising is to shorten the metal in the direction of the lines of force. The twist taken by a nickel wire, subjected to superposed longitu- dinal and circular magnetising forces, is accordingly opposite to that of iron, as Prof. Knott has shownf by making a current traverse a nickel wire, which was at the same time exposed to the action of a magnetising solenoid. * This absence of reversal is referred to in Kelvin's Paper as a difficulty ; but the difficulty disappears when it is recognised that the Villari reversal depends rather on the value I in the direction of pull and push than on the value of H. Though the components of H along direc- tions inclined at 45deg. to the axis may be indefinitely increased by in- creasing the whole magnetising force, the components of I along these lines remain too small to allow pull to produce reduction of magnetism. t Trans. Roy. Soc. Edin., Vol. XXXII. (1883), p. 193. TRANSIENT CURRENTS DUE TO TWISTING. 237 140. Transient Currents produced by Magnetising Twisted Rods, or by Twisting Magnetised Rods. The sud- den development of circular magnetism when a longitudinally magnetised rod is suddenly twisted, or when a longitudinal magnetising force is suddenly applied to a rod that is held in a - state of torsion, is well shown by connecting the ends of the; rods to a galvanometer, when it will be found that a transient; current is induced along the rod. A still more effective ex- ! periment may be arranged by substituting a tube for the solid rod, and by placing within it an insulated wire in circuit with 10 i \/eo OF 'fwiST -30 -40 60 FIQ. 117. Circular Magnetisation produced by Twisting Magnetised Iron. the galvanometer.* In experiments of this class the existence of hysteresis is shown in an interesting way by making back and forth twisting take place in a series of steps, when, by summing the transient currents, it is at once seen that the circular magnetisation exhibits hysteresis with respect to the angle of twist a result which is of course to be anticipated from the known effects of pull and push. Thus in Fig. 117 an iron wire rather strongly magnetised in the direction of its length was twisted alternately to opposite sides, but the twist- * Ewing, Proc. Roy. Soc, 1883, p. 117 ; 1881, p. 21. 238 MAGXETISM IN IRON. ing was done in a series of steps, and the transient current for each step was noted. Summing up the transient currents we obtain the circular magnetisation in arbitrary units. The full lines of the figure show how the circular magnetisation was cyclically reversed by reversing the twist, but the change of circular magnetism lagged behind the change of twist.* The dotted line in the same figure exhibits the amount of circular magnetism found by first applying a given torsion and then reversing the longitudinal 25 / /' g |^7 ' *, / *r : If X, / /I f NGLEC 2; FTWIS r / f / 7 J / O 3 * / oy e 9 7 \^^ / V 1 : - ll " isthmus" of iron he has in this way found a val .e of B as high as 74,'tOO C G,S. units, Jour. Soc. Arts, Sept. 12. 1890. THE PERMEAMETEU. 261 : ; Spring balance distribution of induction is rather unequal where the bar meets the yoke, and better results might be obtained by making the sample in two pieces with a plane of contact at the middle. Apart from this, however, no traction method can be regarded as a very satisfactory means of examining the magnetic quality of a metal. The presence of tensile stress itself affects the quality which is undergoing measurement, and, as will be shown later, a divided rod or ring does not behave magnetically quite like a whole rod, even when the ends are surfaced as carefully as is practicable. The existence of a cut lessens the permeability of the piece.* The traction method is at the best inexact, but it affords a ready means of making rough measurements, especially for purposes of comparison. A more elaborate apparatus for determining magnetisation by aid of the tractive force is the mag- A netic balance of Dr. du Bois, in which the magnetic circuit, of which the rod under examination forms part, has a gap in the yoke, and the tractive force across this gap is measured. This appa- ratus will be referred to more particularly in the Chapter on Practical Magnetic Testing. The author has also designed a simple form of magnetic balance which compares, for a single value of H, the value of B acquired by one rod with that acquired by a standard rod in which the relation of B to H is already known. In this instrument, which will also be referred to more particularly in the last Chapter, the traction test is used merely as a means of comparison, no attempt being made to measure it absolutely or to determine the induction directly from the absolute value of the force. The author finds that for comparison of one rod with another the tractive method answers well. ~* Phil. Mag., Sept., 1888. Wires that bring the Electric current FIG. 130. The Permeameter. CHAPTER X. THE MAGNETIC CIRCUIT. 149. The Magnetic Circuit. For many purposes, the most convenient way of treating the magnetisation of iron is to con- sider what is happening at a point within the metal. This is, in fact, the basis on which our exposition of the subject in earlier chapters has been developed. We have learnt to con- ceive of a magnetic force H acting in a definite direction at the point considered, and also of a magnetic induction B at the point. If the material is isotropic, and has no residual mag- netism superposed upon the magnetism which H induces, the direction of B is the same as that of H. The ratio of B to H is the permeability /A. Passing from point to point of the metal, we may in certain cases find that H and B do not change ; more generally they do change. Thus, in a uniformly wound circular ring magnet, of uniform section and material, H has the same value at all points on any circle co-axial with the ring. In a long straight bar magnet the value of H is nearly uniform, except in the neighbourhood of the ends. Whether H be uniform or not, it has a single definite value and definite direction at each point, and the same is true of B. At points where there is no magnetisable substance, the value and direction of B are the same as the value and direction of H ; this applies, for instance, to all points in air. The value of H at any point is determined by finding the resultant of the force produced at that point by (1) all the conducting circuits, and (2) all the free magnetism in the neighbourhood ; that is, by finding the resultant mechanical force which would be felt by a unit pole of free magnetism if placed at the point in question. THE MAGNETIC CIRCUIT. 263 From this point of view, when our object is to discuss the magnetisation of a piece of metal, we have first to consider what is the value of H at each point within the piece. Thus, in dealing with a uniformly-wound ring, we treat the case by finding that the magnetic force H is 4 TT C n, when C is the cur- rent and n is the number of turns in the magnetising coil per centimetre of the ring's length. And in dealing with a uni- formly-wound rod, we find H to be 4 TT C n minus a certain quantity due to the free magnetism at and about the ends, which becomes unimportant when the rod is exceedingly long. Many problems in magnetism are best treated in this way, namely, by considering the condition of things at individual points in the magnetised piece. But there is another way of regarding the matter, not in the least antagonistic to this, but sometimes more convenient. Instead of thinking about what happens at individual points, we may view the magnetism of the piece as a whole, by considering what is called the magnetic circuit. This is the method which has been applied by J. and E. Hopkinson* and by Kapp,f to pre-determine the magnetism of dynamos. Its applicability to dynamos and transformers gives it peculiar im- portance on the practical side ; moreover, apart from that, the conception of the magnetic circuit has much interest as an alternative standpoint from which the facts of electro -magnetism may be viewed, and as suggesting methods of experimental enquiry. 150. Tubes of Magnetic Induction. Definition of Mag- netic Flux and of a Perfect Magnetic Circuit. The lines of magnetic induction, as has been already pointed out ( 14), are continuous through space, whether the space be filled with magnetisable or non-magnetisable substance, or partly with one and partly with the other. There is no discontinuity of B no sudden change in its value or direction when the lines pass from metal to air or from air to metal. Each line of in- duction is a continuous curve; moreover, it is a closed curve that is to say, if traced along its whole course it returns to the point at which the tracing began. We may conceive of * Phil. Trans., 1886, p. 331. t Jour. Soc. Tel. Eng., 1886, p. 518. 264 MAGNETISM IN IRON. all space as filled with sheafs of lines of induction, or (which is the same thing in other words) as partitioned into tubes, the boundaries of which are formed by lines of induction. Every such tube contains a number of lines of induction, and if we follow the tube along its whole length until -it returns into itself we find everywhere the same number of lines of induction in it. We may take a large sheaf or a small one to constitute the tube, but, whatever be the number of lines in it to start with, the same number is present at every part of its length. Its cross-section may vary ; the tube may widen or contract from place to place along its length, but if this happens it is by the lines spreading out or coming closer ; the number of the lines does not change. At places where the induction B is strong, the tube is contracted ; at places where the induction is weak, the tube is expanded. But if we take any cross-section (s) of the tube perpendicular to the direction of B, the product B s (or, to be more exact, the surface-integral fBds taken over the section, since B is not necessarily the same over all parts of s*) is a constant quantity for any one tube. At any sections s and s', the values of the induction B and B' are such that / B d s =/ B' d s'. It is convenient to have a name for this constant quantity, which is the whole number of lines of magnetic induction in the tube. Following the usage of several recent writers we shall call it the magnetic flux in the tube. Any tube of magnetic induction, considered as a whole that is to say, considered as a circuit which returns into itself may be called a perfect magnetic circuit. The perfect magnetic circuit is analogous to a perfectly insulated electric circuit con- ducting a current. The lines of induction correspond in this analogy to lines of flow of current. The cross-section of the conductor may vary from place to place, but the current density varies in inverse proportion to the cross-section, so that the product of current density into area of cross-section which is simply the whole current is constant at all sections, just as the flux Bs is constant in the perfect magnetic circuit. * The cross-section, over which this integral is calculated, is taken BO that every element of the surface is perpendicular to the lines of B which cut it. Thus, if the lines of B in the tube are not parallel, the surface forming the cross-section will be curved. MAGNETOMOTIVE FORCE. 265 151. Imperfect Magnetic Circuit. An imperfectly insu- lated electric circuit allows some of the lines of flow to enter it or to leave it through the sides. We have the magnetic analogue of this when we have to deal with the magnetisation of a material ring of any form, in which the sides of the ring do not coincide with the sides cf a tube of induction. This means that there are places where some of the lines of induc- tion leak out, so to speak, from the substance of the ring through its sides into the surrounding medium. It is often convenient, especially when the greater part of the whole flux remains in the ring, still to speak of such a ring as a magnetic circuit. We shall distinguish it from a true tube of induction by calling this leaky ring an imperfect magnetic circuit. It is imperfect, inasmuch as it leaves out those portions of the sur- rounding medium through which some of the lines of induction stray, the inclusion of which would be necessary in order to mako the tubes of induction complete. Examples of imperfect cir- cuits will be given presently. 152. Line-Integral of Magnetic Force, or Magnetomotive Force. We have now to express the relation of the magnetic flux in a perfect magnetic circuit to the whole magnetising agency acting on the circuit, just as in a perfectly insulated electric circuit we express the relation of the current to the whole electromotive force that is operative throughout the circuit. We have in the magnetic circuit an agent to which (when we are dealing with induced magnetism) the magnetic flux is due, which corresponds to the electromotive force of the electric circuit. To this agent Bosanquet* has given the name of magnetomotive force. One way of defining the electromotive force of an electric circuit is to say that the electromotive force is the amount of work which would be done in carrying unit quantity of elec- tricity completely round the circuit. In the same way we may define the magnetomotive force of a magnetic circuit as the amount of work which would be done in carrying a unit magnetic pole completely round the circuit. At any point of its path the unit pole is acted on by a mechanical force which is equal to and in the direction of the magnetic * Bosanquet, Phil. Mag., 1883, Vol. XV., p. 205. 266 MAGNETISM IN IRON. force H, and it is against this mechanical force that the work is done. Another name for the same quantity is the Line-Integral of Magnetic Force, taken round the circuit.* Conceive the path along which the unit pole is moved to be made up of a great many short pieces, any one of which is so short as to be sensibly straight and to have a sensibly uniform value of H from end to end of it. Let the length of any short piece be 3 /, and let its inclination to the direction of H be e. Then the work done in moving the unit pole along this short piece of the path is measured by the product of the length of the path (S fc) into the component of the force H along the path ; that is to say, it is H cos 8 I. The whole work done in moving a unit pole along the path is got by summing up the work done at each short piece ; that is to say, it is 2 H cos 8 I, or/H cos e d I when the elements into which the path is divided are indefinitely numerous and indefinitely short. The expression/ H cos edl is the line-integral of the magnetic force along the path. We may integrate the magnetic force in this manner along any curve whatsoever. The term line-integral of magnetic force is not in the least restricted to cases in which the integration takes place round a magnetic circuit. Let the path through which the unit pole is supposed to be carried extend through space in any manner, the line-integral, namely, / H cos d I, measures the work done in carrying the pole along it. In cases where the direction of the line coincides at all points of its course with the direction of H, cos e is everywhere unity, and the expression for the line-integral of the magnetic force becomes/ H d I. This is generally! the case when the line in question is a line of magnetic induction, which it may always be when the line-integral of magnetic force is calculated for a perfect magnetic circuit. 153. Value of the Line-Integral of Magnetic Force. When the integration is extended all along any closed curve in other words, when the imaginary unit magnetic pole makes * Maxwell, "El. and Mag.," Vol. II., 401. t Namely, when the medium is isotropic and has no residue of previous magnetisation in a direction inclined to the direction of H. LINE-INTEGRAL OP MAGNETIC FORCE. 267 a complete journey along any path which returns into itself it may be shown that the value of the line-integral of magnetic force admits of very easy calculation. If the curve along which it is reckoned does not thread its way through any circuit in which a current is flowing, then the value of the line-integral of mag- netic force along the closed curve is zero. If the curve does thread its way once through a circuit in which a current C is flowing, then the value of the line-integral of magnetic force along the closed curve is 4 TT C ; and if the curve threads its way N times through such a circuit, the value of the line- integral is 4 TT C N. For, example, if the line along which the line-integral of magnetic force is reckoned is any closed curve which is threaded through the interior of a coil of N turns, the line-integral is 4 TT C N, for the line is interlinked with the current circuit as many times as there are turns in the coil. The principle that the line-integral of magnetic force is equal to 4 TT C N, when taken along any closed curve is an abso- lutely general one. It is true whatever be the position and direction of the curve, whether it lie along a line of force or no, and whether it lie wholly or partly in a non-magnetisable sub- stance, such as air, or wholly or partly in a magnetisable sub- stance, such as iron. If the closed curve threads through more circuits than one, the sum of the terms 4 TT C N is to be taken. Two simple cases will serve as instances. Suppose we ha^e a uniform solenoid of n turns per centimetre, and I centimetres long. Let the ends be bent together so that it forms a closed ring. The length of a closed curve in the centre of the solenoid is I. The magnetic force H is uniform all along that line, and is equal to 4 TT C n. The value of / H d I is, therefore, H I or 4 TT C n I, or 4 TT C N, since N the whole number of turns = n I. Again, consider the magnetic force around a long straight conductor (the remainder of the circuit being supposed to lie so far off as to be uninfluential) and integrate / H d I along the circumference of a circle of which the conductor is axis. The 2 f 1 force at any distance r from the axis of the conductor is _. r This is uniform throughout the circular path, and is in the direction of the path. The length of the path is 2 TT r. The line-integral of magnetic force round the path is, therefore, 268 MAGNETISM IN 2 C x 2 TT r or 4 ?r C. In this case the path along which the line-integral is taken is interlinked with the circuit only once. The principle set forth in this paragraph may be stated thus : The line-integral of magnetic force along any closed curve is equal to O^TT, or 1-2566, into the number of ampere- turns in the coil or coils which are threaded by the curve. 154. Equation of the Magnetic Circuit. Returning now to the case of a perfect magnetic circuit, we have to consider the connection between the magnetomotive force or line-integral of magnetic force along the circuit and the magnetic flux. Suppose the circuit to be divided up into a number of tubes of induction, in each of which the cross-section is small, so that B and H may be taken as uniform over any one cross section of the (small) tube. The relation which we establish for each small tube may easily be extended to apply to the whole magnetic circuit, which is built up of such small tubes placed side by side. Let s be the area of cross-section at any part of the small tube, and B the magnetic induction there. The flux in the tube is B s. If /* be the permeability of the p substance, the magnetic force H at the same place is ; hence, flux B ,, = = H. fl,8 /* Multiply each side by an indefinitely short length of the tube dl fluxx =Hd pi Integrate both sides, remembering that the flux is constant at all sections ; flux x I = IHdl = magnetomotive force, J ft.9 J when the integration is extended round the whole circuit ; magnetomotive force hence, flux= " " r^l J~jTs The meaning of the denominator may be most readily seen if we write p for _ and call /> the specific magnetic resistance of EQUATION OF THE MAGNETIC CIRCUIT. 269 the substance. Then p is evidently the magnetic resistance I of that portion of the magnetic circuit which has the length d I and the cross section s. The idea of magnetic resistance is intro- duced here in a sense strictly analogous to the idea of electric resistance in the electric circuit. The specific magnetic resist- ance p is the analogue of the specific resistance to conduction namely, the resistance of a piece of the conductor of unit length and unit area of cross-section. The quantity IL is J s simply the sum of the resistances of successive short portions of the length of the circuit. We may, therefore, write the equation of the perfect magnetic circuit thus fl _ magnetomotive force magnetic resistance of the circuit* which is the magnetic analogue of the familiar equation of conduction . electromotive force conduction resistance of circuit" There is, however, this reservation to be borne in mind in pursuing the analogy. In the conduction circuit the specific resistance of the material is not a function of the current that is to say, its value is independent of the amount of the current. In the magnetic circuit p and /x are functions of the flux, for they depend on the value of B. More than that, they may have many possible values even when the value of B is assigned, for they depend not only on the existing magnetic induction, but on the previous magnetic history of the piece. But the equation of the magnetic circuit will be correct and intelligible if we define JJL as nothing more or less than the value D which the quotient _ happens to have at that place in the H circuit to which reference is made ; and if we define p as the LJ reciprocal of that quantity, or _-, we may have a magnetic B circuit in which there is no magnetomotive force, but in which there is (residual) magnetic flux. In that case the " magnetic resistance " of the circuit must vanish, and the mean value of p must be zero. We may even have a magnetic circuit in 270 MAGNETISM IN IRON. which the direction of the flux is (on account of past mag- netisation) opposite to the direction of the magnetomotive force, which implies a negative value of p and of p. In most of the cases to which the conception of the magnetic circuit may be usefully applied, the effects of previous magneti- sations are absent or negligible, so that the values of /A which are to be used are the permeabilities which are derived from the ordinary curve of magnetisation (for the particular material of the circuit) that is to say, from the curve which expresses the relation B to H when H is progressively increased from zero and the metal is free of magnetism to begin with. In many instances the circuit may be treated as (very ap- proximately) made up of a series of portions, in any one of which /x is constant and s is constant. Thus, calling ^ the length of one of these portions, /^ its permeability, and s l its cross-sectional area, 1 2 the length of the next, /^ 2 its permea- bility, and s 2 its sectional area, and so on, we have ^ _ magnetomotive force as many terms being taken in the denominator as are needed to complete the circuit. And if the object is to express the value of the induction at any place in the circuit in terms of the magnetomotive force, we have only to divide the flux by the area of cross-section there. Thus, if it is wished to express B I} the induction in the first portion of the circuit, where the area of section is s v we have D _flux_ magnetomotive force ft /* 2 S 2 /*3 S 3 Or, again, if what is wanted be to calculate the number of ampere turns which are required to produce a stated magnetic flux in a magnetic circuit made up of a series of portions of which the lengths, sections, and permeabilities are known, we may find the magnetomotive force from the formula magnetomotive force = flux x ( L_ + i_ + _JL_ + &c. Y \Pl'l /V2 /*3 S 3 / EXAMPLES OF MAGNETIC CIRCUITS. 271 and then find the number cf ampere turns by dividing the magnetomotive force by (Mr. This is, in effect, the problem which is attacked in calculating the winding of the field- magnets of a dynamo. The problem is analogous to that of finding the electromotive force necessary to drive a stated current through a circuit composed of a series of conductors of which the specific resistances, the lengths, and the cross-sections, are assigned. 