THE ELECTRIC ARC. By HERTHA AYRTON, MEMBER OF THE INSTITUTION OF ELECTRICAL ENGINEERS. Of THF UNIVERSITY NEW YORK : THE D. VAN NOSTRAND COMPANY, 23, MURRAY STREET, AND 27, WARREN STREET. LONDON: THE ELECTRICIAN" PRINTING AND PUBLISHING COMPANY LIMITED, SALISBURY COURT, FLEET STREET, B.C. [All Rights Reserved.] ' Printed and Published by 1 THE ELECTRICIAN " PRINTING AND PUBLISHING CO., LIMITED 1, 2, and 3, Salisbury Court, Fleet Street, London, B.C. PREFACE. *TPHIS book, which owes its origin to a series of articles published in The Electrician in 1895-6, has attained to its present proportions almost with the growth of an organic body. In experimenting on the -arc, my aim was not so much to add to the large number of isolated facts that had already been dis- covered, as to form some idea of the bearing of these upon one another, and thus to arrive at a clear con- ception of what takes place in each part of the arc and carbons at every moment. The attempt to correlate all the known phenomena, and to bind them together into one consistent whole, led to the deduction of new facts, which, when duly tested by experiment, became parts of the growing body, and, themselves, opened up fresh questions, to be answered in their turn by experiment. Thus the subject grew and developed in what might almost be called a natural way. From the first it seemed to me that the fact that the resistance of the material in the gap between the carbons must not only depend upon the current, but that it must depend upon it in many apparently contra- dictory ways, could not but lead to curious complications iv. PREFACE. in the relation between the P.D. and the current quite apart from any back E.M.F. that the arc might possess, In the attempt to disentangle the various effects on this resistance that a change of current must produce, and to see how far all that was apparently mysterious in the arc might be the natural result of such complexity in the resistance of a portion of the circuit, the theory presented in Chapter XII. gradually evolved itself. This theory, whatever may be its shortcomings, has at least not been hastily built up to fit a few of the more salient characteristics of the arc ; it has literally evolved itself, during the course of a detailed study, from many points of view, of each separate phenomenon. For although the central idea, that the carbon vapour changed into mist at a short distance from the crater, occurred to me at a very early period of the work, its complete application to the whole series of phenomena, and the full recognition of all that it entailed, followed but slowly, as each part of the subject was considered in turn. The experiments of other observers have been em- ployed in two ways: (i) In confirmation of theory developed from my own experiments, and (2) as the basis of theory, for which further tests were devised. The law connecting P.D., current, and length of arc, for instance, was first constructed from my own results, and then was shown to be applicable to those obtained much earlier by Messrs. Edlund, Peukert, Cross and Shepard, and Ayrton. The theory concerning the light, on the other hand, was entirely deduced from the experiments of others. M. Blondel's interesting and systematic researches, the admirable work of Mr. Trotter, and Prof. Ayrton's Chicago Paper were all laid under PREFACE. v< contribution, and the deductions drawn from them were then tested by new experiments. In seeking to compare my results with those of other observers, and in searching for accounts of experiments that might furnish material for theory, I have often been struck with the excellent work that has been done by men whose names are quite unfamiliar to us in England. There are admirable Papers on the arc, for instance, by Nebel, Feussner, Luggin, Granquist, and Herzfeld, to which reference is seldom seen in any English publi- cation ; while other work, which is in some cases far inferior, is constantly quoted. I have, therefore, given in Chapter II. short abstracts of most of the impor- tant Papers on the direct-current arc that appeared up to the end of the nineteenth century, while those referring principally or entirely to the light are discussed in Chapter XL At the end of