155. Particular Cases: Continuous Ring wound uni- formly and otherwise. The utility of the idea of the magnetic circuit will be apparent when we consider one or two examples. Take first the case, already familiar, of a uniform ring uniformly wound with a magnetising coil of N turns. Let I be the length of the ring, measured round any circle within the ring parallel to the sides. The magnetic force at all points of such a circle is - , and the line-integral of this, or the 6 magnetomotive force, is 4 TT C N. If s be the area of cross- section, the magnetic resistance of the ring is , and the flux, 116 which is equal to the magnetomotive force divided by the resistance, is 47I-CN We might, of course, have derived this expression for the flux otherwise, namely : L The line-integral of magnetic force has the same value for all lines that thread through the magnetising coil. Moreover, the magnetic force H is itself constant at all points of the circle I, parallel to the sides of the ring ; so that the line- integral is H L To compare the values of H at different points in the substance of the ring, at distances r v r 2 , &c., from the axis of the ring, we have H x ^i = H 2 Z 2 , ^ = 2 TT r lt and Z 2 = 27rr 2 ; hence, H 1 r 1 = H 2 r 2 . In other words, the magnetic force due to uniform winding on a uniform circular 272 MAGNETISE IN IRON. ring varies across any section in inverse proportion to the distance of the point from the axis of the ring. (See 57, ante.) In the case of a uniformly-wound uniform ring there is no special advantage in applying the conception of the magnetic circuit. The results to which it leads are obtained, with no less ease, by considering the magnetisation and magnetic force at any individual point of the metal. But it should be noted that the conception of the magnetic circuit makes it possible to avoid any use of, or reference to, the quantity H. We have derived the notion of magnetomotive force from that of mag- netic force, by taking the line-integral of H round the magnetic circuit. But that is by no means a necessary order of ideas ; nor is the notion of H indispensable in the treatment of the subject. The magnetomotive force may be defined without reference to it, and the flux may be stated in terms of the magnetomotive force and magnetic resistance, so that all use of H may be excluded. It is even thsoretically possible to treat all cases of magnetisation in the same way. With a magnetised bar, for instance, the magnetic circuit is completed through the surrounding non-magnetic medium, and a sufficiently powerful analysis might determine the resistance of the circuit, and so allow the relation of magnetic flux to mag- netomotive force to be treated without any allusion to the magnetic force at individual points of the bar. But to apply this method universally, though theoretically possible, is quite impracticable ; and there are very many problems in regard to which the older modes of viewing the subject, described in earlier chapters, are infinitely more convenient. The student must not think to abandon the consideration of magnetic force and magnetisation at individual points because he finds that the notion of the magnetic circuit is remarkably useful in certain cases, and has, in theory, no limits to its application. Its real value lies in the fact that Dy its help problems which would otherwise be intractable may be solved with sufficient exactness for practical purposes. To trace, for example, from point to point in the core of a transformer or the field magnets of a dynamo the value of H, and so determine the magnetisation, would be a task the diffi- culty of which would be prohibitive. But by applying in such RING WOUND NON -UNIFORMLY. 273 cases the method of the magnetic circuit, a solution is readily arrived at not, indeed, a rigorous solution, but one that satis- fies the requirements of the electrical engineer. In the case dealt with above that of a uniform ring uni- formly wound the metal of the ring forms a perfect magnetic circuit. None of the lines of induction stray into surrounding space ; the ring itself is a tube of induction, and the flux is constant at all cross sections. Suppose, however, that, instead of being uniformly wound, part of the ring, Q, is bare and the magnetising coil is heaped up Fia. 131. on the other part P (Fig. 131 ). In that case the flux through P is greater than the flux through Q, for some of the lines of induction which thread through the coil close themselves by passing not through the bare part of the ring but through surrounding space in the manner indicated by the dotted lines. The ring is now an imperfect magnetic circuit. If, however, the material is very permeable, like soft wrought iron (the magnetic permeability of which, when not too strongly magnetised, is some two or three thousand times as great as permeability of air), and if the ring is short that is to say, if its diameter is not too great in com- parison with the dimensions of its section this leakage of lines of induction into surrounding space will take place to only a 274 MAGNETISM IN IRON. very limited extent ; by far the greater number of the lines through P will complete their circuit within the substance of the ring, and the flux at Q will be only a very little less than the flux at P. We may, therefore, in such a case, as a first approximation, treat the flux in the ring as constant, and apply the equation of the perfect magnetic circuit, flux = ^- , to find it. This quantity is, in fact, slightly less than the flux in the part P, because the resistance of the actual magnetic circuit is a trifle less than that of the ring, through the " shunting " of a part of the ring by the surrounding air. On the other hand, the flux, as calculated above, is greater than the true flux at Q. The case is analogous to that of a conducting circuit, which instead of being perfectly insulated is immersed in a poorly conducting fluid. Imagine a ring of copper with a seat of electromotive force at P to be immersed in a liquid, the con- ductivity of which is only one two-thousandth or one three- thousandth of the conductivity of copper. The current at Q will be only a little less than the current at P; the current which leaks into the surrounding fluid will be an inconsiderable part of the whole. We must repeat the proviso that the ring is short; in other words, that the surface through which leakage occurs is not very great in comparison with the area of cross section through which what we may call legitimate conduction occurs. The advantage of regarding the iron ring as a magnetic circuit, nearly, though not quite, perfect, is at once apparent when one considers how difficult it would be to determine directly the magnetic force H at individual points. In the case of a uniformly wound ring there is no difficulty in determining H, because the magnetic force is then wholly due to the mag- netising coil. In the present case H is by no means due to the coil only. The coil acting alone would produce a strong magnetic force at points within and close to it, and would produce very little magnetic force in more distant portions of the ring. But we know that H must actually be pretty nearly uniform throughout the ring, because the magnetisation is pretty nearly uniform. What tends to equalise H is the free magnetism in the ring itself the free magnetism which exists in consequence of the very fact that the flux is not quite uniform. RING WITH A GAP. 275 The magnetic force at any point is due partly to the action of the free magnetism and partly to the action of the coil; at points within and near the coil the free magnetism diminishes H by opposing the action of the coil, but at points on the bare side of the ring augments H. It is just because the ring is not a perfect magnetic circuit because there is some leakage of the flux into surrounding space that the magnetic force (and, therefore, the induction) is fairly uniform all round. In a short ring of very permeable substance, a slight variation in the flux from point to point of the ring implies the existence of enough free magnetism to correct very nearly that excessive inequality in the magnetic force which is produced by the magnetising coil ; in other words, the circuit then establishes itself with but little leakage. 156. Ring Magnet with an Air Gap. We shall next con- sider a magnetic circuit consisting of a uniform iron ring, in which a narrow radial crevasse has been cut. When the ring is magnetised there is some leakage of lines of induction through its sides into surrounding space, especially near the crevasse, but most of the lines go directly across the crevasse. We may conceive the magnetic circuit of the ring to be completed though not quite perfectly by a plate of air filling the crevasse, of the same area of cross-section as the ring itself. The lines of induction spread somewhat in crossing the crevasse, and a closer approximation to the condition of a per- fect circuit would, therefore, be reached by supposing the plate of air to have an area of cross-section rather larger than the cross-section of the ring, the extent of this enlargement being dependent on the thickness of the crevasse. In the case which we postulate, however, the crevasse is very narrow, and it will suffice to take its area of section as no more than equal to that of the ring. Let s be the area of section, I the mean length of the complete ring (before the crevasse is cut), and 8 1 the (small) mean thickness of the crevasse. Let the ring be magnetised, as before, by a coil of N turns, carrying a current C. The per- meability of the ring is p, and that of the gap is unity. Then, Flux = magnetomotive force _ . ^ 4 IT C N p s magnetic resistance ~ ~ + = I + 8 1 (u. - 1)" /* * T2 276 MAGNETISM IN IRON. If there had been no gap, the flux would have been - ^ 8 . The effect of removing a short length, 8 I, of the iron, and sub- stituting air as the material through which the magnetic circuit is completed, is to increase the resistance of the circuit as much as it would be increased by the addition of a length of iron equal to 8 1 (/A- 1). 157. Comparison of a Split-Ring with an Ellipsoid. It is interesting to compare the case of a ring in which there is a gap with that of an ellipsoid of finite length.* In the ellip- soid, as we have already seen ( 26), the free magnetism pro- duces a self-demagnetising force, which is proportional to the amount of magnetisation, and opposes the action of the mag- netising coil. If we call H the true magnetising force acting on the metal, and H' that part of the magnetising force which is due to the action of the coil alone, then H = H'-^I, where I is the intensity of magnetisation, and N is a numerical factor, the value of which depends on the relation of the length of the ellipsoid to its transverse dimensions. We shall see that a precisely similar formula may be obtained for the ring with a gap by treating it as a nearly perfect magnetic circuit. Since the magnetisation of the cut ring is very nearly uniform, the actual magnetic force in the iron, which is the resultant of that due to the coil and that due to the free mag- netism, must also be very nearly uniform. Call this force H, and call H' the magnetising force due to the coil alone, which (on the supposition that the coil is uniformly wound) is - The H - B - Flux - 47TCN/.S 4 ?rCN ' u , 7r and H = 9 Therefore, H' I = H {I + S I (jt - I)}, H-.HJ 1+^0-1) See a Paper by H. E, J. Q. du Bois, Phil. Mag., Vol. XXX., 1890, p. 335. SELF-DEMAGNETISING FORCE DUE TO GAP. 277 since JK = 4 TT K + 1, K being the magnetic " susceptibility," or Hence, I H' and The factor ^ * therefore takes the place of the factor N L in the formula for ellipsoids. Its magnitude depends on the proportion of the width of the crevasse to the whole length of the circuit. Taking the case of a circular ring, this proportion may be expressed by reference to the angular aperture of the crevasse that is to say, the angle subtended by the crevasse at the 7 A centre. Calling this angle a in degrees, = - - and JV = . I 360 360 The following table has been calculated by Du Bois, to show what aperture of crevasse in a circular ring produces the same self-demagnetising force as exists in ellipsoids of certain stated elongations : Ratio of Length to Diameter of Ellipsoid. Factor N. Equivalent Aperture in Circular Ring (degrees). 20 30 40 50 100 0-0848 0-0432 0-0266 0-0181 0-0054 2-41 1-22 0-76 0-52 0-15 It is scarcely necessary to add that the self-demagnetising force which is introduced by the presence of the crevasse affects the residual magnetism of the ring as well as the induced magnetism, precisely as it does in the ellipsoid. When the magnetising-circuit of the split-ring is broken, the residual magnetism causes a reversed force to act on the metal, the value of which is | r , where l r is the residual intensity of magnetism. This prevents the residual magnetism from being nearly so great as it would be were the ring complete 278 MAGNETISM IN IRON. indeed, a very narrow crevasse is sufficient almost wholly to destroy the (otherwise very great) residual magnetism of a soft iron ring. For example, in a ring of soft annealed iron, which, when uncut, would retain, after being strongly magnetised, a residual induction, B r , of 12,000 units, the presence of a gap only half a degree wide will reduce the residual value of the induction to about 1,000. 158. Graphic Representation of the Influence of a Narrow (Jap. The influence of a narrow gap, both in resisting mag- netisation and in promoting demagnetisation, is best seen by resorting to the graphic construction which has been already explained in relation to ellipsoids and long rods ( 48). Let a, a, a (Fig. 132) be curves of magnetisation (curves of I and H) for the iron of which the ring is composed. Find the A / factor N, equal to , and draw the line A, so that i A M (drawn parallel to the axis along which H is measured, and interpreted on the scale of H) shall be to M as . (/ is to I. Then the intercepts between M and A represent the values of the self-demagnetising force, due to the corre- sponding values of I, and if we wish to represent the relation of the magnetism to the magnetising force produced by the coil alone (the force which has been called H' above), we have only to draw a diagram in which the lines a, a, a are sheared into the position b, b, b by taking the abscissas from A 7 I A instead of from M, or, in other words, by adding to H in every case. Thus, any point F in the new curve is found from the corresponding point P by taking P' R = P R + Q R. The residual magnetism, which was S in the ring without a gap, is reduced to S' in the ring with a gap. If the object of the construction had merely been to find the residual magnetism, S', that could have been done more readily by drawing T inclined at the same angle as A, but on the other side of the axis of I, to meet the descending curve a, and projecting S' from the point of intersection of T with the curve. The same construction will, of course, serve to find the residual magnetism of ellipsoids, GRAPHIC TREATMENT OF RING WITH GAP. 279 or of long rods, which may be treated as approximating to ellipsoids.* In Fig. 132 we have supposed that the magnetisation of the iron is exhibited by means of a curve of I and H. If, instead of this, the curve of B and H were given, a similar graphic construction would still serve to show the effect of the gap. Since I = B ~ H , the self demagnetising force N\ = N ( B ~ H ), which, in a very permeable substance like iron, is practically FIG. 132. NB equal to , since B is very great compared with H. Sub- 4 7T stituting for N its value 4 v 8 1 , this becomes ?A?. The L t, line A has, therefore, to be drawn, in a diagram of B and H, at D <> -I such an inclination that when M represents B, M A is B - H From the equation H = H' - N \, by substituting for I, we have or H-H'-L'(B-H), L H'/:= HC-80 + B8J. * This construction, for finding the residual magnetism of ellipsoids, is given by J. Hopkinson, Phil. Trans., 1885, p. 465. 280 MAGNETISM IN IRON. H' I is 4 TT C N; it is the line-integral of the magnetic force taken round the whole circuit, or, in other words, the magnetomotive force. H is the magnetic force in the iron, and H (I - 8 1) is that part of the line-integral which is taken through metal. B is equal to the magnetic force in the gap, and therefore B 8 I is that part of the line-integral that is taken through air. The equation might evidently have been written down directly ; it expresses the simple fact that the line integral for the complete circuit is made up of two parts, in one of which namely, the iron, whose length is I - 8 1 the magnetic force has the sensibly uniform value H, while in the other namely, the gap whoso length is 81 the magnetic force has the sensibly uniform value B. We have derived it otherwise, in order to accustom the student to observe the connection between the treatment of the ring as a magnetic circuit and that other treatment which deals with the magnetic condition at individual points. In the language of the magnetic circuit, H (1 81) represents that part of the whole magnetomotive force which is used in overcoming the magnetic resistance of the iron, and B 8 1 represents the remainder of the magnetomotive force, which is used in overcoming the resistance of the gap. In soft iron, if the gap is of any considerable width, its resistance is so great compared with that of the iron that nearly the whole magneto- motive force is used in forcing the induction across the gap. 159. Graphic Representation of the Relation of Flux to Magnetomotive Force. In dealing with the magnetic circuit as a whole, it is convenient to modify and generalise the graphic construction exemplified in Fig. 132, by drawing the abscissas to represent the whole magnetomotive force, and the ordinates to represent the whole magnetic flux in the manner first described by J. and E. Hopkinson.* Such a curve may obviously be derived for any part of a magnetic circuit from the curve of induction and magnetic force for the material by multiplying fche induction by the area of section s to find the whole flux, and by multiplying the magnetic force by ihe length of the piece to find the magnetomotive force re- quired for the magnetisation of that part of the circuit. Then, * Phil. Trans., 1886, Part I., p. 331. GENERAL GRAPHIC METHOD. 281 by graphically summing the abscissas for successive parts of any composite magnetic circuit, the whole magnetomotive force is represented in relation to the flux. An example will make the method intelligible. Take, as before, the case of an iron ring of uniform section with a gap in it, the length of the gap being 8 1, and that of the iron 1-81. From the curve of B and H for the metal of which the ring is formed which we suppose to be known draw the curve P (Fig. 133), for the iron, in which any ordinate, Pp, is the flux, B s, and the correspond- ing abscissa, Op, is H (1-8 I). Next draw the curve Q P q MAGNETOMOTIVE FORCEi FIG. 133. for the gap, in which the ordinate Q q is again B s, and the corresponding abscissa q is the magnetomotive force required for that part of the circuit, namely B 8 1. The line Q is evidently straight, as it relates to a non-magnetic substance in which induction is proportional to magnetic force. Then draw the resultant curve R, in which for each ordinate the abscissa is the sum of the abscissas of the curves already drawn, namely, Or = 0p + 0q. Or is the magnetomotive force required for iron and gap together, and the curve K shows the relation of the flux to the magnetomotive force in the circuit as a whole. 282 MAGNETISM IN IRON. Moreover, the construction may be applied with equal facility to the descending limb of the curve, or to exhibit the behaviour of the circuit in any cycle of magnetisation. In the line R the descending and ascending limbs coincide ; in the iron part of the circuit the ascending and descending limbs have to be drawn separately, and the process of summing the abscissas has to be applied successively to each limb (as in Fig. 132) in order to determine a curve which will show the effects of hysteresis in the magnetic circuit as a whole, and all the varia- tions of magnetic flux under cyclic variations of magnetomotive force. Again, the method may evidently be extended to magnetic circuits of a more complicated form, containing, let us say, successive pieces of different material, of lengths l v / 2 , 1 3 , &c., and sections s v s 2 , s 3 , &c. We must know, to begin with, the curve of B and H for each material. From these curves draw a set of curves in which the ordinates are respectively B s lt B s 2 > B s 3 , &c., and the abscissas are Hj l lt H 2 1%> H 3 / 3 , &c. The required curve of flux and magnetomotive force for the whole circuit will be found by compounding these curves ; that is to say, by drawing a curve in which, for a given ordinate, the abscissa is the sum of the abscissas of the separate curves. The complete curve exhibiting what happens when the complex circuit is carried through a cyclic process of magnetisation may be found in this way, provided the cyclic curves for each of the materials are determined beforehand. 160. Application to Dynamos. A principal use of this method is to determine the magnetomotive force, and conse- quently the number of ampere-turns, required to produce a stated magnetisation in a circuit made up of pieces the dimen- sions and magnetic qualities of which are known. The method was, in fact, invented by J. and E. Hopkinson as a means of solving practical problems in the design of a dynamo, where the magnetic circuit is made up of (1) the cores of the field magnets, (2) the yoke, (3) the pole pieces, (4) the core of the armature, and (5) the non-magnetic spaces on either side of the armature core, between it and the pole pieces. This last is much the most important item in the resistance of the circuit. The magnetic circuit of a dynamo is far from perfect, and the APPLICATION TO DYNAMOS. 283 estimation of the effective length and effective cross-section of each part is subject to some uncertainty, so that the results are no more than rather roughly approximate. To pursue this application in detail would be beside our present purpose : the student should in any case refer to the original Paper.* One point, however, must be briefly mentioned, being of general interest in relation to other magnetic circuits as well as to the circuit of the dynamo. In the dynamo circuit the flux is by no means uniform throughout ; there is much leakage. The flux is greatest in the magnet limbs, which are the seat of the magnetomotive force, and in the armature it is considerably less. Its value in the armature is, however, the matter of chief interest in the prac- tical problem. Calling F x the value of the flux in the armature, the fluxes F 2 , F 3 , &c., in other parts of the circuit may be expressed by the use of factors intensity of magnetisation. The limit is reached when all the molecules have become turned to face exactly in the direction of the applied magnetising force ; no increase of the force beyond what is required for that can add to the magnetisation. The fact that a definite saturation value is now known to exist* adds much probability to Weber's hypothesis. Further, the * The evidence of this has been fully stated above ( 91 to 107). 296 MAGNETISM IN IRON. process by which the molecules are supposed to turn hither and thither under varying magnetising forces, leaves ample room, as we shall presently see, for a satisfactory explanation of all the features which the curves of magnetisation are known to present, and the various manifestations of hysteresis become intelligible. Again, the effects of vibration in augmenting mag- netic susceptibility are readily accounted for in consequence of the greater freedom which vibration gives the molecules to fall into line with the magnetising force. Additional evidence is furnished by experiments such as that of Beetz*, in which the effects were observed of applying a weak magnetising force to iron at a time when the molecules were peculiarly free to respond to its directive action, namely, while they were in the act of being deposited by the electrolysis of an iron salt. The iron was deposited along a line made by scribing a longitudinal scratch on a straight piece of varnished silver wire. The wire was immersed in the iron salt, and was placed in a magnetic field in such a manner that the lines of force ran in the direc- tion of the length. The silver wire formed one pole of an electrolytic cell, and it was found that the metal deposited on the scratch was so highly magnetised that the subsequent application of a much stronger magnetic field failed to aug- ment its magnetism more than a very little. The molecules had been ranged at the moment when they escaped from im- prisonment in the salt, and before they had the opportunity of forming fresh entanglements by their action on one ano- ther ; just as criminals are said to be most easily diverted into regular courses at the moment of their release from gaol, before they have time to resume the ties of their usual companionship. Not only is Weber's notion of mole- cular magnets strongly supported by this experiment of Beetz, but the cumulative evidence in its favour which is supplied by many facts of more recent observation may be said to give it almost conclusive proof. We may even build up a model consisting of small permanent magnets, such as Weber's theory postulates, in which all the chief characteristics of mag- netic induction can be closely imitated. The study of a model of this kind leaves little room for doubt that the basis of * Pogg. Ann., CXI, 1860, p. 107. CONSTRAINT OP THE MOLECULAR MAGNETS. 