Chapter II. is a chrono- logical list of all the original communications that I could find when that chapter was written ; but the names of a few to which my attention has since been directed, and of some that appeared after the list was made, together with the dates of my own contributions to The Electrician . and to various societies, are added at the end of the Appendix. The latest paper of all an extremely interesting one " On the Resistance and Electromotive Forces of the Electric Arc," read by Mr. Duddell before the Royal Society in June last I should much have liked to discuss in connection with this book, but, as it is not yet published in full, that is unfortunately impossible. As it seemed better not to wait till the whole book was ready, before publishing the most important of the new results obtained, some part of almost every chapter A2 vi. PREFACE. has been made the subject of a Paper that has been read before one or other of the societies interested in such work. These Papers generally covered but a portion of the ground, however, giving the main experiments and conclusions only, without following them up, or showing how they bore upon one another. In the book these are all connected together, and many new results are set forth which have been developed during the process. At the end of each chapter is a summary of the most important conclusions reached in it, which, it is hoped, may be found useful in making each step perfectly clear before the next is taken. Besides the light experiments already mentioned, all those on the time-change of P.D. immediately after starting the arc, and after sudden changes of current originally formed part of Prof. Ayrton's ill-fated Chicago Paper, which, after being read at the Electrical Congress in 1893, was accidentally burnt in the Secretary's office, whilst awaiting publication. These highly important experiments were not only the first of their kind, but, as far as I know, they still remain unique. Most of the figures in the first chapter, all the experiments and curves that relate to cored carbons in the fourth and fifth, and some of those on hissing in the tenth, also belonged to this Chicago Paper, which was as full of suggestion as it was rich in accomplished work. Although the book is concerned entirely with the arc itself, and does not touch at all upon lamps and their devices, it is hoped that it may appeal to the practical man as well as to the physicist. For not only the cause but the practical bearing of each peculiarity of the arc has been considered ; the directions in which improvements may be hoped for have been pointed out, PREFACE. vii. and the conditions requisite to secure the maximum production of light from a given expenditure of power in the generator have been fully discussed. In conclusion, I have to thank Prof. Blondel, Prof. Fleming and Mr. Trotter for kind permission to use figures from their Papers ; Mr. Fithian for taking the beautiful photographs of the Hissing Arc reproduced in Fig. 8 1 ; Mr. Mather for much valuable advice and assistance with experiments, and Mr. Maurice Solomon for his suggestive criticism of the MS. and careful revision of the proofs. HERTHA AYRTON. TABLE OF CONTENTS. CHAPTER I. PAGE THE APPEARANCE OF THE ARC 1 Colours of Different Parts of Arc. General Shapes of Arc and Carbons. Influence of Current and Length of Arc on Shape and Size of Arc and Shapes of Carbons. Positive Crater. Effect of Core on Colour, Size and Shape of Arc. Crater in Negative Carbon. CHAPTER II. A SHORT HISTORY OF THE ARC 19 Uncertainty of Discoverer and of Date of Discovery of Arc. Mutual Attraction between Arc and Magnet. First Observation of Crater, " Mushrooms," Smell of Arc, and Difference of Temperatures of Electrodes. Application of Laws of Elec- trolysis to Arc. Experiments on Arcs in Various Gases. Photographic Power of Arc. First Experiments on Arcs between Carbons Steeped in Metallic Salts. Hissing. Trans- ference of Matter from One Pole to the Other. Electric Blowpipe. Water as One Electrode. Edlund's Discovery of Straight Line Law of Resistance and Length of Arc, and Suggestion of a Back E.M.F. Fall of P.D. with Hissing. Internal Pressure of Arc. Measurements of P.D. and Current with Constant