297 Weber's theory, namely, the hypothesis of permanently mag- netic molecules, is essentially sound. 168. Constraint of the Molecular Magnets in Weber's Theory. It is clear that if the process of magnetic induction is to be explained as the turning of molecular magnets so that they tend to face one way, the molecules must be subject to some directive force which prevents them from responding with perfect freedom to the magnetising field. Without some such constraint they would at once take the direction of the applied field, and the weakest magnetising force would suffice to pro- duce saturation. In fact, however, magnetisation goes on pro- gressively as the magnetising force is increased, and at every stage the direction taken by each molecule is determined by a balance between the force of the field which tends to turn the molecule, and some other controlling force which opposes the turning. Weber supposed that in a piece of virgin iron the axes of the molecular magnets point indifferently in all directions, and that when a magnetising force H is applied, each molecule is deflected against a directive force, which tends to restore it to its original position. He assumes this force to be that which would be exerted by a magnetic force of some constant value, K, acting in the primitive direction of the molecule's axis*. The direction in which the molecule points while the magnetising force acts is consequently the direction of the resultant of H and K, and when the external force H is removed, the molecule is brought back by K to its primitive position. This theory of the constraint of the molecules gives no explanation of residual magnetism or other manifestations of hysteresis. According to it, the magnetic susceptibility should be constant for all values of H less than K, and should diminish for higher values of H. At the stage when H becomes equal to K, and the proportion- ality of magnetisation to magnetising force ceases, the value of I should be of the final or saturation value. This hypothesis is inconsistent with the fact that the early part of the curve of magnetisation is not straight ; that the susceptibility is small * Fogg. Ann., LXXXVIL, 1852, p. 167. See Maxwell's El. and Mag. t Vol. II., 443. 298 MAGNETISM IN IRON. at first, and increases with increasing magnetising force. This, indeed, is an example of hysteresis, and for the phenomena of hysteresis the theory, in this form, affords no room. 169. Maxwell's Modification of Weber's Hypothesis. To remedy this defect Maxwell suggested a further assumption based on the analogy of magnetisation to mechanical strain, with the object of admitting conditions under which the position of equilibrium of the molecular magnets may be permanently altered. He supposes that when a molecule is deflected by a magnetising force H it returns completely to its primitive position on the removal of H provided the deflection has been less than a certain value, but returns only partially if the deflection has exceeded that value. In the latter case its axis, when H is removed, remains turned through an angle which may be called the permanent set of the molecule. Maxwell has examined the consequence of this supposition at some length, assuming the molecules in a given piece to be all capable of the same or nearly the same amount of elastic deflection, and assuming a constant or nearly constant controlling force, K, to act on each in the primitive direction of its axis. This hypothesis accounts for the existence of residual magnetism, and for some of the phenomena of hysteresis ; it fails, however, to explain why hysteresis should be found when, after the first application, a magnetising force is removed and reapplied, and its postulates about controlling force and the condition of permanent set are arbitrary. We shall see presently that by considering the action of the molecular magnets upon one another conclusions are reached which really embody Maxwell's idea of elastic and non-elastic deflection, though the controlling force and the amount of elastic deflection are no longer arbitrary and no lorger the same or nearly the same for all the molecules. 170. Hypothesis of Frictional Resistance to the Deflection of the Molecules. The suggestion has been made by Wiede- mann and others that the deflection of Weber's molecular magnets is opposed by a species of frictional resistance, which not only resists the magnetisation, but accounts for residual magnetism and the effects of hysteresis by tending to hold the molecules from returning after they have been disturbed. A CONSTRAINT DUE TO MUTUAL FORCES. 299 directive force, such as that postulated by Weber, is, of course, still necessary. Several of the observed phenomena might be adduced as supporting this notion ; in particular, it harmonises well with the effects which are known to be produced by vibra- tion and other mechanical disturbance in augmenting magnetic susceptibility, and in reducing residual magnetism; and also with the comparative suddenness with which the resistance to magnetisation breaks down when a certain stage in the mag- netising process is reached. But if the molecules were held fast by friction until the applied force became sufficiently strong to start them, the susceptibility with respect to very feeble forces should be zero, whereas, in fact, it has a small posi- tive and initially constant value ( 86, 87). To make the notion of frictional control agree with the facts, it would be necessary to assume some further complication, such as that a few of the molecules in any given piece are sensibly free from friction, and may begin to turn under the influence of the weakest forces. 171. The Constraint of the Molecules due to their Mutual Action as Magnets. The matter becomes immensely simplified if we put aside all these arbitrary postulates re- garding controlling force and resistance to turning, and inquire what is the character of the constraint the molecules necessarily suffer through the forces which they exert on one another in consequence of the fact that they are magnets. It has been pointed out by the author* that this restraint is sufficient to account for the observed characteristics of the process of magnetisation, that it completely explains hysteresis, and that it at least offers a clue to those complicated variations of magnetic quality which are known to be caused by the variation of such physical conditions as temperature or stress. In proceeding to consider the equilibrium of the molecules under their mutual magnetic forces, it is clear that we cannot confine our attention to any one molecule. For the directive force that acts on any one molecule depends on the positions of the molecules which surround it, and becomes altered when these are disturbed. We cannot investigate the equilibrium of the * See " Contributions to the Molecular Theory of Induced Magnetism," Proc. Roy. Soc., Vol. XLVIII., 1890, p. 342, Phil. Mag., Sept., 1890. 300 MAGNETISM IN IRON. individual without including in the question the equilibrium of its neighbours. When an external force is applied, they, as well as it, are deflected, and the constraint they exercise on it suffers change. What must be studied is the configuration of the group as a whole, and the manner in which the group becomes distorted, broken up, and rearranged in the process of applying and removing an external magnetising force. In seeking to find in the mutual constraint excited by the magnetic molecules, an explanation of the changes of suscepti- bility which are observed as a magnetising force is gradually applied to a piece of iron or other magnetic metal, it should be borne in mind that the magnetising process may be broadly divided into three stages (as was remarked in 141), namely, the stages A, B, and C of the typical curve (Fig. 136). MAGNETIC FORCE Via. 136. These admit, in general, of being distinguished from one another without difficulty, though the passage from one stage to the next is never perfectly abrupt. In some cases, however, it is remarkably sharp, as in the curves of Figs. 120 and 121 (pp. 230, 231), which relate to nickel under torsion, and under a combination of torsion with longitudinal pull. In the first stage the susceptibility is small, and there is almost no retentiveness. In the second stage the magnetism is acquired with great readiness, and much of it may be retained if the force be removed. In the third stage the growth of magnetism is again slow, and what is acquired in it does not contribute much to the residual magnetism. We shall see that STABILITY OF MOLECULAR GROUPS. 301 these stages are just such as the molecular theory would lead us to anticipate. 172. Imaginary Molecular Groups. A Single Pair. By way of leading up to the consideration of groups consisting of many magnetic molecules, we may begin by thinking of a FIG. 137. group which consists of a single pair. Each member of the pair is to be conceived of as a short magnet capable of free rotation about a fixed centre. In the absence of all external magnetic force this pair of molecules will arrange themselves as FIG. 138. In Fig. 137, with opposed poles exactly in the line joining the centres. Let an external magnetic force, H, now be applied in any direction (Fig. 138). If H is weak the molecules will be but slightly deflected. But as H is gradually increased a stage will be reached at which 302 MAGNETISM IN IRON. the molecules part company, and fly round into a position in which the direction of the magnetic axis of each is nearly parallel to H (Fig. 139). Except in special cases perfect parallelism with H will be reached only when H becomes indefinitely strong. Then as H is gradually reduced there will at first be little change in the configuration, until a stage is reached at which a sudden return to the condition of Fig. 138 occurs. This will happen at a lower value of H than that which was needed to break up the group of Fig. 138; here we have, in fact, an elementary example of hysteresis. If the direction of H is chosen so that it is perpendicular to the line of centres this return will occur only when H is reduced to zero. In the more general case, illustrated by the figures, the sudden return FIG. 139. will happen when H has a small finite value, and then the subsequent reduction of H to zero will be associated with a gradual change from the state of Fig. 138 to that of Fig. 137. During the application of H we have three stages ; there is, first, the slight deflection of the molecules (Fig. 138) which precedes what may be called the rupture of the tie that holds them in line with one another. Then there is the sudden swinging into a position of much greater deflection when that tie is broken. Finally there is the continued approach towards perfect alignment, made under stronger values of H. During each of these three stages the group is acquiring resultant magnetic polarity in the direction of H, though the magnetisation of the individual molecules is, by assumption, a constant quantity. In the first stage the process is, so to speak, perfectly elastic EQUILIBRIUM OF A SINGLE PAIR. 303 that is to say, it corresponds to the elastic stage in the straining of a solid when there is no permanent set left after the removal of the straining force. If we suppose H to be removed at any part of the first stage, the molecules at once return to their primitive positions. But after the critical value of H has been passed, which separates the first stage from the second, this is not so ; there is then a tendency to retain the new configuration. We shall see presently that this tendency, which is the very essence of hysteresis, becomes much more conspicuous when we have to deal with larger groups. Finally in the third stage we have again a quasi-elastic part of the process of mag- netisation. To begin with, the equilibrium of the group is, of course, stable with respect to small displacements. Any small casual disturbance, applied and removed, will leave the magnets swinging about the position of equilibrium, shown in Fig. 137. The equilibrium continues to be stable so long as the deflecting force is weak (stage A). Bat as the critical point is approached, the stability becomes reduced just at the end of stage A it is neutral, and any further increase of H brings about instability. The molecules then precipitate themselves into the new form (Fig. 139) in which they are once more stable so long as H continues to act. To express the matter in symbols, let us suppose that each magnet may be treated as a pair of poles of strength m t separated by a distance 2 r, which is the length of the magnetic axis. Let a (Fig. 140) be the angle which the direction of the applied deflecting force H makes with the line of centres C C', and let 6 be the amount of deflection, which is the same for both magnets. It is assumed, in the first place, that H is not so strong as to produce instability. The field H exerts a mechanical force m H on each pole, or a couple on each magnet, the distance between the parallel forces of the couple being 2 r sin (a - 0). The deflecting moment which acts on each magnet is, therefore, 2 H m r sin (a - 0), and this is to be balanced by what we may call the restoring moment, due to the forces which the magnets exert on one another. 304 MAGNETISM IN IRON. These forces are (1), the attraction of the poles P Q ; (2), the attraction of the poles P' Q' ; (3), the repulsion of the poles P' Q j and (4), the repulsion of the poles P Q'. Of these forces the moments of the third and fourth balance one another, and the moment of the second is insignificantly small compared with that of the first, provided the distance C C' is not much greater than the length of one magnet, and the deflection is not great. Under these conditions it will suffice to consider the restoring moment as due to the first force only, namely, to 140. mutual attraction of P and Q. Its value is PQ* ' C N being the perpendicular distance from C to the line P Q ; and the condition of equilibrium is that P Q2 * * * * V /' As is increased the restoring moment at first increases, but passes a maximum at a value of 6 which depends on the rela- tion of the length r, or C P, to the length C C'. GROUPS OP PAIRS. 805 When H and are sufficiently increased the equilibrium becomes neutral. This occurs when { "- From these two equations (1) and (2) it is possible to deter- mine the values of H and of 9 corresponding to the critical point in the deflection, at which the equilibrium of the deflected molecules becomes neutral. Any greater value of H will cause instability ; the molecules will then swing violently round into a new position of equilibrium with their axes nearly parallel to the direction of H. If there were a number of such pairs of magnets, of the same strength and the same pitch, all acted on by the same deflecting field, but with their lines of centres inclined at various angles to the direction of H, it is clear that some would reach instability sooner than others, as H was strengthened. The first pairs to become unstable would be those which were inclined at something more than a right angle to H, so that a 6 became a right angle when the value of corresponding to instability was reached. Other pairs would escape passing through the unstable state altogether, namely, those pairs which lay initially in directions nearly parallel to H. How nearly parallel to H they must lie initially in order to escape instability depends on the extent by which the distance between the centres exceeds 2 r. If we suppose that this excess of distance, or clearance be- tween the poles, as one may call it, is very small, then the state of instability in pairs which lie well across the direction of H is reached approximately when dB PQ* which happens when tan = j^ $ being the inclination of the line P Q to the line of centres C C'. In these circumstances the value of H which breaks up the pair is i H _ m 12 ^3 . (a - r) 2 sin a ; v 306 MAGNETISM IN IRON. where a stands for half the distance between the centres C and C'. This does not apply when the line of centres is nearly parallel to H. In the special case when the line of centres has the same direction as H, but the magnets point initially in the direction opposed to H, there is no stable deflection previous to the occurrence of instability. The critical point is reached in such a pair when Hra = - . The general behaviour of a crowd of groups, each consisting of two magnets, can be readily enough imagined, and still more readily examined by aid of a model. Until the first of the groups breaks up, as the field is increased, we have nothing but quasi-elastic deflection. Then the groups successively reach the critical point, so that a rapid, though not perfectly sudden, development of resultant polarity on the part of the crowd as a whole is observed. Finally, there is a slight further increase, under the action of stronger fields, as the state corres- ponding to saturation is approached. Again, as the field is gradually reduced many of the groups will return to their initial state. Many others, however, will assume new forms, namely, with their poles pointing just the other way from the way they pointed at first, and the effect of these will be to contribute a resultant residual polarity which persists when H is reduced to zero. The application and removal of H will leave a majority of groups pointing, more or less, towards the direction in which the force was applied, although at first there was no preponderance in any direc- tion. We find, therefore, even in so simple a grouping of magnetic molecules as this namely, a grouping in isolated pairs many of the features which are presented in the magnetisation of iron. We find analogues of the first, the second, and to some extent the third stages, which are observed in curves of I and H, and we find evidence of hysteresis and residual magnetism. But a very much more complete reproduction of the phenomena of magnetisation becomes possible, as will be shown presently, if we suppose the molecules to be distributed either continuously or in groups consisting of a considerable number of members. GROUPS OP FOUR MAGNETS. 807 The behaviour of two-member groups would agree fairly well with what is known to happen in the first and second stages of the magnetising process in iron. It seems, however, to leave too little supplementary magnetisation to be acquired during the third stage. And a more obvious difficulty is, that though two-member groups suffice to account for the existence of some residual magnetism, they fail to explain the high retentiveness which is found in, say, soft iron, where we often find more than 90 per cent, of the induced magnetism surviving the removal of the magnetising force. To account for that, something more is needed than the constraint exercised by each member of a pair on the other member ; the molecules must, in fact, form new ties after the old ones have been ruptured, and Fia. 141. to allow of that each molecule must have more neighbours than one. 173. Group of Four Members. A better approximation to the facts will be obtained if we deal with a group consisting of four little magnets, with their centres at the four corners of a square (Fig. 141). When the field H begins to act, the members of the group are all slightly deflected, but without at first becoming unstable. If during this first stage the force H is removed, there is no residual displacement. But when H is sufficiently increased the original lines of the group break, and the members tend to pair themselves anew in lines which are more favourably inclined to the direction of H {Fig. 142). Finally, when H is further increased, the members x2 308 MAGNETISM IN IRON. of the group are gradually ce*npelled to take the position sketched in Fig. 143. Next, suppose H to be removed. There will be a return from the condition of Fig. 143 to- that of Fig. 142, but the pairing shown in Fig. 142 will be< FIQ. 142. maintained, and this implies a large amount of residual mag- netisation. If the direction of H be then reversed, and its value gradually increased, a stage will presently be reached when the- resultant polarity of the group suffers an abrupt change through. the reversal of the lines in Fig. 142. FIG. 143. The curve of magnetisation that is to say, the curve- showing the resultant polarity in terms of H for the single? group of four members is sketched in Fig. 144. AGGREGATE OP GROUPS. 309 From this it is easy to see, in a general way, what would be the form of the curve for an aggregate of many such groups, variously inclined to the direction of H. The transition from one stage to another will be gradual in the aggregate, for it will happen at different values of H in different groups. Hence the curve will assume a rounded outline in place of the sharp corners of Fig. 144. Moreover, the curve obtained during the removal of H will not coincide with that obtained during the application of H, except the process be stopped at a very early point in the first FIG. 144. Whenever the process is' extended far enough to cause any of the groups to reach the unstable state we shall find hysteresis. The- two curves will not coincide, even in the third stage. Some of the members will pass through an unstable state even there. After the first re-arrangement of the, group has taken place, and the lines have become directed as in Fig. 142, there may be a second breaking up and passage through in- stability on the way to the state of Fig. 143. This will happen when the lines of centres have a considerable inclination to H, and especially when the poles of the members are close together. In such an aggregate of groups we may therefore expect to 310 MAGNETISM IN IRON. find hysteresis in all possible cyclic changes of the magnetising force. The form of the curve obtained during reversal of H will evidently agree with the general form given by the mag- netic metals. In proportion as the corner between stages A and B in the first curve is comparatively sharp or comparatively rounded so will be the corner at which the rapid descent of the curve begins while H is being reversed. Fio. 145. 174. Continuous Distribution in Cubical Order. From these considerations regarding groups of four members it is- easy to pass to the case of a manifold group or a continuous distribution of members arranged so that the lines of centres form squares. All that has been said above is still applicable. The members arrange themselves in lines, and each individual is mainly constrained by its two neighbours in the same line, instead of by one neighbour as in the case already spoken of. The equations of 172 are readily adapted to members of GROUPS OP MANY MEMBERS. 311 long row by substituting 2 m 2 for m 2 in the expression for the restoring moment. The three stages of (1) stable deflection, (2) instability, with rupture of the original lines and formation of new lines, and (3) further stable deflection are as readily traced as before, as will be evident by an inspection of Figs. 145, 146, and 147. Fig. 145 represents an imaginary primitive arrangement. Fig. 146 is the configuration reached after the breaking up of the primitive lines, and Fig. 147 corresponds to saturation. ., FIG. 146. It appears, then, that the theory that the magnetic molecules their stability to the magnetic action of their neighbours gives results which agree with the observed facts, whether we conceive the molecular structure to consist of isolated groups, with a limited number of members in each, or to be continuous. Even with a continuous distribution the lines of molecules will, in consequence of the imperfect homogeneity of the piece, be variously inclined at various places, so that the condition 312 * MAGNETISM IN IRON. necessary to give a rounded outline to the curve will in any case be present. In -no piece, except perhaps in a single crystal, could we expect to find that perfect regularity of structure which would be necessary to make the transition from one stage of the magnetising process to another quite sudden, and to give the curve the form of a series of sharp steps. Whether we picture the structure as continuous or as built up of isolated groups, special importance attaches to square FIG. 147. patterns from the fact that the magnetic metals crystallise in the cubic system. The behaviour of pyramidal forms presents some interesting features that need not be entered into here. Enough has already been said to show that there is no need, to assume that any arbitrary controlling forces act on Weber's molecular magnets. The theory that their constraint proceeds only from their mutual action as magnets evidently suffices to explain, generally, the characteristics of the magnetising process It may be useful, however, to point out how complete is the AGREEMENT OF THE THEORY WITH FACTS. 