Lengths of Arc. Measurements of Supposed True Resistance of Arc. Tests for Back E.M.F. Determinations of Temperatures of Electrodes. Arcs under Pressure. Measure- ments of Light. Rotation. Apparent Negative Resistance. Attraction of Solid Carbon Particles out of Arc. Suggested -"Thomson Effect" in Arc. List of Original Communications. x. TABLE OF CONTENTS. CHAPTER III. PAQE- 11 STRIKING " THE ARC AND SUDDEN VARIATIONS OF CURRENT 97 Impossibility at First of getting Definite P.D. with Fixed Current and Length of Arc. Cause of Difficulty. Low P.D. and Subsequent Rapid Else on Striking Arc with Cored Positive Carbon. Influence of Current, Length of Arc, and Shapes and Temperatures of Carbons on Time Required for P.D. to become Constant after Striking Arc. First Rise of P.D. with Increase of Current with Cored Carbons. Peculiar Changes of P.D. with Sudden Changes of Current, and their Causes. Summary. CHAPTER IV. CURVES FOR P.D. AND CURRENT WITH CONSTANT LENGTH OF ARC, AND FOR P.D. AND LENGTH OF ARC WITH CONSTANT CURRENT 119* General Character of Curves for P.D. and Current with Constant Length of Arc for Solid Carbons. Same with Positive Carbon Cored. Discussion of Variations Caused by Core. Different Positions of Hissing Points with Solid Carbons and with Positive Carbon Cored. Influence of Strength of Current on Diminution of P.D. due to Core. Hypothesis as to Action of Core in Modifying P.D. Curves showing Straight Line Law con- necting P.D. with Length of Arc, for Constant Current, with Solid Carbons. Curves for Same Connection with Cored Positive Carbon, showing P.D. Practically Independent of Current for One Length of Arc. Discussion of Differences between the Two Sets of Curves, and Explanation, on Above- mentioned Hypothesis. Soft and Hard Crater Ratios. Deduc- tions from them as to Influence of Current and Length of Arc on Area of Crater. Summary. CHAPTER V. AREA OF CRATER AND CRATER RATIOS. VARIATION OF P.D. WITH DIAMETERS OF CORED CARBONS. CONSTANT CURRENT-RESISTANCE CURVES. CONSTANT P.D. CURVES 151 Measurements of Diameter of Crater with Arc Burning. Curves of Area of Crater and P.D. between Carbons for Various Currents and Lengths of Arc. Curves of Area of Crater and Length of Arc, of Soft Crater Ratio and Length of Arc, and of TABLE OF CONTENTS. xi . Hard Crater Eatio and P.D. Curves of Area of Crater and Current. Measurements of Depth of Crater. P.D. Unin- fluenced by Depth of Crater. Comparison of P.Ds. for Same Current and Length of Arc but Different-sized Carbons. Curves of Apparent Resistance and Length of Arc. Constant P.D. Curves. Summary. CHAPTER VI. THE EQUATION FOB P.D., CURRENT, AND LENGTH OF ARC, WITH SOLID CARBONS, AND ITS APPLICATION TO THE RESULTS OF EARLIER EXPERIMENTERS 175 Two Fundamental Straight Line Laws Found to Exist with Solid Carbons. Power and Length of Arc with Constant Current, and Power and Current with Constant Length of Arc. Equation for Power, Current, and Length of Arc found by Combining these. Equation for P.D., Current and Length of Arc, Deduced from it, having Four Constants Depending Solely on Nature of Car- bons. Straight Line Power Laws Shown to Fit Experiments of Edlund, Frolich, Peukert, and Cross and Shepard, and Equations for P.D., Current and Length of Arc similar to Above, Deduced from their Results. Summary. CHAPTER VII. THE P.D. BETWEEN EACH CARBON AND THE ARC, AND THE FALL OF POTENTIAL THROUGH THE ARC 207 Repulsion and Attraction of Arc, and other Disturbances caused by Third Carbon. Definitions of Positive Carbon P.D., Negative Carbon P.D., Vapour P.O. Variation of Positive Carbon P.D. with Current and Length of Arc. Resemblances and Differences between Positive Carbon P.D. Curves and Total P.D. Curves. Variation of Negative Carbon P.D. with Current, but not with Length of Arc. Curves and Equation for Positive Carbon P.D., Current and Length of Arc ; Negative Carbon P.D. and Current ; and Sum of Carbon P.Ds., Current and Length of Arc. Simi- larity between Independent Constant in the Last Equation and Similar Constant in Equation for Total P.D., Current and Length of Arc, Showing that if this Latter Represents a Back E.M.F., it must be Located at Junctions of the Two Carbons with the Arc. Equation for Total P.D., Current