313 agreement, in point of detail, between the deductions which may be drawn from the theory and the facts which have been described in earlier chapters. 175. Agreement of the Theory with known Facts about Susceptibility. In the first stage there is no rupture of molecular ties until the magnetising force is sufficiently increased to bring about instability in the least stable lines or groups of molecules, and until that happens the application and removal of the force has no residual effect. Up to that point the deflections are small, and they are initially proportional to the applied force. All this is in complete agreement with Lord Rayleigh's experiments on the susceptibility of iron and steel to feeble magnetising forces ( 87), which show that the initial value of the susceptibility is a small constant quantity, and that residual magnetism begins to show itself only when the mag- netising force is so much increased that the proportionality of magnetism to force ceases. Again, it accords with the result that a small alternating change of H, superposed on a constant value of H, or acting on a piece which has residual magnetism in consequence of the action of previous forces, produces (after the first application) but a small coming and going of the mole- cules without breaking their ties, and that if this small alter- nating force is applied when the magnetisation is already strong, the changes which it causes are reduced in amount ( 87). Again, the theory might lead us to anticipate the fact that if at any point of the ordinary ' magnetising process we stop increasing H and begin to decrease it, 1 or stop decreasing H and begin to increase it, the initial 'rate of magnetic change or value of _ - is very small, depending, as it does, only upon d H the quasi-elastic movement of the deflected molecules. Their movements through the condition of instability do not begin until the reversal of procedure has been carried some little way. Again, in strong fields the behaviour of the little magnets accords with the gradually falling off in susceptibility which actually occurs in magnetic metals as the state of saturation is approached. To reach the state of perfect saturation would require an indefinitely strong directing force, but the alignment of the molecules is to all intents complete long before that. In 814 MAGNETISM IN IRON. view of the molecular theory it is not surprising that in iron, where many molecular groups break up under a force of no more than two or three C.-G.-S. units, a force of two or three thousand units produces (as we saw in 102) so nearly perfect saturation that augmenting the force tenfold adds nothing perceptible to the magnetisation. The quantity which tends to a limit when saturation is approached, is, as was shown in 93-102, the intensity of mag- netisation I, not the induction B. According to the molecular theory, I is the sum per unit of volume of the moments of the molecular magnets resolved in the direction of magnetisa- tion. If n be the number of molecular magnets in unit volume, and m the moment of each, the saturation value of I is m n. 176. Retentiveness and Residual Magnetism. An equally satisfactory agreement is found when the results of experiments on retentiveness are examined in the light of the molecular theory. We shall take advantage of the opportunity which this discussion of the theory affords to describe some of these results more fully than has yet been done. In the first stage of the magnetising process, as has been already remarked, there is no retentiveness : the magnetism that is induced under very weak forces disappears entirely when the inducing force is removed. This accords with the view that the molecular magnets are then being as it were elastically displaced from a position of stable equilibrium, without rupture of the ties by which the initial grouping maintains itself, so that each molecule simply returns to itSc primitive position when the displacing force is withdrawn. Theory and experiment alike show that this condition persists only so long as the susceptibility is very small. In the second stage the susceptibility has become much increased as a consequence of the large deflection the molecular magnets suffer in breaking away from their original grouping to form new combinations. The movements they then accomplish are in great measure irreversible, that is to say, they are not undone as the magnetising force is being withdrawn. We may therefore expect to find a rapid development of residual mag- netism during that part of the magnetising process in which the susceptibility is high. The theory shows that in favourable RETENTIVENESS AND RESIDUAL MAGNETISM. 315 cases nearly the whole of the magnetism acquired during that stage will persist as residual magnetism. Experimental instances of this are given below. The third stage, on the other hand, contributes little to the residual magnetism, for the molecular deflections that occur in it are for the most part undone as the magnetising force is withdrawn. A result of this is that the residual magnetism approaches saturation sooner (that is, under the action of weaker magnetising forces) than does the induced magnetism. Another result is that the residual magnetism has a satura- tion value which is definitely less than the saturation value of the induced magnetism. It is indeed possible to imagine a molecular structure such that all the magnetism of saturation would be retained on the withdrawal of the force. This would be the case in a cubical formation if the lines of centres were parallel and perpendicular to the direction of the field through- out the whole piece. But the imperfect homogeneity of any actual piece of iron puts such a conception out of court, and when any of the lines of centres are inclined to the field, it is clear that the saturation value of l r is less than that of I. It will be shown presently that a continuous cubical formation with lines of centres uniformly distributed as regards inclina- tion is a structure which gives more than sufficient possibility of residual magnetism. The value of \ r which the theory shows to be possible in such a structure is in fact greater than the values which are found in experiments with even the most re- tentive metal. The molecular theory makes it easy to understand the difference between retentiveness and what may be called coercive capacity, by which is meant the quality that the coercive force ( 47) measures the quality in virtue of which a substance holds its residual magnetism so strongly that a con- siderable magnetic force, acting in the reversed direction, is necessary to remove it. Retentiveness, on the other hand, is the quality in virtue of which much residual magnetism is held, though it may be held very weakly. Probably no magnetic sub- stance has so much retentiveness as soft annealed iron, and prob- ably none has so little coercive capacity. Eetentiveness, by the molecular theory, is the result of a regular molecular structure of such a kind that the molecules readily arrange themselves 316 MAGNETISM IN IRON. in lines which are but little inclined to the direction of the applied force. The molecular ties may, however, be extremely weak. Coercive capacity is a result of strong ties, such as might be formed by reducing the distances between the mole- cular centres or between some of them, and this condition may very well exist in a structure where the lines or groups are unfavourably arranged for retentiveness. 177. Experiments on Residual Magnetism in Iron. The following experimental results* were obtained with straight iron wires, 400 diameters long, using the direct magneto- metric method. The magnetising force was gradually raised to an assigned value, then gradually withdrawn, to allow the Table XXX. Induced and Residual Magnetism in a Soft Iron Wire, Annealed and Hardened by Stretching. Before stretching. After stretching. H 1 induced. Ir residual. Ratio of residual to induced. H 1 induced. r residual. Ratio of residual to induced. 0'42 16 3-9 0-24 0-42 3-6 0-58 24 6-6 0"J7 0-99 13-1 2-9 0-22 0'70 33 9-9 0-30 1-44 21-1 6-5 0-31 0-99 62 24 0-40 1-73 26-9 11-8 0-38 1-16 91 46 0-50 2*14 41 15-3 0-38 1-30 140 85 0-61 2-88 72 32-7 0-46 1-44 195 133 0-68 3-58 116 61-7 0-53 1-58 280 209 074 4-20 167 98 0-59 176 364 283 078 4-90 218 132 0-61 2-02 468 380 C-81 5-76 265 167 0-63 2-14 507 418 0-S2 7-20 359 225 0-625 2-28 549 455 0-83 10-78 566 327 0-58 2-51 614 513 0-84 11-90 613 348 0-57 274 673 568 0-85 15-20 751 381 0-51 2'88 702 598 0-85 17-50 817 399 0-49 3'16 764 650 0-85 23-61 947 414 0-44 3-58 842 711 0-85 29-81 1017 417 0-41 4-20 926 783 0-85 35-71 1078 419 0-39 5-02 984 832 0-84 41-90 1114 419 0-38 576 1020 848 0-83 6-46 1050 864 0-82 7'20 1070 877 0-82 8-64 1110 897 0-81 10-26 1130 910 0-80 11-91 1150 913 0-80 17-50 1190 929 0-79 23-61 1195 929 0*78 35*71 1230 933 0-76 45-51 1230 933 0-76 Ewing, Phil. Trans , 1885, Part II., pp. 556 et seq. EXPERIMENTS ON RESIDUAL MAGNETISM. 317 residual magnetism to be noted ; then raised to a slightly higher value, again withdrawn, and so on ; so that the values of I and \ r were ascertained, corresponding to successive steps in the magnetising process. The results will be seen to bear out what has just been stated, and to furnish strong evidence in favour of the theory that the constraint of the molecular magnets is due to their mutual magnetic forces. Table XXX. gives the results of an experiment* in which an iron wire, l'58mm. in diameter, was tested, first in the annealed state, and then after being hardened by stretching beyond its elastic limit. Inspection of the figures will show that the ratio of residual to induced magnetism, which is at first small in both cases, rises to a maximum. This maximum, 1200 1000 800 600 400 300 vV / s Residua After tret Before stretching. 1 >efor e stretching. Mi gnet hint, Jf. O 4 40 44 48 12 16 20 34 28 32 H Fio. 148. Induced and Residual Magnetism in Iron, in the soft state and hardened by stretching. in the annealed wire, is so high as to imply that the rate of increment of residual magnetism is then not far short of the rate of increment of induced magnetism. The ratio afterwards falls off as the magnetising process passes into its third stage. Fig. 148 is drawn to exhibit the same results. It shows well how the residual magnetism approaches its maximum faster than the induced magnetism does, notably in the hardened wire. This mode of representing the results, where I and l r are given in terms of H, is not, however, well adapted to show Loc. . 559-60. 318 MAGNETISM IN IRON. what is the saturation limit towards which \ r is tending, nor what is the relative rate of increment of the two at various stages of the magnetising process. To bring these points out we may draw a curve showing \ r in relation to I (Fig. 149). We already know the saturation value to which I tends, namely, about 1,700 C.-G.-S. units ( 98), and it is not difficult by extrapolation of the curve in this new figure, to deduce ai approximate value for the saturation limit of l r . This is done in Fig. 149, where the broken lines form a con- jectural extension of the curves, beyond the range of the experi- ment, up to the saturation value of 1,700 for the induced I. It 1000 800 60 400 200 * COO 4OO 600 800 1000 1200 J40O 1600 1800 Induced Magnetism \ FIG. 149. Proportion of Residual to Induced Magnetism in Iron. appears from these that the saturation values of the residual magnetism in this specimen are approximately 970 when the metal is annealed, and 430 when it is hardened by stretching. An inspection of the curves in Fig. 149 will also show that after the initial stage is over, in which the residual magnetism is acquired less rapidly, the proportion which the increment of l r bears to that of I becomes as nearly as possible constant, &nd remains so (in the annealed wire) throughout a large part of the whole process of magnetisation. From the point 1 150, or so, up to 800 the curve is practically straight, and during that part of the process nearly the whole of the mag- EXPERIMENTS ON RESIDUAL MAGNETISM. 319 netism that is acquired goes to form residual magnetism. By Table XXX. we have H 1 Ir 1-30 3-16 Difference 140 764 624 85 650 565 So that, during this time, |-f , or quite 92 per cent, of the magne- tism that is being induced, contributes to the residual magnetism. After this the curve bends over rather quickly and ^becomes d\ much reduced. In other specimens of annealed iron the value of - during the steep stage was even more nearly unity. d\ This was the case in the experiment of Table XXXI., made with apiece of annealed iron wire 0'72mm. in diameter.* In this case a supplementary experiment was made to determine the Table XXXI. Induced and Residual Magnetism in Annealed Iron Wire, with and without Longitudinal Pull. Load = 0. Load = 4 kilos., or 976 kilos, per sq. mm. H 1 induced. Ir residual. Ratio L Ir H induced. T residual. Ratio I r _ 1-08 66 32-5 0-49 0-54 38 21 0-53 1-62 202 141 0'70 1-08 141 94 0-69 2-16 460 381 0-83 1-62 325 242 0-745 270 684 601 0-879 2-16 532 419 0-788 3-24 846 767 0-907 2-70 677 543 0-802 378 939 860 0-916 3-24 796 640 0-805 4-32 999 920 0-921 3-78 876 705 0-805 5-40 1071 994 0-928 4-37 937 754 0-804 6-48 1109 1024 0-923 4'86 978 787 0-805 7-56 1139 1046 0-919 5-51 1022 816 0-800 8-64 1157 1063 0-919 6-48 1067 856 0-800 972 1168 1074 0-919 8-64 1121 891 0-795 10-8 1178 1032 0-918 10-8 1162 913 0-786 13-5 1196 1095 0-916 13-5 1186 926 0-781 16-2 1210 1105 0-913 16-2 1204 933 0775 18-9 1219 1111 0-911 18-9 1211 939 0-775 21-6 1226 1116 0-910 21-6 1219 942 0-773 25-6 1236 1119 0-905 26-2 1232 946 0-768 * Loc. cit.,p. 629. MAGNETISM IN IRON. influence of longitudinal pull on the residual magnetism. After the test made in the ordinary condition of no load. a steady load of 4 kilos, or 9 '76 kilos, per sq. mm., was applied (a load well within the elastic limit), and the observations in the second portion of the Table were made. The pro- portion of \ r to I in each case is shown in Fig. 150, where the dotted line refers to the experiment in which wire was in a state of longitudinal tension. The full curve is for no load, and is conjecturally extended to find the saturation value of ! which is higher in this specimen than in the last, namely, 1210. The rate of increment of l r , relatively to I during the 1200 1000 800 600 400 200 r O 20Q 400 600 800 1000 1200 1400 1600 1800 Induced Magnetism I. Fia. 150. Proportion of Residual to Induced Magnetism in Soft Iron Wire, loaded and without Load. steep part of the curve is also greater, and the curve is prac- tically straight throughout a wider range. The following supplementary Table will bring this out : 1 V Differences of l r for 100 of 1. 1 w Differences of \ f for 100 of 1. 300 232 __ 800 722 99 400 328 96 900 822 100 500 426 98 1,000 921 99 600 524 98 1,100 1,020 99 700 623 99 1,200 1,100 80 EXPERIMENTS ON RESIDUAL MAGNETISM. 321 It appears from these figures that in the stage lying between = 300 and I = 1,100, or so, nearly 99 per cent, of the induction of magnetism was taking place by the turning round of the mole- cules into new lines, in which they remained when the magnetis- ing force was withdrawn. Scarcely any of the induced mag- netism was then being contributed by quasi-elastic deflections. After 1,100, the part played by quasi-elastic deflections began to be considerable. In the test made while the wire was loaded the limit to which the residual magnetism apparently tended was about 1020. A feature to be remarked is that in the earliest stage the curve taken with load lies above the curve taken without load, crossing it when I is about 200. The presence of longitudinal pull, though unfavourable to the retention of magnetism by annealed iron when the magnetisation is strong, is favourable to it when the magnetisation is decidedly weak Experiments made with other specimens gave results which agreed well with these. With another piece of annealed iron wire, 0'78mm. in diameter, the following (amongst other) readings were taken : * H 1 \r H i \r 0-86 26 6 5-40 991 898 198 164 96 6-81 1,067 946 2-66 478 378 11-20 1,166 1,014 378 806 696 17-24 1,212 1,042 [n this case between H = 2*66 and H = 6'81 the increment of I is 589, and that of \ r is 568 or 96 per cent, of the other. One more experiment of the same class may be referred to in further illustration of the influence of longitudinal pull on the retentiveness of iron.f In this instance the piece tested, a wire, 0'72m. in diameter and 30'5cms. long, had been hardened by stretching beyond its limit of elasticity before the observations were made. Its retentiveness was then examined when without load and also when various amounts of steady pull were in action. The curves of I, also of l r , each in rela- * Loc. cit. } p. 559, 40. Reference to the same Paper should be made for similar experiments with steel in the soft and hard states. \Loc. cit., pp. 625-8, 110. 322 MAGNETISM IN IRON. tion to H, have already been given in Figs. 105 and 106 (pp. 201-202) respectively ; but the points to which attention is now directed may be better seen by reference to Fig. 151, where curves of I r in relation to I are drawn for no load and for two values of the load. These show that a moderate amount of pull is very favourable to retentiveness in hardened iron, and greatly augments the saturation limit towards which I,, tends. A stronger pull, on the other hand, is less favourable, though under the greatest pull that was used in these experiments the wire continued to be more retentive than it was in the unloaded state. In a similar experiment made with steel wire, the amount of pull was further increased, and was then found to 1000 200 400 1600 1800 600 800 1000 1200 400 Induced Magnetism I Fia. 151. Proportion of Residual to Induced Magnetism in Hard Iron Wire, loaded and without Load. have an unfavourable effect, that is to say, it reduced the retentiveness in the upper part of the process below the value possessed by the unloaded wire. In Fig. 151 the apparent saturation limit of l r is about 460 when there is no load, and this is raised to 860 by the presence of a load of 12-2 kilos, per square mm. It is, of course very possible that a slightly greater or slightly less load than this would produce a still more favourable effect on the saturation value of the residual magnetism. When there is no load the rate of increment of l r with respect to I at the steepest part of the curve is about 0-7 ; but the presence of a suitable amount of load raises that to at least - 85. RETENTIVENESS AND THE MOLECULAR THEORY. 823 178. Retentiveness of Nickel. A reference to the curves which were given for nickel when the effects of stress were discussed in Chapter IX. ( 121-122, Figs. 95, 96, 98, and 99,) will show that the presence of longitudinal push has a highly favourable effect on the retentiveness of that metal, and on the maximum of residual magnetisation. Pull, on the other hand, is extremely unfavourable to the retentive- ness of nickel. A comparison of the results set forth in Figs. 98 and 99 shows that the value of , which is at no d\ stage great in unstressed nickel, rises to a maximum approach- ing unity when the metal is tested under the influence of strong longitudinal push. And it is, at least, highly probable that the same thing occurs at the steep stage of the magnetising process in the tests under torsion figured in Figs. 120 and 121, 141. 179. Amount of Retentiveness possible under the Mole- cular Theory. The full bearing of these experimental results on the molecular theory is not easily traced, and it would be scarcely profitable to speculate at present on the forms in which the groups of molecular magnets may conceivably be arranged. It is, however, important to notice that the theory leaves ample room for even the high retentiveness which iron is found to possess. To show that this is so we may consider what would be the saturation value of the residual magnetism if the structure consisted of lines like those of Fig. 145, with the centres of the molecules grouped in cubical order. It would be unreasonable to postulate any particular directional relation between the lines of centres and the direction in which the piece is to be magnetised. We shall suppose that the structure is an aggregate of tribes of molecules, with a cubical formation for each tribe, but with all possible variety in the direction of the lines of centres.* In the piece as a whole the directions of the lines of centre may be taken as uniformly distributed ; in other words, they might be represented by all possible radii of * The structure may be continuous ; in other words, the transition from one direction in the line of centres (at one place in the metal) to another direction at another place may occur through very slight distortion of the cubical formation. 824 MAGNETISM IN IRON. a sphere, drawn so that the points in which they meet the spherical surface are equally spaced. Suppose that a very strong magnetising force H is applied, so that saturation is produced, and that the force is removed. We have to consider how much residual magnetism will be found when the molecules have returned into lines in which they are stable, and which are as favourably directed for giving residual magnetism as the assumed structure of the substance will permit. Let a be the angle at which any line of molecules is inclined to the direction of H, before the process of magnetisation begins. Since the distribution of direction is by assumption uniform, the number of molecules whose inclinations are less than a will be to the whole number in the proportion which that part of a spherical surface cut off by a cone of semi-angle a (with its vertex at the centre), bears to the whole spherical surface. In the same way the number of molecules whose inclinations lie between c^ and a 2 will be proportional to the area of that belt of the sphere's surface which is cut off between cones with ^ and a 2 for semi-angle. Let the whole number of molecular magnets per unit of volume be n. Then the number whose inclinations lie between a 1 and a 2 will be .(V -n \ sm a a a. J a i Let be the inclination of a molecule after it has been dis- placed by the application and removal of H. If m is the moment of a single molecule, it contributes m cos 9 to the residual magnetism. The whole amount of residual mag- netism contributed by those molecules whose original direction ranged from a 2 to a lf will therefore be mn sm a cos 6 d a. And to find the whole residual magnetism we have to extend the limits of this integration to include all the initial direc- tions, from a = to a= 180 deg. We have next to consider the relation of 0, the inclination after H has been applied and removed, to the original inclina- tion a. Our assumption as to the structure makes the per- RESIDUAL MAGNETISM OP SATURATION. 325 ent deflection of the molecule necessarily either 0, or deg., or 180 deg. (1) Molecules for which a is less than 45 deg. will suffer no permanent deflection. This is because the original lines are more favourably directed than lines at right angles to them. For these molecules = a. (2) Molecules for which a is greater than 45 deg. and less than 135 deg. will be permanently turned through one right angle. For these molecules 6 = a - 90 deg., and cos = sin a. (3) Molecules for which a is greater than 135 deg. will be permanently turned through two right angles. For these molecules 9 = a - 180 deg. The whole residual magnetism, therefore, consists of the sum of three terms, namely _ mn [4- mn [ * -s-j smacosaacH--pr- 1 sm 2 a# A J Q A J 7T mn f ~9~J sinacos(a- 180)c/a. 4 The first and third terms are of equal value. The integral of the first term is 7T m n Fcos 2 a~~l 4 mn 1 The integral of the second term is m n Fa - sin a cos a~"| 4 __ m n /TT 1 \ 2 o ^~\I + 9/ l_ I " *^ X -* ~* s ~4 The whole residual magnetism is therefore This is the residual magnetism of saturation, and is to be compared with the induced magnetism of saturation, which is mn. Assigning to m n the value 1,700 this calculation shows that a continuous structure of the kind postulated, cubical in 826 MAGNETISM IN arrangement, is competent, on the molecular theory, to have nearly 1,500 units of residual magnetism, an amount consider- ably greater than experiments show even the most retentive iron to be capable of holding. It is clear, therefore, that the intermolecular magnetic forces are abundantly sufficient to account for residual magnetism, and that the actual structure of soft iron, and still more that of hard iron, steel, nickel, and cobalt, is less favourable to retentiveness than is the simple structure we have been discussing here. 180. Hysteresis and the Dissipation of Energy. The molecular theory shows that hysteresis is to be expected when- ever the magnetism of iron is caused to alter through anything more than a very narrow range. It occurs when the molecular movements are sufficiently great to involve the breaking up of old ties, and the formation of new ones, on the part of some, at least, of the molecules. In other words, the necessary and sufficient condition for hysteresis is that there must be an un- stable phase in the movement of some of the molecules. The change of magnetism will then lag behind the exciting cause of the change, whatever that may be. When the change is restricted within very narrow limits there is no hysteresis, for the molecular movements are then of the quasi-elastic type, occurring without rupture of the mole- cular ties. A very weak magnetic force, applied and removed (whether acting alone or superposed on a steady force), or a very small change of mechanical strain, will, if it be many times repeated, cause small changes of magnetism which do not involve hysteresis, because the molecular magnets are then suffering deflections with respect to which they are stable. But when the action is extended by using larger magnetic forces or larger variations of mechanical strain, so that the molecules are deflected far enough to become unstable, hysteresis comes into play. We find hysteresis, in fact, manifesting itself in all save the narrowest cycles of magnetising force, of longitudinal pull, of torsional strain, and so on. 181. Rotation in a Magnetic Field. Disappearance of Hysteresis when the Field is Strong. The molecular theory outlined in 171 receives striking confirmation from experiments ROTATION IN A MAGNETIC FIELD. 327 on the hysteresis due to rotation in a magnetic field. In. ordinary processes of magnetic reversal the field is reduced to zero and is then re-applied in the opposite sense. But reversal may also take place through a rotation of the field relatively to the iron, or of the iron relatively to the field, while the field preserves a constant intensity. In fields whose force is moderate, such rotation involves the breaking up of molecular groups in much the same way as that which occurs during a reversal of the field . The magnetic molecules, constrained by the force which they exert on one another, pass through conditions of instability and their movements involve dissipation of energy. Measurements of the work expended in causing a laminated cylinder of iron or steel to revolve between the pole of a magnet show that, for moderate magnetic forces, more energy is dissipated in this mode of reversal than in the other.* According to Prof. Baily's experiments it may be as much as fifty per cent, greater, when the force is such as to produce an induction not exceeding 10,000 C.-G.-S. units. But when the induction rises to about 15,000, the hysteresis in the rotating iron passes a maximum; after which it diminishes rapidly, with the result that, with an induction of 20,000 or so, it practically disappears and there is almost no work spent in rotating the iron. This very remarkable result was predicted by Mr. James Swinburne as a consequence of the author's molecular theory. Imagine a model consisting of a group of pivoted magnets placed near enough to one another to allow their mutual forces to take effect, and suppose a strong directing field to be applied to it with the result that the magnets are brought into sensibly perfect alignment, corresponding in iron to the condition of saturation. Then suppose the model to be slowly turned round while the strong field is maintained in action. Each little magnet will simply turn with the field, preserving its direction along a line of force, forming no ties with its neighbours, and showing no tendency to be set into oscillation. There is no breaking up of stable groups and no passage through unstable phases in the motion. In other words the group as a whole exhibits no hysteresis. But when the field * Baily, " On the Hysteresis of Iron and Steel in a Rotating Magnetic Field," Phil. Trans., 1896, Vol. 187, p. 715. 328 MAGNETISM IN IRON. is sufficiently reduced the inter-molecular forces resume their ascendancy, stable combinations are formed and broken as the rotation of the group proceeds, and work has consequently to be spent in keeping up the rotation. The conclusion that hysteresis should vanish when iron is rotated in a very strong field seemed at first so improbable that it was advanced by way of criticism of the author's 30,000 FIG. 151A. molecular theory. Mr. Baily's demonstration that hysteresis does, in fact, nearly vanish may be claimed as going far to prove its fundamental soundness.* Fig. 151 A shows Mr. Baily's results for soft iron. The Curve I. gives the relation of the hysteresis loss to B when the magnetic force was reversed in the usual fashion, and Curve II. gives this relation when the reversals occurred through rotation * Mr. Baily's results are supported by the experiments of Messrs. Beattie and Cliiiker, The Electrician, Oct. 2, 1896. INFLUENCE OF MOLECULAR AGITATION. 329 of the iron in the field. It will be noticed incidentally that in Curve I. the rate of increase of hysteresis with respect to B becomes much reduced when the iron is highly saturated a result which illustrates the fact that the Steinmetz formula ( 83a) has no application to such conditions. 182. Reduction of Hysteresis by Vibration, &c., and other Disturbances. We heave seen ( 84, 85, 129) that mechanical vibration lessens the differences of magnetic condi- tions that are brought about by hysteresis. It makes the metal readier to respond to any influence which tends to alter the magnetism. In a soft iron wire, where its effects are most conspicuous, it practically abolishes the distinction between what we have called the first and second stages of the magne- tising process, it destroys the retentiveness almost entirely, and it makes the magnetic effects of strain nearly reversible, so that the u on" and "off" curves for a cycle of loading come to be not far from coincident. The molecular theory makes all this intelligible. Vibration, producing small periodical displacements of the molecular centres, sets the molecular magnets oscillating. The displace- ment of the centres, and still more, perhaps, the oscillation to which that gives rise, allows the molecules intervals of com- parative freedom, and probably even goes so far as to vary the combinations in which they are grouped. Then if there is an external field the molecules yield readily to it in their freer intervals, and even when there is no external field a kind of shuffling goes on, one effect of which is to reduce residual magnetism. It may be, that in the removal of residual mag- netism vibration acts in the first place locally ; a cluster of molecules shaken up so that the residual magnetism of the cluster is less than that of surrounding portions will act to some extent like a cavity in the metal, producing a demag- netising field round about it. In the same way the demagneti- sation of a long iron rod under vibration no doubt begins at and about the ends, where there is a self-demagnetising field, and then extends itself towards the central portion. Any kind of disturbance that will give the molecular mag- nets intervals of freedom, or of diminished constraint, will tend to do away with hysteresis. Interesting examples of this will 380 MAGNETISM IN IRON. be found in a Paper by G. G. Gerosa and G. Finzi* in which experiments are described showing how cycles of reversal of magnetism become modified when a continuous, or periodically interrupted, or alternating current is made to traverse the piece under test, while slow reversal of the field goes on. The experiments dealt with iron, steel, and nickel wire in their an- nealed and hard state. A continuous current, traversing the ,vire while its longitudinal magnetism was being changed by applying and varying a longitudinal magnetic force by means of a surrounding solenoid, was found, as might be expected, to reduce the susceptibility of iron : the circular magnetisation maintained by the current in the wire left the molecules less than their usual freedom to obey the longitudinal force. When the longitudinal current, instead of being continuous, was rapidly interrupted without changing its sign, a mole- cular oscillation was set up which made the iron more than usually susceptible to weak longitudinal forces ; but when the field was strengthened the iron was still found to be less susceptible than when no current was passing through it. The mere make and break of the longitudinal current would, in fact, cause no more than a smajl variation of circular magnetisation, and would consequently do little to agitate the molecules. But when a rapidly alternating current of moderate strength traversed the wire, the suscep- tibility to longitudinal magnetisation was notably increased ; the magnetisation curve was found in that case to lie above the normal curve everywhere except in the region of strongest magnetisation. The violent agitation which was brought about by rapid reversals of circular magnetism destroyed nearly all trace of hysteresis, and obliterated the usual dis- tinctions between successive stages in the magnetising process. An illustration is given in Table XXXII. and Fig. 152, which relate to an experiment in which a piece of soft iron wire, 0'84mm. in diameter, was magnetised, first under the usual conditions (without any longitudinal current), and then when traversed by a rapidly alternating current of three amperes. * Kendiconti del R. Istituto Lombardo. Vol. XXIV., fasc. x., April, 1891. See also a Paper by Dr. Finzi in The Electrician, April 3, 1891, p. 672. SUPPRESSION OS 1 HYSTERESJS. 331 Table XXXII. Magnetisation of Iron U'itli and without an alternating longitudinal current. Without current. With current. H 1 H 1 1-43 50 0-17 75 2-24 119 0-82 290 3-62 367 4-33 803 576 773 12-3 1,178 12-5 1,162 42 1,537 42 1,500 76 1,121 2468 10 12 14 16 H In Fig. 152 the curve a is the normal curve, and b is the curve obtained when the alternating current was in action. The table shows how little residual magnetism is left in the second case. Fig. 153 exhibits in the same way the influence of the alter nating longitudinal current on a cycle in which the longitudinal magnetism of another iron wire was reversed. The normal figure a a collapses, as an effect of the molecular shaking, into b b, which is very nearly a single curve. Effects of the same kind were observed in steel and in hard iron, but the suppression of hysteresis was less complete. 332 MAGNETISM IN IRON. The single curve by which the relation of I to H may be represented when hysteresis is done away with by sufficiently violent agitation of the molecules, may be expressed, with fair accuracy, by the formula in which a and /3 are constants for a given specimen, and - is the saturation value of I. This formula, which was pro- 600 1200 10 8 10 H posed by Lamont and Frbhlich as a general means of ex- pressing the relation of magnetism to field, is, of course, of no service so long as hysteresis is operative, since I then depends not only on the existing value of H but on previous values : it will not even serve to express the curve of initial magnetisation in a virgin piece. But when hysteresis is eliminated, as in these experiments, it may be made to fit the curve reasonably well. Values of the constants a and /? will be found in the Paper from which these results are quoted. EFFECTS OP TEMPERATURE. 333 183. The Molecular Theory and the Effects of Tempera- ture. To see the bearing of the molecular theory on experi- mental results regarding the effects of temperature on mag- netic quality, we have to revert to Figs. 79, 80, and 81, 111, which show Hopkinson's determination of the permeability of iron at various temperatures, for a small, a moderate, and a fairly strong magnetic force respectively. In the first of these figures (Fig. 79) the magnetic force is only 0'3, and consequently the susceptibility at ordinary temperatures has the comparatively small value which we expect to find in the first stage of the mag- netising process. As the temperature is raised the susceptibility increases, at first but slightly, until a temperature of about 600C. is passed. Then the rise in susceptibility becomes very rapid. It quickly increases more than ten-fold, show- ing that the effect of this heating is to bring on the second stage of the magnetising process. Finally, at a temperature of 775C. or so there is an extraordinarily sudden fall of suscepti- bility, so sudden and complete that when the temperature reaches 785C. practically all magnetic quality is lost. Under a moderate force (of 4 C.-G.-S. units, see Fig. 80) there is none of the sudden rise of susceptiblity during heating which occurred when the force was weak. This is because, under the stronger magnetic force, the second stage in the magnetising process had already been entered before the piece was heated. Further, the loss of susceptibility at high temperature occurs much more gradually. Still more is this the case when the field is comparatively intense (Fig. 81). The first effect of heating is to hasten the transition from the first to the second stage of the magnetising process, that is to say, to make this transition occur at lower values of the magnetic force. This is probably due to two causes. Heating expands the structure, and that weakens the ties between the molecules by increasing the distances between their centres. We may conjecture that it also sets up oscillations which contribute to make the ties be more easily broken. When the field is weak, so that the second stage has not been reached while the metal is cold, heating is consequently favourable to magnetisation, and with an appropriate relationship of tempera- ture to field the metal is in a critical state, in which a small rise of temperature produces an immense augmentation of S34 MAGNETISM IN IRON. susceptibility by making groups of molecules which were stable at the lower temperature become unstable at the higher. This effect of heating cannot occur if the field is strong enough to have upset most of the molecules before heat is applied. Hence the curve of Fig. 80 has no sharp apex like that of Fig. 79. The case of a fairly strong field is more simple. Heating has two antagonistic influences. On one hand, the alignment of the molecular magnets is still being facilitated by the weakening of their mutual forces. On the other hand, the oscillations which they acquire have virtually the effect of reducing the moment of each molecule. Throughout a wide range of tem- perature the two influences nearly counterbalance one another ; the curve in Fig. 80 or Fig. 81 is nearly level for a great part of its course; but as the temperature becomes rather high the prejudicial effect becomes stronger, and the curve bends down. At this stage the molecules seem to acquire oscillation very rapidly, and a plausible conjecture to account for the complete loss of magnetic quality which ensues when the temperature rises a little higher, whether the field be weak or strong, is that the oscillation then becomes so violent as to develop into rotation. The establishment of this rotation would account for the energy which we know to be absorbed during heating, while the iron passes from the magnetic to the non-magnetic state ; and the rapid subsidence of this rotation into oscillations of com- paratively narrow range, during cooling, would in the same way account for the energy which the iron then gives out as it recovers its power of being magnetised ( 109). 184. Time-Lag in Magnetisation. The phenomena of magnetic viscosity, described in 88 and 89, have some light thrown on them by the molecular theory. We saw that when a weak magnetic force is applied to soft iron, or is raised a step, the resulting change in the magnetism is not completed instantly. There is a protracted creeping up of the magnetism, which goes on long after the magnetic force has become constant. We saw that the softness of the iron and the thick- ness of the specimen had a great influence on the extent of this EFFECTS OF PERMANENT SET. 335 time-lagging. A piece of hard iron, or a very thin piece of soft iron, showed little or no lag ; a thick piece of soft iron showed much, especially when the experiment was made at an early part of the second stage (stage B, Fig. 136) of the mag- netising process. It appears probable that an explanation of this is to be found by referring to the part that is played by the inertia of the molecules during the development of instability in molecular groups. The process of breaking up the primitive configuration takes time. The disturbance begins at a point where the primitive constraint is comparatively weak, and then slowly spreads itself even when the deflecting force is kept constant. An outlying molecule is first upset ; then its neighbours, weakened by the loss of its support, follow suit, and the action propagates itself from moleeule to molecule throughout the group. The surface molecules may be con- jectured to be the least securely held, and, therefore, to be the first to yield. In a very thin piece of iron, such as a fine wire, there are so many surface molecules in proportion to the whole number, and consequently so many points that may become origins of disturbance, that the breaking-up of the molecular communities is too quickly completed to allow much of this lagging to be noticed. Again, when iron is hardened by me- chanical strain the structure ceases to be even approximately homogeneous ; the molecules become as it were parcelled out into small groups with too few members to require much time for the spreading of the disturbance through a group, and in that case also the lagging is scarcely perceptible (see 185, belcw). 185. Effects of Permanent Mechanical Strain. It was shown in 66 that when a piece of iron is hardened by being strained sufficiently to take permanent set, the curve of I and H assumes a rounded form which allows this condition of the metal to be readily distinguished from that of an annealed piece. The successive stages of the magnetising process, in the hardened metal, become much blended. No part of the curve has nearly so steep a gradient as we find in dealing with annealed iron. The susceptibility is less throughout, and satu- ration is approached with greater difficulty. There is much less retentiveness ; on the other band, there is much more 836 MAGNETISM IN IRON. coercive force. We may refer back, in illustration of these differences, to Fig. 34, 66, where the curves for a cyclic pro- cess of reversal are drawn side by side for the same piece of iron in the annealed and hardened states. These differences, regarded in connection with the molecular theory, seem to indicate that mechanical set resolves a struc- ture which is relatively homogeneous and continuous into one which may be described as a patchwork of more or less distinct molecular groups. Hardening the metal by set makes only a slight change in the density, and it appears probable that it brings some of the molecules closer together, while the intervals between others are widened, with the result that groups aro formed in which the intermolecular forces between members of any one group are stronger than the forces which are exerted across the wider gaps between members of different neighbour- ing groups. The "gaps" tend to shear over the curve of I and H, to round the outlines of the curve, and to reduce the residual magnetism. The closeness of the members within each group increases the coercive force. Thus, without any necessary change in the density of the mi-tal, this modification of the structure would bring about the alteration in magnetic quality which is observed. Another consideration lends some support to this view. In hard metal there is exceedingly little, if any, "time- lag "in magnetisation. The explanation of "time-lag" suggested in the last paragraph seems to require that the structure of annealed iron be continuous throughout platoons of many mole- cules. As soon as the platoons are split up into little groups the action described there cannot be expected to take place. In connection with this it may be remarked that any inter- ruption of the continuity of the molecular structure tends in some measure to shear over the diagram of I and H, and, in par- ticular, to reduce residual magnetism, by making the conditions of constraint of molecules at and near the boundary differ from those of molecules far from the boundary. It seems probable that this consideration gives a clue to the " magnetic resist- ance" of joints, described above in 162-165. Let the separated parts of a cut bar be ever so well fitted together, the molecules at the boundary, and for some little distance from it, are not subject to the same conditions of constraint as subsist in the uncut bar, REPETITION OP MAGNETIC PROCESSES. 337 186. Effects of Repetition of Magnetic Processes. Space may be found here to refer shortly to one or two of the minor phenomena of magnetisation, which the molecular theory goes far to make intelligible. A consequence of the irreversible displacements which the molecular magnets suffer, together with the fact that the stability of each molecule depends on the configuration as- sumed by many molecules in its neighbourhood, is that in general a magnetising process has to be repeated more than once before its effects become strictly cyclic. In some cases a progressive change may be traced even during many repe- titions of the process. For instance, let a magnetising force be applied to a piece of soft iron, the strength of the field being regulated so that it brings the metal into what we have called the second stage of the magnetising process, when many of those molecules which are not already upset are on the verge of being upset. Let the force then be removed and reapplied. The configuration of the group during this re-application is by no means the same as it was during the first application, and accordingly we may expect that some of the molecules which were just able to stand in the first instance yield in the second owing to the changes which have meanwhile taken place in the grouping of their neigh- bours. The re-application of the magnetising force may there- fore be expected to produce a somewhat stronger magnetisation than was produced when the force was first applied. To a less degree, a third application of the force should make the mag- netisation rise a little higher still, and so on. Similarly, the second removal of the force should leave more residual magnetism than is left after the first removal. But we may expect that the limits between which the magnetism changes when the magnetising force is applied and removed will come to be closer in each repetition of the process ; the molecular " accommodation " which goes on as one after another of the doubtful molecules is upset has the effect of narrowing the range through which the magnetism alters in succeeding cycles. That these anticipations are in accord with the results of experiment will be seen from the following paragraphs, mainly extracted from a Paper which was written without reference 338 MAGNETISM IN IRON. to the light which the molecular theory throws upon the matter.* When a magnetising force is first applied, then removed, and then re-applied, whether suddenly or gradually, theresulting value of I is somewhat higher than that reached by the first application. A third application gives a somewhat higher value, and so on, the effects apparently approaching an asympotic limit. This appears to have been first shown by the experiments of Fromme.f At each removal of the magnetising force the residual mag- netism is also left somewhat greater than before. And this second action (the increase of the residual magnetism) exceeds the increase of the induced magnetism, with the result that the changes of magnetism between residual and induced diminish in range with successive removals and re-applications of the magnetising force. The following observations (Table XXXIII.) were made by the ballistic method on a long piece of soft annealed iron wire. The readings are given without reduction to absolute measure ; they relate to a point which falls early in the steep part of the curve of magnetisation. Table XXXIII. Magnetising current. Throw of ballistic galvano- meter. Magnetism. Induced. Kesidual. First made 203 -53-6 + 54-2 -47-8 + 487 -457 + 46-6 -44-9 + 46-1 -44-0 + 45-6 -42-6 + 43-1 -39-5 + 39-8 203 203-6 204-5 205-4 206-6 208-2 149*-4 155 : 8 158 : 8 160 : 5 162 : 6 broken . . . made broken ... made broken made broken made . broken made After many makes and breaks broken made After many more makes and breaks made * Ewing, Phil. Trans., 1885, p. 570, 54-58. t Pogg. Ann., Ergbd., vii., 1875, and Wied. Ann., iv., 1878. REPEATED MAGNETISATIONS. 339 Similar results were repeatedly obtained, both with freshly annealed wires and wires from which a previous strong mag- netism had been shaken out by tapping. In curves showing the relation of B or I to H the same thing exhibits itself in what may be called the over-closing of loops formed by re- moving and re-applying a given value of H. A good example of this is furnished by Fig. 44, 78, which shows how much more considerable the action now spoken of is at early than at late stages of the magnetisation. The following experiment (Table XXXIV.) dealing also with annealed iron shows that the same kind of action occurred when the current was slowly changed by the liquid rheostat of Fig. 17, 41, and the magnetism was determined by a magnetometer : Table XXXIV. Magnetising current. H Magneto- meter deflec- tion. 1 In- duced. Resi- dual. Gradually raised to ... 70 2-46 2-46 2-46 93 65 97 70 103 80 298 sib 330 208 224 256 ... ,, raised to ... 70 , , reduced to ... Then 100 sudden makes and breaks ,, reduced to ... Incidentally, this experiment illustrates another point, to which attention was long ago directed by Von Waltenhofen that the amount of magnetisation gained or lost by applying or removing a given magnetising force is greater when the change of force is sudden than when it is gradual. Other instances of the same thing will be found in the experiment quoted below. When a magnetising force is applied and then repeatedly reversed, the changes of magnetism, instead of being strictly cyclic, form what may be termed unclosed loops. An instance of this is given by Fig. 52, 82, which shows a series of these unclosed loops in the magnetisation of steel wire. The result is, as in the case of repeated removals and reapplications of 340 MAGNETISM IN IRON. magnetising force, that successive repetitions of the process give a gradually diminishing range of magnetic change. This action, like the one just described, occurs most conspicuously at points in the early part of the curve of magnetisation. The observa- tions in Table XXXV. were made specially to exhibit it, on a piece of annealed iron wire, 400 diameters long, by the magneto- metric method. Table XXXV. Magnetising current. Magneto - meter deflection. Remarks. Gradually raised to + 190 190 + 190 -190 + 146 -141 + 127 -133 Here there is gradual diminution of range. > This part of the ope- reversed -^o + 190 -190 + 120 -132 ration is shown in Fig. 154. Suddenly + 190 -190 + 190 + 124 -136 + 123 fHere there is an in- 1 crease of range due I to the suddenness of |^ these reversals. Fifty double reversals, then Suddenly reversed to + 190 -190 + 111 -127 ( But after repeating 1 the sudden reversals { often enough the range becomes (^ smaller than ever. f And a gradual repe- Then gradually ,, + 190 + 108 J tition of the cycle 5 J > -190 -126 I causes still a further L reduction of range. In the first part of the above operations, during the five gradual reversals of magnetising force, intermediate readings were taken, which enabled the curves shown in Fig. 154 to be drawn. These show at a glance the manner in which the range of magnetic change diminishes. Sudden reversals, following on these, cause at first an increase of range, thus illustrating the comparative effects of gradual and sudden change of H, but on being repeated many times they reduce the range to a lower value than before. The same piece of wire was next subjected to a magnetising force about five times greater than the above, and was then demagnetised by reversals. Experiments similar to the above REDUCTION OF RANGE IN SUCCESSIVE CYCLES. 341 were then made on it, when it was found that the tendency to a diminution of range with repetition of a cyclic alteration of mag- netising force had disappeared. The diagram, Fig. 155, shows the effect of applying, reversing, and re applying the same mag- netising force as in the former case, after the wire had been demagnetised by reversals. It shows that the changes of mag- netism are now cyclic. The same result was given by other specimens, which when freshly annealed gave much diminution FIG. 154. Repetition of Magnetic Cycles in Annealed Iron "Wire. of range, but when demagnetised by reversals after the magne- tising force had been raised to a high value, were found to have lost this property. In this respect, then, a wire demagnetised by reversals differs from the same wire in its primitive annealed state. It will be seen, too, by comparing figures 154 and 155, that the unsymmetrical susceptibility with respect to forces of opposite signs which exists in the annealed wire has given place to a very perfect symmetry after demagnetisation by reversals. 342 MAGNETISM IN IRON. Re-annealing the wire restored all the characteristics of the pri- mitive state. The following observations (Table XXXVI.), made with another piece of annealed iron wire at a part of the curve very sensitive to the actions now spoken of, show well the reduction of range by reversals, and then the rise of magnetism, induced and -H -I H Fio. 155. Cyclic Process in Annealed Iron Wire previously demagnetised by reversals. residual, which is produced by successive removals and re-applica- tions of H. This last occurs in a very marked way after the range of magnetic change has been reduced by reversals of H. The two directions of the current will for brevity be distinguished as A and B. The changes were sudden, and the magnetism was determined by the direct magnetometric method. A want of symmetry is very noticeable here between the positive mag- netisation due to the current A, which is first applied, and the subsequent negative magnetisation due to the equal and opposite current B. MAGiNETlC SET IN STEEL. 343 Table XXXVI. Magnetising Current. Magneto- meter deflection. Kemarks. MadeA + 232 B -110 A + 180 ' B -101 A + 172 Diminution of range B -100 by reversals. Twenty reversals, then Made B - 95 A + 158 Broke A + 150 Made A + 200 Broke A + 193 Rise of magnetism (in- IVIade A + 206 duced and residual) BrokeA + 201 }- by successive re- Twenty makes and breaks, then-- + 205 movals and re-appli- tions of H. Made A + 209 1 Then reversals again Made B -105 A + 178 The diminution of Forty reversals then Made A + 163 > range by reversals is I again conspicuous. B... -105 Broke and remade B -136 Ditto twenty times -175 The magnetisation of steel exhibits, even more than that of iron, reduction of range with successive reversals of H, and want of symmetry between the values of I induced by suc- cessively applied + and - values of H. Fig. 156 shows the changes of magnetism which were undergone by an annealed steel wire wben a magnetising force of 15 C.-G.-S. units was applied, removed, re-applied, reversed, and again reversed twice. The want of symmetry between the positive and negative values of tbe magnetism is very marked in this example : the steel acquires a strong magnetic set towards the side of the first magnetisation. 187. Effects of Elastic Strain. In an earlier chapter ( 120 142) an account has been given of experiments made to investigate the effects of stress on the magnetic quality of 344 MAGNETISM IN IKON. iron and the other magnetic metals. Without attempting any full discussion of these results from the point of view which the molecular theory affords, we may refer to one or two general features where a molecular explanation seems comparatively easy. That stress should produce an influence on magnetic quality is a probable result of the strain to which the stress gives rise. The effect of a simple longitudinal stress is, as we have seen, to make the metal, originally isotropic in its magnetic quality, FIG. 156. Repetition of Magnetic Cycles in Annealed Steel. become scolotropic, and it may be conjectured that this happens through differences becoming established in the pitch of the molecular magnets, in lines respectively along and across the direction of the stress, whereby old lines of molecules break up and new lines are formed. A uniform dilation or a unifoi m compression (with equal intensities of stress in all directions) might be expected to have a much less considerable influence on magnetic quality than a simple stress has. Experiments on the effects of such stresses are wanting ; it may be antici EFFECTS OF STRAIN. 345 pated that effects resembling those due to change of tem- perature would be observed. Thus we might expect to find a uniform pressure in all directions associated with a general reduction of magnetic susceptibility. The experiment would be an interesting one to carry out, especially in nickel, where ( 122) the susceptibility is known to be greatly increased by a single stress of compression applied in the direction of magnetisation. A stress of simple pull will lengthen those rows of molecules which lie more or less along the axis of the stress, and will shorten those rows which lie more or less across the axis. This is enough of itself to develop differences of magnetic sus- ceptibility in the longitudinal and transverse directions ; and the difference is probably much intensified by a re-arrange- ment of the molecular rows, the longitudinal rows being more or less broken up and transverse rows formed. The length- ening of the longitudinal rows will tend to increase the sus- ceptibility ; the shortening of the transverse rows, and still more the secondary consequence of stress, namely, the forma- tion of new transverse rows, will tend to reduce it. It seems that in nickel the reducing effect is the dominant one ; in iron, on the other hand, we find a conflict of influences which makes pull favourable or otherwise according as the magnetisation is less or greater than a critical value. The large magnetic changes due to torsion which are seen in experiments on nickel, such as the reversal of magnetism which Nagaoka found when a loaded nickel wire was twisted to and fro to alternate sides ( 142) appear to be secondary effects, due to the reconstruction of molecular rows which become unstable when the molecular centres are displaced by the strain. It is the existing magnetism of the piece that is being affected, rather than its susceptibility to induction by the field. An obvious conclusion from the molecular theory is that there should be, as we know there is, hysteresis in the changes of magnetic quality that are associated with changes of stress, and also that the condition arrived at by first applying a load and then magnetising should in general be different from the condi- tion arrived at by first magnetising and then applying a load. (See 120131.) Another fact which the molecular theory serves to explain is the important difference which experiments reveal between 346 MAGNETISM IN IRON. 260 .240 230 the effect that is produced by the first application of a stress, and the effect that is produced when the same stress is applied after it has been previously applied and removed many times. After what has been said above in 1 27, a brief reference to this matter will suffice. Provided the magnetising force is not very strong, the first application of load, when the piece hangs in a steady magnetic field, upsets molecules which were nearly upset before the load was applied. Removal of the load does not make these molecules recover the position from which the application of the load disturbed them. Thus successive loadings and unloadings, especially in a weak field, serve, as it were, to shake in the magnetism; and, if residual magnetism is dealt with, the field having been removed, suc- g A I cessive loadings and unloadings serve to shake it out. Examples of this have already been given in Figs. 108 and 109, where the effects of a first loading and unloading are readily distinguishable from those that oc- cur after a cyclic regime has be- come established by repetition of the cycle of loads. Fig. 119, exhibit- ing certain effects of successively ap- plied twists to alternate sides, is also an instance in point. When we load a wire in a strong field we find, as the theory would lead us to expect, that the cyclic regime is quickly attained ; a second loading is enough to show that the initial disturbing influence of the stress is exhausted. In weak fields, the loading has to be repeated many times before that is the case, and the first disturbance is sometimes immensely greater than the alter- ation of magnetism that accompanies each application and O l 2 Load %n kilos. FIQ. 157. Effects of Loading a Soft Iron Wire in a Weak Magnetic Field. HYSTERESIS IN MOLECULAR GROUPING. 347 removal of the load after a cyclic condition has been reached. Fig. 157 gives an example. The specimen dealt with there was a long wire of soft annealed iron, 0'76mm. in diameter, which hung in a weak field (H=0'34). A load of 1 kilo- gramme applied for the first time raised the magnetism from 159 to 220 (in arbitrary units). Removal of the load reduced it only to 218. Re-application brought it up to 222 ; a second removal reduced it to 220J. A third application made it 224, a third removal 222, and a fourth application 225J. Then the load was increased to 2 kilogrammes, and the magnetism went up at a bound to 247, after which successive removals and re-applications of that load produced but slight changes which tended gradually to assume a cyclic character when the operation was repeated many times.* 188. Hysteresis in Changes of Molecular Configuration, apart from the Existence of Magnetisation. In 133-135 experiments have been referred to which show that when iron is subjected to cyclic variation of stress, its structure undergoes changes that involve hysteresis, even when no magnetic force acts upon it, and when there is no magnetisation of the piece as a whole. The molecular theory makes the reason of this suffi- ciently apparent. Elastic strain brings about a rearrangement of the molecular grouping; old combinations break up and novel combinations are formed, although no magnetic forces are con- cerned other than the forces which the molecular magnets exert on one another. These changes of configuration involve unstable movements on the part of the molecules, and hysteresis consequently manifests itself, when the piece is carried through a cycle of strain. We find, for instance, that when an iron wire under tension is loaded and unloaded, by putting on and taking off weights, there is a distinct difference in the physical state of the metal, under one and the same intermediate amount of weight, during loading and during unloading. The difference shows itself in magnetic susceptibility, in thermo-electric quality,! and possibly in many other physical qualities of the material. It continues to be found when the cycle of loading * For details of this and other experiments illustrating the point now referred to, see Phil. Trans., 1885, p. 594, et seq. t See a Paper by the Author, Phil. Trans., 1886, p. 361. 348 MAGNETISM IN IRON. is repeated, and its character is just such as the molecular theory would lead us to expect. This hysteresis in molecular configuration, apart from all actual magnetisation, which exhibits itself when the piece is carried through a cycle of elastic strain, has one important consequence. It implies that the elasticity of the substance is not perfect. The unstable movements of the molecules, to which it is to be ascribed, result in a dissipation of energy. More work has, therefore, to be spent in stretching the piece, while loads are being put on, than is recovered when the loads are taken off in other words, the stress that corresponds to any given intermediate value of the strain must be greater during the application of the load than during its removal. There FIG. 158. must be hysteresis in the relation of strain to stress ; and, as we have seen already ( 135), this conclusion is borne out by experiment. 189. Experimental Study of Molecular Groups by means of Models. It is extremely helpful, in considering the con- straint which the molecular magnets suffer in consequence of their polar forces, to experiment with a model consisting of a number of short steel magnets, pivoted like compass needles on fixed centres, and placed near enough to one another to allow their mutual control to be felt.* Such a model is readily made out of pieces of stout magnetised steel wire, bent, as in Fig. 158, to bring the centre of gravity below the pivot point. A recess for the pivot is stamped by a centre punch in the hollow of the *Proc. Roy. Soc., 1890, Vol. XL VIII., p. 342 j PhiL Slag , September, 1890. MODEL ILLUSTRATING MOLECULAR THEORY. 349 bend, and the pivot itself is a needle stuck, with the point upwards, in a small block of lead or of wood. Instead of a wire, a piece of steel plate may be used for the magnet, and this may have any form given to its polar extremities, from sharp points to semicircles. The magnets being of hard stee\ strongly magnetised, are practically unaffected (as to the intensity of their magnetism) by the comparatively weak external mag- netic forces which are applied for the purpose of turning them into line. The external force may be applied by a coil wound in an open manner over a light framework, within which the group of magnets is placed, the open winding allowing the behaviour of the magnets within to be observed. Or a larger coil placed entirely underneath the group may be used ; or, better still, a pair of closely-wound short coils placed one on either side of the group. This last form is especially convenient when the behaviour of the group is to be exhibited by projecting them on a lantern screen. For that purpose short magnets are neces- sary, and the magnets used for small pocket compasses will be found very suitable ; the pivots themselves may also be cut out of such compasses and cemented, at proper distances, on a glass plate. To exhibit the effects of strain, the pivots may be arranged on a framework of jointed wooden rods, forming two crossed sets of parallel lines; by placing the pivots at the joints, or midway between the joints, some of the effects of simple shear or simple pull and push may be studied. Fig. 158A shows such a model, in which the field is produced by two coils at the ends, and the magnets are supported on centres cemented to a sheet of glass, which may bs turned round to exhibit effects of rotation. A model of this kind allows the three stages of the mag- netising process to be readily distinguished. The phenomena attending reversal of magnetism, the dissipation of energy in hysteresis, the conditions that promote residual magnetism, the comparative effects of slow and sudden changes in magnetic force, the primitive and final effects of strain, the influence of vibration, the existence of time-lag, are all matters of which the model gives effective illustration. The manner in which the resultant polarity of the group of pivoted magnets changes when the field is applied, reversed, or varied in any way, is sufficiently evident on mere inspection of 350 MAGNETISM IN IRON. the group. It may, however, be determined quantitatively by using a magnetometer in the ordinary way, taking care to com- pensate for the action of the coil which supplies the magnetic field by placing in series with it a second coil, the position of which is adjusted so that it may annul the deflection which the first coil by itself would produce. A group of magnets examined in this way, when carried through a cycle of con- figuration by applying and reversing the directive force of the coil, gives what we may call curves of magnetisation, in which all the main characteristics of the ordinary curves for iron FIG. 158A. appear, though, of course, the limited number of magnets which it is practicable to use in such an experiment makes the steps of the process more jerky than they are when we have to deal with the multitudes of molecules in a piece of solid metal. Curves obtained by this means, showing the reversal of a group of twenty -four little magnets (like the one shown in Fig. 158) under reversal of the magnetising field, are given in Fig. 159.* * Fig. 159, for which the author is indebted to Mr. Glazebrook, repre- sents the results of an experiment by Mr. J. W. Capstick, made in answer to a question set in the practical examination of the Cambridge Natural Science Tripos. 1891. Curves of this kind were first published by Mr. Arthur Hoopes in the Electrical World (New York), May, 1891. See The Elec- tricifw, May 29, 1891. EXPERIMENTS WITH GROUPS OF MAGNETS. 351 The correspondence between the curves of magnetisation and those got from a group of little magnets becomes even closer when the number of magnets in the group is largely increased. In experiments by Miss Klaassen and the author* as many as 130 magnets were used to form the group, and it was found that not only the main features of the magnetising process, but also some of the less obvious features referred to in 186, FIG, 159. Cyclic Process applied to a Group of Twenty-four Pivoted Magnets. were reproduced with surprising fidelity. Thus, for instance, differences resembling those illustrated in Fig. 154 are found when successive cyclic variations are made to take place in the directing field to which the group is exposed, provided the group of magnets has simply been left to settle after a casual "shuffling." But if the group has previously been Phil. Trans., 1894, p. 1,036. 352 MAGNETISM IN IRON. exposed to reversals of a gradually diminishing directive orce, the subsequent behaviour resembles that of the iron in Fig. 155. The study of what happens in a group of small magnets goes to confirm the theory that the molecules of a magnetic metal are controlled, as to direction, simply by the forces which they exert on one another as magnets, and, as has been pointed out, the theory receives its most complete confirmation when the group is made to revolve in a strong directing field, 190. Ampere's Hypothesis as to the Nature of the Mag- netic Molecules. Granting, as we very well may (in view of the considerations summarised in this chapter), that the process of magnetising consists in turning round molecules that are already magnetic, so that their axes tend, under the directing force of the applied field, to approach a particular direction, the question still remains, to what is the primitive magnetism of the molecules due ? Weber's theory does not help us to an ex- planation of the fact, which it postulates, that each molecule is a permanent magnet. According to the hypothesis of Ampere the magnetism of the molecule is due to an electric current continually circulating within it in other words, the molecule is a conducting circuit in which a current flows, and when a directing field acts, the channel in which this current flows tends to set itself at right angles to the direction of the field, just as does the coil of an electro-dynamometer. Ampere's theory, therefore, explains all the phenomena of magnetisation as consequences of the mutual action of electric currents. According to it, in magnetising a piece of iron we are dealing with the forces which exist between the current in an external conductor and the currents in molecular circuits within the metal, which are prevented from immediately putting themselves into perfect parallelism with the external circuit only because of the forces which the currents in the molecules exert on one another. In this view the model of a magnetic metal should be constructed by using not pieces of permanently magnetised steel to represent the molecules, but little coils, free to turn, in each of which an electric current flows continually. HYPOTHESES OP AMPERE AND WEBER. 353 The molecular channels must be supposed to offer no resist ance as conductors, otherwise the primitive currents would require energy to be expended in maintaining them. When a field is applied it tends to turn the molecular cir- cuits, and it also induces supplementary currents in them. These induced currents are superposed on the primitive cur- rents ; their strength depends on the inclination of the circuit to the field ; and their general effect is to reduce the primitive currents. Whether they will do so to any considerable extent depends on the area and the self-induction of the molecular circuits, and on the primitive strength of the currents in them.* Thus if the primitive currents are strong and the other conditions favourable, very little reduction of the primitive strength takes place through this induction of current by the applied field. In that case the molecular circuits are nearly equivalent to strictly permanent magnets, and merely turn in response to the field, without suffering any material loss of intensity. Probably this represents what occurs when iron or any of the other strongly magnetic metals is magnetised. When the primitive molecular currents are weak the induction of opposing currents by the application of a magnetic field may modify the resultant strength very greatly ; and in particular, when there are no primitive currents at all, but only conduct- ing molecules ready to have currents induced in them, the application of the field will induce currents which give to tho piece a polarity of the kind opposite to that which it acquires in ordinary magnetisation. By recognising the existence of these induced currents Weber thus extended Ampere's theory of molecular conducting circuits to account for diamagnetism. But even when there are strong primitive currents, as we must suppose there are in the molecules of iron, the induction of opposing currents, in consequence of applying a magnetic field, will go on to some extent, and there is a stage at which its influence may be appreciable. This is when the piece is saturated when all the molecular circuits are turned into planes perpendicular to the direction of the field. In that position they are as favourably placed as possible for the * See Maxwell's " Electricity and Magnetism," Vol. II., chap. xxn. A A 354 MAGNETISM IN IRON. induction in them of currents opposed to the primitive cur- rents. When the field is further strengthened, the resultant current in each molecular channel is reduced, and as the channels are already all perpendicular to the field, the only effect of increasing the field is to reduce the magnetisation of the piece by reducing the strength of each molecule. The Ampere -Weber theory, therefore, leads us to conceive of the magnetism of iron as tending to pass a limiting value when saturation is reached, after which a stronger magnetising force should actually weaken the magnetism. The results of experiments with very strong fields neither confirm this nor contradict it. They show that when the condition of saturation has been approached the field may be strengthened ten-fold or more without any material change in the magnetisation, either in the way of addition or loss. But the conditions under which such experiments are carried out make very accurate measure- ment impracticable, and a small reduction of the magnetism might pass undetected. It is probable enough that stronger fields still must be used to discover it, for the reduction which is to be expected as a consequence of induced currents in the molecular channels is slight at the most, and in the approach to saturation, which is long drawn out, the continued deflection of the molecules tends to counterbalance any effect that may be produced by a small loss of moment on the part of each. CHAPTER XII. PRACTICAL MAGNETIC TESTING. 191. Practical Magnetic Tests. Of the various methods of magnetic measurement described in earlier chapters, a considerable number are suited only for use in laboratory research. In this chapter an account will be given of some methods which recent experience has shown to be useful where the problem is to make such tests of iron and steel as will serve the purposes of the electrical engineer. The ballistic method, in one form or another, is largely used in such tests, both directly and for the purpose of testing standard pieces which may afterwards be used in methods of testing where the process consists in simply comparing the specimen under examination with a standard piece whose magnetic quality is known beforehand. It is scarcely too much to say that the ballistic method, whether as a direct means of testing specimens or as a means of testing standards to be used in comparison with specimens, is the basis of practically all workshop tests of magnetic quality. The materials to be tested are chiefly wrought iron and mild steel forgings and steel castings, for permeability, these metals being used for dynamo field-magnets, and also rolled sheets of iron or steel, for hysteresis and occasionally for permeability, these forming the cores of transformers and armatures. The " steel" castings, which are now very extensively used for field-magnets, consist of very nearly pure iron, and are called steel only because they are made not by puddling, but by a modified Bessemer or other " steel " process. Much of the sheet metal is rolled from Swedish charcoal iron, but sheet metal produced by steel processes is also AA 2 356 MAGNETISM IN IRON. used for magnetic purposes, and some of it appears to have more immunity than Swedish iron from " ageing " under exposure So prolonged warmth. The sheet metal is supplied in the form of annealed stampings, and any tests should be made on specimens which have been treated in the same way as the rest ; that is to say the test pieces, after being stamped in a form appropriate for testing, should be annealed under the same conditions as other stampings. In permeability tests of forgings and castings for dynamo magnets it is generally useful to obtain data for a curve giving the relation of B to H from, say, B = 10,000 to B = 18,000. The lower part of the curve is not, as a rule, wanted, and it is very rarely that inductions above 18,000 are in question. In hysteresis tests of iron or steel stampings for transformers a knowledge of the hysteresis loss in a cycle where the limits of B are about 4,000 will generally suffice, the formula of Steinnietz serving sufficiently well to calculate from that the hysteresis at higher or lower inductions within a moderate range. If, however, the hysteresis of armature stampings working at much higher induction is in question, it is more satisfactory to make a direct determination of the loss in a correspondingly high cycle than to infer the loss from a low cycle measurement. Permeability tests are not, as a rule, required in dealing with transformer iron. There the question of hysteresis is all-important, and a material which is good in respect of hysteresis may safely have its permeability taken for granted. With dynamo stampings the question of permeability under strong or moderately strong forces comes in, just as it does in dynamo forgings or castings, and similar tests are appropriate. 192. The Ballistic Method. Fig. 160 shows an arrange- ment for ballistic tests which the author has found convenient. It is equally applicable to tests of permeability only and to tests in which B-H cycles are to be determined in order to evaluate the hysteresis. The specimen A is wound with primary and secondary coils, which are shown diagram- matically on separate parts of the ring in the figure, but are BALLISTIC TESTS OP RINGS. 357 actually wound in a uniform or nearly uniform manner round the whole circumference. The magnetising current comes from the battery B, which consists preferably of three or four storage cells ; its strength is regulated by the adjustable resistance E and is measured by the ampere-meter G. The reversing key K has its terminals e and d connected through an adjustable resistance E 2 , which may be short circuited by the key S. The effect is that when S is closed the throwing over of the reversing key simply reverses the current without FIG. 160. Arrangement for Ballistic Tests. altering its strength, but when S is open the reversing keynot only reverses the current, but changes its strength by an amount depending on the value of B 2 . This device is required in taking cyclic B-H curves, but is not used in simple tests of permea- bility ; and if the arrangement is to be used for permeability tests only the key S and resistance K 2 may be dispensed with, and a permanent connection is then made between e and d. The two-way key C allows the current to be sent either into the primary coil of the specimen or into the primary coil of E, which is an induction coil without an iron core. It consists 358 MAGNETISM IN IRON. of a primary wound on a brass tube or other non-magnetic core, the dimensions of which are carefully measured, and in the middle of the length a short secondary coil is wound over this, which is permanently connected in series with the secondary coil on the specimen and with the ballistic galvano- meter G r The function of E is to serve as a means of standardising the ballistic galvanometer. From the known dimensions and winding of the coils it is easy to calculate the number of lines of induction which cut the secondary circuit when a given current, say one ampere, is reversed in the primary of E. The ballistic effect of this reversal is observed, and in this way it is ascertained how many lines of induction correspond to one scale division of the ballistic galvanometer. In calculating the induction constant for the coil E account must, of course, be taken of the effect of the ends. A resistance E 3 in the secondary circuit allows the sensibility of the ballistic galvanometer to be regulated, and this resistance must be made sufficiently great to prevent a too rapid damping of the swing. The author prefers a galvanometer of the D'Arsonval type for this work : its period is readily made long, and the swinging chief object of the Author has been to enable those who are not familiar with the principles and practice of rating to ascertain for themselves whether the Rateable Value of their property is reasonable or excessive, and thus avoid unnecessary expense at the outset. Boult COMPREHENSIVE INTERNATIONAL WIRE TABLES FOR ELECTRIC CONDUCTORS. By W. S. Boult. Price 43. post free. Broughton ELECTRIC CRANES AND HOISTS. By H. H. Broughton. In Ihe Press. Carter MOTIVE POWER AND GEARING FOR ELECTRICAL MACHINERY: A Treatise on the Theory and Practice of the Mechanical Equipme.it of Power Stations for Electric Supply, and for Electric Traction. By the late E. Tremlett Carter, C.E., M.I.E.E. 650 pages, 200 Illustrations, Scale Drawings and Folding Plates, and over 80 Tables of Engineering Data. In one volume. New edition rvised by G. THOMAS-DA VIES. Now Ready. 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"MOTIVE POWER AND GEARING FOR ELECTRICAL MACHINERY" is a handbook of modern electrical engineering practice in all parts of the world. It offers to the reader a means of comparing the central station practice of the United Kingdom with that of America, the Colonies or other places abroad ; and it enables him to study the scientific, economic and financial principles upon which the relative suitability of various forms of practice is based, and to apply these principles to the, design or working of plant for any given kind ot work, whether for electrical supply or for electric traction. It is a treatise which should be in the hands of every electrical engineer throughout the world, as it constitutes the only existing treatise on the Economics of Motive Power and Gearing for Electrical Machinery. Cooper PRIMARY BATTERIES: THEIR CONSTRUCTION AND USE. By W. R. Cooper, M.A. Fully Illustrated. Price IDS. 6d. nett. Authors Preface Extract, Primary Batteries form a subject from which much has been hoped, and but little realised. But even so, it cannot be said that the advance has been small ; and consequently no apology is offered for the present volume, in which the somewhat scattered literature of the subject has been brought together. Recent years have seen important additions to the theory of the voltaic cell, and therefore a considerable number of pages have been devoted to this part of the subject, although it is impossible to do more than give a superficial sketch of the theory in a volume like the present. With regard to the practical part of the subject, this volume is not intended to be encyclopaedic in character ; the object has been rather to describe those batteries which are in general use, or of particular theoretical interest. As far as possible, the Author has drawn on his personal experience, in giving practical results, which, it is hoped, will add to the usefulness of the book. Owing to the importance of the subject, Standard Cells have been dealt with at some length. Those cells, however, which are no longer in general use are not described ; but recent work is summarised in some detail so as to give a fair idea of our knowledge up to the present time. It has also been thought well to devote a chapter to Carbon- Consuming Cells. Very little has been written upon this subject, but it is of great interest, and possibly of great importance in the future. Cooper See "THE ELECTRICIAN" PRIMERS, page n. Dick and Fernie MAINS AND CABLES. By J. R. Dick, B.Sc., and F. Fernie. Down " THE ELECTRICIAN" HANDY COPPER WIRE TABLES AND FORMULAE FOR EVERYDAY USE IN FACTORIES AND WORKSHOPS. By P. B. Down, Wh.Ex., A.M.I.M.E. Price 2s. 6d. nett. Ewing MAGNETIC INDUCTION IN IRON AND OTHER METALS. By Prof. J. A. Ewing, M.A., B.Sc., F.R.S., Professor of Mechanism and Applied Mechanics in the University of Cambridge. 382 pages, 173 Illustrations. Price los. 6d. nett. Third Edition, Second Issue. Synopsis of Contents. After an introductory chapter, which attempts to explain the fundamental ideas and the terminology, an account is given of the methods which are usually employed to measure the magnetic quality of metals. Examples are then quoted, showing the results of such measurements for various specimens of iron, steel, nickel and cobalt. A chapter on Magnetic Hysteresis follows, and then the distinctive features of induction by very weak and by very strong magnetic forces are separately described, with further description of experimental methods, and with additional numerical results. The influences of Temperature and ot Stress are discussed. The conception of the Magnetic Circuit is then explained, and some account is given ot experiments which are best elucidated by making use of this essentially modern method of treatment. Fisher THE POTENTIOMETER AND ITS ADJUNCTS. (A Universal System of Electrical Measurement.) By W. Clark Fisher. New Edition in Preparation, The extended use of the Potentiometer System of Electrical Measurement will, it is hoped, be sufficient excuse for the publication of this work, which, while dealing with the main instru- nient, its construction, use and capabilities, would necessarily be incomplete without similar treatment of the various apparatus which extend the range and usefulness of the whole system. 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Bound _ cloth as. nett, post free. _ _______ _ " THE ELECTRICIAN " PRINTING & PUBLISHING CO., LTD., I, 2 and 3, Salisbury Court, Fleet Street, London, E.C. ( 5 ) Fleming A HANDBOOK FOR THE ELECTRICAL LABORA- TORY AND TESTING ROOM By Dr. J.A.Fleming, M.A., F.R.S., M.R.I., &c. Vol. I., price 125. 6d. nett, post free 133. Vol. II., 145. nett. This Handbook has been written especially to meet the requirements of Electrical Engineers in Supply Stations, Electrical Factories and Testing Rooms. The Book consists of a series ot Chapters each describing the most approved and practical methods of conducting some one class of Electrical Measurements, such as those of Resistance, Electromotive Force, Current, Power, &c., &c. It does not contain merely an indiscriminate collection ot Physical Laboratory, processes without regard to suitability for Engineering Work. The Author has brought to its compilation a long practical experience of the methods described, and it will be found to be a digest of the best experience in Electrical Testing. The Volumes contain a Chapter on the Equipment of Electrical Laboratories and numerous Tables of Electrical Data, which will render it an essential addition to the library of every practical Electrical Engineer, Teacher or Student. SYNOPSIS OF CONTENTS. Vol. I. Chapter I. Equipment of an Electrical Test- ing Room. II. The Measurement of Electrical Resistance. III. The Measurement of Electric Current. IV. The Measurement of E.M.F. V. TheMeasurementofElectricPower. Vol. II. Chapter I. The Measurement of Electric Quantity and Energy. II. The Measurement of Capacity and Inductance. III. Photometry. IV. Magnetic and Iron Testing. V. Dynamo, Motor and Transformer Testing. Fleming THE ALTERNATE CURRENT TRANSFORMER IN THEORY AND PRACTICE. By Prof. J. A. Fleming, M. A., D.Sc., F.R.S., M.R.I., &c. Vol. I. New Edition Almost entirely Rewritten, and brought up to date. More than 600 pages and 213 illustrations, i2s. 6d. post free; abroad, 135. Vol. II. Third issue. More than 600 pages and over 300 illustrations, 123. 6d. post free ; abroad 133. Since the first edition of this Treatise was published, the study of the properties and appli- cations of alternating electric currents has made enormous progress The Author has, accordingly, rewritten the greater part of the chapters, and availed himself of various criticisms, with the desire of removing mistakes and remedying defects of treatment. In the hope that this will be found to render the book still useful to the increasing numbers of those who are practically engaged in alternating-current work, he has sought, as far as possible, to avoid academic methods and keep in touch with the necessities of the student who has to deal with the subject not as a basis for mathematical gymnastics but with the object of acquiring practically useful knowledge. Dr. Fleming's manual on the Alternate-Current Transformer in Theory and Practice is recognised as the text book on the subject. Vol. I., which deals with '' The Induction of Electric Currents," has passed through three editions, each edition having, in its turn, passed through several issues. Vol. II., which treats of ''The Utilisation of Induced Currents," has also passed through numerous issues. Fleming ELECTRICAL LABORATORY NOTES AND FORMS. Arranged and prepared by Dr. J. A. Fleming, M.A., F.R.S., &c. This important Series of Notes and Forms for the use of Students in University and other Electro-technical Classes has a world-wide reputation, and many thousands of copies have been sold. From time to time, as considered desirable, the Notes and Forms have been corrected or re-written, but the original divisions of the forty Forms into "Elementary" and "Advanced" has hitherto been observed. The object of this arbitrary division has now been fully served, and it has been decided that in future only the numerical order shall be retained. At the same time itis realised that the timehas come for additions to be made to the original Set, and Dr. Fleming lias written Ten Additional Notes and Forms (Nos. 41 to 50). It should be remembered that the numerical order observed in the above list has no relation to the difficulty or class sequence of the exercise, but is simply a reference number for convenience. The Subjects of the additional Notes and Forms are : No. SUBJECT. 41. Determination of Dynamo Efficiency by Routin's Method. 42. Separation ot Hysteresis and Eddy Cur- rent Losses in Continuous-Current Dynamo Armatures. 43. Efficiency Test of Two Equal Trans- formers by the Differential (Sumpner*s) Method. 44. Measurement of the Efficiency and Power Factor of a Polyphase Induc- tion Motor by the Wattmeter Method. No. SUBJECT. 45. Determination of the Characteristic Curves of Dynamo Machines. 46. The Absolute Measurement of Capa- city. 47. The Measurement of Inductances. 48. The Test of a Rotary Converter. 49. The Parallelisation of Alternators. 50. The Examination of an Alternating- Current Motor. These " Electrical Laboratory Notes and Forms " have been prepared to assist Teachers, Demonstrators and Students in Electrical Laboratories, and to enable the Teacher to economise time. They now consist of a series of 50 Exercises in Practical Electrical Measurements and Testing. For each of these Exercises a four-page Report Sheet has been prepared, two and some- times more pages of which are occupied with a condensed account of the theory and practical in- structions for performing the particular Experiment, the other pages being ruled up in lettered columns, to be filled in by the Student with the observed and calculated quantities. Where simple diagrams will assist the Student, these have been supplied. These Exercises are perfectly general, and can be put into practice in any Laboratory. Each Form is supplied either singly at 4d nett, or at 33. 6d. per dozen nett (assorted or otherwise as required) ; in Sets of any Three at is. nett ; or the Complete Set of 50 Exercises, price I2S. 6d. nett, or in a handy Portfolio, 145. nett, or bound in strong Cloth Case, price 155. nett. Spare Tabulated Sheets for Observations, price id. each nett. Strong Portfolios can also be supplied, price is. 6d. each. The best quality Foolscap Sectional Paper for Drawings (i6in. by i3in.) can be supplied, price gd. per dozen sheets nett. A Sample Copy of any one of the Notes and Forms will be sent post free to any Teaching Establishment, or to the Professor or Demonstrator of a Class for Electro-Technology. A complete Prospectus will also be sent post free on application. N.B. A limited number of the first 40 of the above NOTES AND FORMS can be supplied in a smaller size (io|| by 8). bound in strong cloth, price ys. 6d. nett, post free. THE ELECTRICIAN " PRINTING & PUBLISHING CO., LTD. I. 2 and 3. Salisburv Court. Flppt Sfrp^t. T.onHnn K.C. ( 6 ) Fleming HERTZIAN WAVE WIRELESS TELEGRAPHY ; A Reprint of a series of articles in the " Popular Science Monthly," based upon Dry Fleming's Cantor Lectures before the Society of Arts, 1903. By Dr. J. A. Fleming, F.R.S. 108 large 8vo. pages, fully illustrated. 35. 6d. nett. Fleming. ELECTRIC LAMPS AND ELECTRIC LIGHTING. By Prof. J. A. Fleming, M.A., D.Sc., F.R.S., M.R.I. New Edition. Very fully illus- trated, handsomely bound, on good paper, price 6s. nett The original aim of a course of four lectures by Prof. J. A. Fleming on " Electric Illumina- tion " was to offer to a general audience such non-technical explanations of the physical effects and problems concerned in the modern applications of electricity for illumination purposes as might serve to further an intelligent interest in the subject. The author has brought the second edition into line with recent practice without departing from the elementary character of the work. Fleming THE ELECTRONIC THEORY OF ELECTRICITY. By Prof. J. A. Fleming, M.A., D.Sc., F.R.S. Price is. 6d. post free. Fynn THE CLASSIFICATION OF ALTERNATE CURRENT MOTORS. By V. A. Fynn, M.I.E.E. Fully Illustrated. 3 s. nett. Geipel and Kilgour A POCKET-BOOK OF ELECTRICAL ENGINEERING FORMULAE, &c. By \V. Geipel and H. Kilgour. Second Edition. 800 pages. 75. 6d. nett ; post free at home or abroad, js. gd. With the extension of all branches of Electrical Engineering (and particularly the heavier branches), the need of a publication of the Pocket-Book style dealing practically therewith. increases ; for while there are many such books referring to Mechanical Engineering, and several dealing almost exclusively with the lighter branches of electrical work, none of these suffice for the purposes of the numerous body of Electrical Engineers engaged in the application of electricity to- Lighting, Traction, Transmission of Power, Metallurgy, and Chemical Manufacturing. It is to supply this real want that this most comprehensive book has been prepared. Compiled to someextenton thelinesof other pocket-books, the rules and formulae in general use among Electricians and Electrical Engineers all over the world have been supplemented by brief and, it is hoped, clear descriptions of the various subjects treated, as well as by concise articles and hints on the construction and management of various plant and machinery. Gerhardi ELECTRICITY METERS, THEIR CONSTRUCTION AND MANAGEMENT. A Practical Manual for Central Station Engineers, Distri- buting Engineers, and Students. By C. H. W. Gerhardi. 8vo. Fully illustrated. 95. nett. This valuable Prastical Manual on the Management of Electricity Meters, which will form. a volume in " THE ELECTRICIAN " Series, will bo, published shortly. The Author has had many years' exceptional experience with Electricity Meters as chief ot the Testing Department of the largest electricity supply undertaking in the United Kingdom. Mr. Gerhardi's intimate acquain- tance with the working of all existing meters on the market, and with the details of their construc- tion, is a guarantee that the book will meet the requirements of those engaged in work in which the Electricity Meter forms an essential part. In the division of the book devoted to " Testing," Mr. Gerhardi's experience will prove of the greatest service to supply station engineers and managers. Goldschmidt ALTERNATING CURRENT MOTORS. By Dr. R. Goldschmidt. In the Press. Gore THE ART OF ELECTROLYTIC SEPARATION OF METALS (Theoretical and Practical). By George Gore, LL.D., F.R.S. Over 300 pages, 106 illustrations. Price xos. 6d. post free. Dr. Gore's work is ot the utmost service in connection with all classes of electrolytic work con- nected with the refining of metals. The book contains both the science and the art of the subject (both the theoretical principles upon which the art is based and the practical rules and details of tech- nical application on a commercial scale), so that it is suitable for both students and manufacturers. Gore ELECTRO-CHEMISTRY. By Dr. G. Gore. Price 25. post free. At the time when this book first appeared no separate treatise on Electro-Cheraistry existed in the English language, and Dr. Gore, whose books on electro-metallurgy, electro- deposition and other important branches of electro-technical work are known throughout the world, has collected together a mass of useful information and has arranged this inconsecutive order, giving brief descriptions of the known laws and general principles which underlie the Subject of Electro-Chemistry. A very copious index is provided. Hawkins THE THEORY OF COMMUTATION. By C. C. Hawkins, M.A., M.I.E.E. Paper covers, as. 6d. nett. Heaviside " ELECTRICAL PAPERS." In Two Volumes. By Oliver Heaviside. Price 3 : 33. nett. The first twelve articles of Vol. 1. deal mainly with Telegraphy, and the next eight with the Theory of the Propagation of Variations of Current along Wires. Then follows a series of Papers relating to Electrical Theory in general. The contents of Vol. II. include numerous Papers on Electro-Magnetic Induction and its Propagation, on the Self-induction of Wires, on Resistance and Conductance Operators and their Derivatives Inductance and Permittance, on Electro-Magnetic Waves, a general solution of Maxwell's Electro-Magnetic Equations in a Homogeneous Isotropic Medium, Notes on Nomen- clature, on the Theory of the Telephone, on Hysteresis, Lightning Conductors, &c. These two Volumes are srarce and are not likely to be reprinted. "THE ELECTRICIAN " PRINTING & PUBLISHING CO., LTD., i, 2 and 3, Salisbury Court, Fleet Street, London, E.G. ( 7 ) Heaviside ELECTROMAGNETIC THEORY. By Oliver Heavi- side. Vol.1. Second issue. 466 pages. Price I2s. 6d., post free 133. Vol.11. 568 pages. Price I2s. 6d. post free ; abroad, 135. Extract from Preface to Vol. I. This work is something approaching a connected treatise on electrical theory, though without the strict formality usually associated with a treatise. The following are some of the leading points in this volume. The first chapter is introductory. The second consists of an outline scheme of the fundamentals of electromagnetic theory from the Faraday-Maxwell point of view, with some small modifications and extensions upon Maxwell's equations. The third chapter is devoted to vector algebra and analysis, in the form used by me in former papers. The fourth chapter is devoted to the theory of plane electromagnetic waves, and, being mainly descriptive, may perhaps be read with profit by many who are unable to tackle the mathematical theory comprehensively. I have included in the present volume the application of the theory (in duplex form) to straight wires, and also an account of the effects of self- induction and leakage, which are of some significance in present practice as well as in possible future developments. Extract from Preface to Vol. II. From one point of view this volume consists essentially of a detailed development of the mathematical theory of the propagation of plane electro- magnetic waves in conducting dielectrics, according to Maxwell's theory, somewhat extended From another point of view, it is the development of the theory of the propagation of waves along wires. But on account of the important applications, ranging from Atlantic telegraphy, through ordinary telegraphy and telephony, to Hertzian waves along wires, the Author has usually preferred to express results in terms of the concrete voltage and current, rather than the specific electric and magnetic forces belonging to a single tube of flux of energy. . . . The theory of the latest kind of so-called wireless telegraphy (Lodge, Marconi, &c.) has been somewhat anticipated, since the waves sent up the vertical wire are hemispherical, with their equatorial bases on the ground or sea, wliich they run along in expanding. (See \ 60, Vol. I. ; also $393 in this volume.) The author's old predictions relating to skin conduction, and to the possibilities of long-distance telephony have been abundantly verified in advancing practice; and his old predictions relating to the behaviour of approximately distortionless circuits have also received fair support in the quantitative observation of Hertzian waves along wires. Vol. III. is in preparation, and ia nearly ready. Jehl CARBON MAKING FOR ALL ELECTRICAL PUR- POSES. By Francis Jehl. Fully illustrated. Price IDS. 6d. post free. This work gives a concise account of the process of making High Grade and other Carbon for Electric Lighting, Electrolytic, and all other electrical purposes. CONTENTS. Chapter I. Physical Properties of Carbon. ,, II. Historical Notes. ,, III. Facts concerning Carbon. IV. The Modern Process of Manu- facturing Carbons. V. Hints to Carbon Manufacturers and Electric Light Engineers. VI. A "New "Raw Material. ,, VII. Gas Generators. VIII. The Furnace. IX.- -The Estimation of High Tem- peratures. Chapter X. Gas Analysis. ,, XI. On the Capital necessary for starting a Carbon Works and the Profits in Carbon Manu- facturing. ., XII. The Manufacture of Electrodes on a Small Scale. XIII. Building a Carbon Factory. XIV. Soot or Lamp Black. XV. Soot Factories. Kennelly and Wilkinson PRACTICAL NOTES FOR ELEC- TK1CAI. STUDENTS. Laws, Units and Simple Measuring Instruments. By A. E. Kennelly and H. D.Wilkinson. 320 pages, 155 illustrations. Price 6s. 6d. post free. These instructive Practical Notes for Electrical Students were started by Mr. A. E. Kennelly prior to his departure from England to join the staff of Mr. Edison in the United States, and were continued and completed by Mr. H. D. Wilkinson, who has prepared a work which is of great service to students. Kershaw- THE ELECTRIC FURNACE IN IRON AND STEEL PRODUCTION. By John B.C. Kershaw, F.I. C. Fully illustrated. 8vo. Price 33. 6d. nett. Lemstrom ELECTRICITY IN AGRICULTURE AND HORTI- CULTURE. By Prof. S. Lemstrom. With illustrations. Price 35. 6d. nett. Extract from Author s Introductory Remarks. It is well known that the question which is the subject of this book has been a favourite field of investigation for a century past. As the sub- ject is connected with no less than three sciences viz., physics, botany and agricultural physics it is in itself not particularly attractive. The causes which induced me to begin the investigation of this matter were manifold, and I venture to hope that an exposition of them will not be with- out general interest. Livingstone THE MECHANICAL DESIGN AND CON- STRUCTION" OF COMMUTATORS. By R. Livingstone. Very fully illustrated. Now Ready. Price 6s. nett. "THE ELECTRICIAN " PRINTING & PUBLISHING CO., LTD., i, 2 and 3, Salisbury Court, Fleet Street, London E.G. ( 3 ) Lodge- WIRELESS TELEGRAPHY. SIGNALLING ACROSS SPACE WITHOUT WIRES. By Sir Oliver J. Lodge, D.Sc., F.R.S. New and Enlarged Edition. Now Ready. Very fully illustrated. Price 55. nett, post free 55. 3d. The new edition forms a complete Illustrated Treatise on Hertzian Wave Work. The Full Notes of the interesting Lecture delivered by the Author before the Royal Institution, London, in- June, 1894, form the first chapter of the book. The second chapter is devoted to the Application 1 of Hertz Waves and Coherer Signalling to Telegraphy, while Chapter III. gives Details of other Telegraphic Developments. In Chapter IV. a history of the Coherer Principle is given, including Professor Hughes' Early Observations before Hertz or Branly, and the work of M. Branly. Chapters are also devoted to " Communications with respect to Coherer Phenomena on a Large Scale," the "Photo-Electric Researches of Drs. Elster and Geitel," and the Photo-Electric Researches of Prof. Righi. Maurice ELECTRIC BLASTING APPARATUS AND EXPLO- SIVES, WITH SPECIAL REFERENCE TO COLLIERY PRACTICE. By Wm.. Maurice, M.Nat.Assoc. of Colliery Managers, M.LMin.E., A.M.I.E.E. Now Ready* Price 8s. 6d.nett. The aim of this book is to prove itself a useful work of reference to Mine Managers, Engineers and others engaged in administrative occupations by affording concise information concerning the most approved kinds of apparatus, the classification and properties of explosives, and the best known means of preventing accidents in the use ot them. Th* work gives not only an explanation of the construction and safe application of blasting appliances, the properties of explosives, and the difficulties and dangers incurred in daily work, but it also serves as an easy introduction to the study ot electricity without at least a rudimentary knowledge of which no mining official can now be considered adequately trained. Particular attention has bef*n devoted to the problem of safe shot firing in coal mines, and an attempt has been made to present the most reliable information on the subject that experience and recent research have made possible. Maurice THE SHOT-FIRERS HAN 1)1 5OO K. In preparation. May MAY'S BELTING TABLE. Showing the Relations between (i)The number of revolutions and diameter of pulleys and velocitv of belts : (2) 'Ihe horse- power, velocity and square section of belts ; (3) The thickness and width of belts ; (4) The square section of belts at different strains per square inch. For office use, printed on cardboard, with metal edges and suspender, price 2s. ; post free, 2S. 2d. For the pocket, mounted on linen, in strong case, 2s 6d. ; post tree, 2s. 8d. May MAY'S POPULAR INSTRUCTOR EOR THE MANAGE- MENT OF ELECTRIC LIGHTING PLANT. An indispensable Handbook for persons in charge of Electric Lighting Plants, more particularly those with slight technical training. Pocket size, price 2s. 6d. ; post free, 2s. 8d. May MAY'S TABLE OF ELECTRIC CONDUCTORS. Showing the relations between: (i) the sectional area, diameter of conductors, loss of potential, strength of current, and length of conductors ; (2) the economies of incandescent lamps, their candle-power, potential, and strength ot current ; (3) the sectional area, diameter of conductors, and strength of current per square inch. For office u e, printed on card- board, with metal edges and suspender. Price 2s. ; post free, 2s. 2d, For the pocket, mounted on linen, in strong: case. 2s. 6d. ; post free, 2s. 8d. Phillips THE BIBLIOGRAPHY OF X-RAY LITERATURE AND RESEARCH. Being a carefully and accurately compiled Ready Reference Index to the Literature on Rontgen or X-Rays. Edited by Charles E. S. Phillips. With an Historical Retrospect and a Chapter, " Practical Hints," on X-Ray work by the Editor. Price 55. post free. Pritchard THE MANUFACTURE OF ELECTRIC LIGHT CARBONS. By O. G. Pritchard. A Practical Guide to the Establishment of a Carbon Manufactory. Fully illustrated. Price is. 6d., post tree is. qd. The object of Mr. Pritchard in preparing this work for pub ication was to enable Pritish manufactuiers to compete with those of France, Austria, Germany and Bohemia in th- pro- duction of electric arc carbon candles. The book is fully illustrated and gives technical d tails for the establishment and working of a complete carbon factory. Ram THE INCANDESCENT LAMP AND ITS MANUFAC- TURE. By Gilbert S. Ram. Fully Illustrated. Price is. 6d. post free. The Author has endeavoured to give such information as he has acquired in the course of a considerable experience in Lamp-making, and to present that information with as little mathe- matical embellishment as possible. The subjects dealt with include : The Filament : Preparation ot the Filament, Carbonising, Mounting, Flashing, Sizes of Filaments, Measuring the Filaments; Glass Making and Blowing, Sealing-in, Exhausting, Testing, Capping, Efficiency and Duration, and Relation between Light and Power. Raphael THE LOCALISATION OF FAULTS IN ELECTRIC LIGHT MAINS. By F. Charles Raphael. New Edition. Price 7 s. 6d. nett. Although the localisation of faults in telegraph cables has been dealt with fully in several hand-books and pocket-books, the treatment of faulty electric light and power cables has never bren discussed in an equally comprehensive manner. The conditions of the problems are, however, very different in the two cases ; faults in telegraph cables are seldom localised before their resistance has become low compared with the resistance ot the cable itself, while in electric light work the contrary almost always obtains. This fact alone entirely changes the method of treatment required in the latter case, and it has been the Author's endeavour, by dealing with the matter systematically, and as a separate subject, to adequately fill a gap which has hitherto existed in technical literature. The various methods of insulation testing during working have been collected and discussed, s.s these tests may be considered to belong to the subject. "THE ELECTRICIAN" PRINTING & PUBLISHING CO., LTD., i, 2 and 3, Salisbury Court, Fleet Street, London, E,C. ( 9 ) Raphael "THE ELECTRICIAN" WIREMAN'S, LINESMAN'S AND MAINS SUPERINTENDENT'S POCKET-BOOK. A Manual for the Mains Superintendent, the Wiring Contractor and the "Wireman. Edited by F. Charles Raphael. New Edition. Price 55. nett, post free 55. 3d. EDITOR'S NOTE. When the preparation of this Pocket-Book was commenced, the original intention of its Editor was to collect in a handy and useful foim such Tables, Instructions and Memoranda as would be useful to the Electric Light Wireman in his work. This has been carried out in Section A of the Pocket-Book. During the past few years, however, many inquiries have been received for a good book dealing with the laying of underground mains, and with matters connected with insulated conductors generally. It was decided, there- fore, to extend greatly the area covered by the book, and to treat the whole subject of erecting and laying electrical and conducting systems in such a manner that the tables, diagrams and letterpress might be useful to engineers in charge of such work, as well as to the wireman, jointer, and foreman. In fact, the section on Underground Work has been compiled largely with a view to meeting the requirements of Mains Superintendents, Central Station Engineers, and those occupied in designing networks. In addition to the tables, instructions and other detailed information as to cables, ducts, junction boxes, &c., contained in the section on Underground Mains.it has been deemed advisable to add a chapter briefly describing the various systems employed for public distributing networks. In this, essential practical information is alone given; two and three-phase systems are dealt with, as well as continuous current and single phase, and the method of calculating the size of the conductors and the fall of pressure from the number of lamps or horse-power of motors is made clear without the elaboration of clock-face diagrams or algebraical exercises. Diagrams for the connections of telephones are given in Section D, including those for subscribers' instruments on the British Post Office exchange system in London. Sayers BRAKES FOR TRAMWAY CARS. By Henry M. Sayers, M.I.E.E. Illustrated. 35. 6d. nett. Now Ready. Snell ELECTRIC MOTIVE POWER. By Albion T. Snell. Over 400 pages, nearly 250 illustrations. Price IDS. 6d. post free; abroad, us. The rapid spread of electrical work in collieries, mines and elsewhere has created^ demand for a practical book on the subject of transmission of power. Though much had been written, there was no single work dealing with the question in a sufficiently comprehensive and yet practical manner to be of real use to the mechanical or raining engineer; either the treatment was adapted for specialists, or it was fragmentary, and power work was regarded as subservient toithe question of lighting. In general, the Author's aim has been to give a sound digest of the theory and practice of the electrical transmission of power, which will be of use to the practical engineer. Shaw A FIRST- YEAR COURSE Oe' PRACTICAL MAGNET- ISM AND ELECTRICITY. By P. E. Shaw, B.A., D.Sc., Senior Lecturer and Demon- strator in Physics at University College, Nottingham. Price 2s. 6d. nett ; 2s. gd. post free. The many small books on Elementary Practical Physics, which are suitable for schools or for university intermediate students, all assume in the student a knowledge of at least the rudi- ments of algebra, geometry, trigonometry and mechanics. There is, however, a large and grow- ing class of technical students who have not even this primitive mathematical training, and who cannot, or will not, acquire it as a foundation for physical science. Their training as boys in a primary school has not been supplemented or maintained until, as skilled or unskilled artisans, they find they require some knowledge of electricity in their daily work. They enter the labora- tory and ask for an introduction to such fundamentals of the subject as most affect the arts and crafts. On the one hand, mere qualitative experiments are of little use to these (or any other) students; on the other hand, mathematical expressions are stumbling blocks to them. In attempting to avoid both these evils. I have sought to make the experimental work as quantitative as possible, yet to avoid mathematics. As novelties in such a work as this the ammeter and volt- meter are freely introduced, also some simple applications of the subject e.g., the telephone, telegraph, &c. There are three introductory exercises, six exercises on magnetism, twenty on electricity and six on the applications. Nothing is done on statical electricity or alternating currents, for the reason that in a simple course like this they are considered relatively unimportant as well as difficult. Extract f>om Preface. Soddy RADIO-ACTIVITY : An Elementary Treatise from the Standpoint of the Disintegration Theory. By Freak. Soddy, M.A. Fully Illustrated, and with a full Table of Contents and extended Index. 6s. 6d. nett. Extract from A uthor 1 s Preface. In this book the Author has attempted to give a con- nected account of the remarkable series of investigations which have followed M. Becquerel'i discovery in 1896 of a new property of the element Uranium. The discovery of this new pro- perty of self-radiance, or "radio-activity," has proved to be the beginning of a new science, in the development of which physics and chemistry have played equal parts, but which, in the course of only eight years, has achieved an independent position. . . . Radio-activity has passed from the position of a descriptive to that of a philosophical science, and in its main generalisations must exert a profound influence on almost every other branch of knowledge. It has been recognised that there is a vast and hitherto almost unsuspected store of energy bound m, and in some way associated with, the unit of elementary matter represented by the atom of Dalton. . . . Since the relations between energy and matter constitute the ultimate ground- work of every philosophical science, the influence of these generalisations on allied branches of knowledge is a matter of extreme interest at the present time. It would seem that they must effect sooner or later important changes in astronomy and cosmology, which have been long awaited by the biologist and geologist. The object of the book has been to give to Students and those interested in all departments of science a connected account of the main arguments and chief expeiimental data by which the results so far attained have been achieved. "THE ELECTRICIAN" PRINTING & PUBLISHING CO., LTD., i, 2 and 3, Salisbury Court, Fleet Street, London, E.G. Telephony BRITISH POST OFFICE TELEPHONE SERVICE. An illustrated description of the Exchanges of. the Post Office Trunk and Metropolitan Telephone Services, giving much interesting information concerning these Exchanges. Now ready, 8vo, very fully illustrated. Price 2s. 6d. nett. In this work an illustrated description is given of the Trunk, Central and other Exchanges ol the British Post Office Telephone Service in the London Metropolitan area. The descriptions of the various exchanges are complete, and the illustratu ns show the disposition ot the plant and the types of all the apparatus used. In view of the early acquisition by the Post Office of the undertaking 1 of the National Telephone Company this work is of considerable interest. MINUTES OF THE PROCEEDINGS AT THE HULL TELEPHONE INQUIRY. Price 3 s. nett, post free 3 s. 6d. MINUTES OF THE PROCEEDINGS AT THE PORTSMOUTH TELEPHONE INQUIRY. Price is. 6d. nett, post free is. od. Thompson THE ELECTRIC PRODUCTION OF NITRATES FROM THE VTMOSPHERE. By Prof.S. P. Thompson, IXSc., F.K.S. Ready shortly. Wade SECONDARY BATTERIES : THEIR MANUFACTURE AND USE. By E. J. Wade. Now ready. 5oopages. 265 Illustrations. Price ios.6d. nett. In this work the Author deals briefly with the Theory and very fully with the Chemistry, Design, Construction and Manufacture of Secondary Batteries or Accumulators. Prospectuses, post free, on application. The scope of Mr. Wade's important work covers t>>e whole class of apparatus embraced in the theory, construction and use ot the secondary battery. The major portion of the book treats the accumulator purely from the point of view of an appliance which fulfils an important and definite purpose in electrical engineering practice, and whose manufacture, use and properties must be understood just as fully as those of a generator or a transformer. The < oncluding chapter (X.) gives a complete description of all modern electrical accumulators. Ihe book contains 265 illustrations and a very copious index. Weymouth DRUM ARMATURES AND COMMUTATORS (THEORY AND PRACTICE). By F. M. Weymouth. Fully Illustrated. Price ys. 6d. post free. Wilkinson SUBMARINE CABLE-LAYING AND REPAIRING. By H. D. Wilkinson, M.I E.E., &c. Over 400 pages and 200 specially drawn illustrations. Price i2s. 6d. post free. Ntw Edition in prepaiation. This work describes the procedure on board ship when removing a fault or break in a submerged cable and the mechanical gear used in different vessels for this purpose ; and considers the best and most recent practice as regards the electrical tests in use for the detection and local isati on *of faults, and the various difficulties that occur to the beginner. It gives a detailed technical summary of modern practice in Manufacturing, Laying, Testing and Repairing a Sub- marine Telegraph Cable. The testing section and details of 'boardship practice have been prepared with the object and hope of helping men in the cable services who are looking further into these branches. Young ELECTRICAL TESTING FOR TELEGRAPH ENGI- NEERS. By J. Elton Young. Very fully illustrated. Price IDS. 6d., post free us. This book embodies up-to-date theory and practice in all that concerns everyday work ot the Telegraph Engineer. CONTENTS. Chapter I. Remarks on Testing Apparatus, ,, II. Measurements of Current, Poten- tial, and Battery Resis- tance. III. Natural and Fault Current. ,, IV. Measurement of Conductor Re- sistance. ,, V. Measurement of Insulation Re- sistance. VI. Corrections for Conduction and Insulation Tests. Chapter VII. Measurement of Inductive Capa- city. ,, VIII. Localisation of Disconnections. IX. Localisation of Earth and Con- tacts. ,, X. Corrections of Localisation Tests. ,, XL Submaiine Cable Testing during Manufacture, Laying and Working. ,, XII. Submarine Cable Testing during Localisation and Repairs. In the Appendices numerous tables and curves of interest to Telegraph Engineers are given. THE INTERNATIONAL TELEGRAPH CONVENTION AND SERVICE REGULATIONS. (London Revision, 1903). The complete Official Fr-ncn Text with English Translation in parallel columns, by C. E. J. Twisaday (India Cffic'-, London), Geo. R. Neilson (Eastern Telegraph Co., London), and officially revised by permission of H.B.M. Postmaster-General. Cloth (foolscap folio), 6s. nett ; (demy iolio), 8s. 6d. nett, or foolscap, interleaved ruled paper, 8s. 6d. nett. INTERNATIONAL RADIO-TELEGRAPHIC CONFERENCE, BERLIN, October-November, 1006, with the International Radio-Telegraphic Conven- tion, Additional Undertaking, Final Protocol and Service Regulations in French and English. Officially accepted Translation into English of the complete Proceedings at this Conference. This translation, which has been made by Mr. G. R. Neilson, is pub- lished under the authority of H. H.M. Postmaster-General, and is accepted as official by the British Government Departments concerned. Strongly bound in cloth, 2is. nett; leather, 253. nett. Postage per copy : U.K. 6d. ; abroad is. 6d. "THE ELECTRICIAN " PRINTING & PUBLISHING CO., LTD. I 2 and 3, Salisbury Court, FJeet Street, London E.G. "THE ELECTRICIAN" PRIMERS s. [COPYRIGHT.] Edited by Mr. W. R. COOPER, M.A., R.Sc., M.I.E.E. There are, in all, over FO PRIMERS in this Collection. 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