and Length of Arc with Third Carbon in Arc. Location of P.Ds. Represented by Three out of xii. TABLE OF CONTENTS. Four Terms of Equation for Total P.D., Current and Length of Arc. Measurements of Carbon P.Ds., Plus Vapour P.D. Car- bon and Vapour P.Ds. with Cored Carbons. Diminution of P.D. due to Core Traced to Junction of Positive Carbon and Arc, and to Lowering of Resistance of Vapour Column. Summary. CHAPTER VIII. RELATIONS BETWEEN E.M.F. OF GENERATOR, RESISTANCE IN SERIES WITH ARC, P.D., CURRENT AND LENGTH OF ARC WITH SOLID CARBONS 241 Graphical Method of Finding Relations between E.M.F. of Gene- rator, Resistance in Series with Arc, P.D., Current and Length of Arc. Impossibility of Keeping either Current or Length of Arc really Constant. Greatest Length of Arc possible with Given Resistance in Series. Reason for Difficulty frequently found in Maintaining Long Arcs with Small Currents. Necessity of "Steadying Resistance" in order that Silent Arc may be Maintained at all. Variation of Minimum Value of Steadying Resistance with Current and Length of Arc. Longest Silent Arc and Smallest Current that can be Maintained with Given E.M.F. and Resistance in Series with Arc. Largest Resistance and Smallest Current that can be Used with Given E.M.F. and Length of Arc. Largest Resistance and Longest Arc that can be Maintained with given E.M.F. and Current. Summary. CHAPTER IX. THE POWER EFFICIENCY OF THE ARC AND THE RESISTANCE NEEDED IN SERIES WITH IT 259 General Conditions for Ratio of Power Expended in Arc to Power Developed by Generator (Power Efficiency) to be Greatest Pos- sible. Conditions for Power Efficiency to be Greatest Possible (1) when Length of Arc alone is Fixed, (2) when E.M.F. alone is Fixed, (3) when Current alone is Fixed, (4) when Resistance in Series alone is Fixed, (5) when P.D. alone is Fixed. Minimum Resistance that can be used in Series with Arc varies Inversely as Square of Current for Fixed Length of Arc. Minimum Resis- tance Required to Maintain Silent Arc at all Depends only on Nature of Carbons. Summary. TABLE OF CONTENTS. xiii. CHAPTER X. HISSING ARCS 277 Variety of Hissing Sounds. Hissing Arc not necessarily Short. Instability of Arc about Hissing Point. Laws of Hissing from P.D.-Current Curves. Cross and Shepard's and Luggin's Experiments. Equation to Curve on which Hissing Points Lie. Largest Current with which Arc, however long, can Remain Silent Equation for P.D. and Length of Arc with Hissing. Fall of P.D. at Positive Carbon, and Diminution of Resistance of Arc, with Hissing. Equation Connecting Change of P.D. when Hissing Begins with Length of Arc. Smallest Hissing Current \*ith given Length of Arc. Connection between Largest Silent and Smallest Hissing Current of same Arc. Change in Appear - anue of Crater, Arc, and Carbons with Hissing. Crater more than Covering End of Positive Carbon with Hissing. Laws of Hissing Deduced from Shapes of Positive Carbons with various Currents. Cause of Hissing. Experiments on Arcs enclosed in Crucible. Blowing Various Gases against Crater. Different Behavour of Arc when Hydrogen is Blown against Crater in Open Air and in Crucible. Cause of Hissing Sound. Summary. CHAPTER XL THE LIGHT AND LUMINOUS EFFICIENCY OF THE ARC. ... 313 Sources of Light in Arc. Obstruction of Crater Light by Negative Carbon. Trotter's Theorem. Quantity of Light Obstructed by Negative Carbon Estimated from Diagrams of Arc and Carbons. Reason for Light being Greater with very fehort Arcs than with longer ones, with Large Currents. Measurements of Mean Spherical Candle- Power of Arc (W. E. Ayrton) and Total Light of Arc (Blondel) Simultaneous* Discovery of Certain Length of Arc and Certain P.D. with which the Light is a Maximum for & Constant Current. Curves Connecting Crater Light with Length of Arc, Deduced from Diagrams of Arc and Carbons. Distinction between Polar Light Curves, Rousseau's Curves, and Curves connecting Illuminating Power with Length of Arc. Suggested Absorption of Crater Light by Arc. Facts tending to show that Arc does Absorb Light. Experiments on Shadows of Candle and Gas Flames. Arc Shadow. Refractive Power of Arc Mist. Arc Vapour turning in o Carbon Mist. Violet Colour of Long Arcs as Proof of Absorption. Light, Length of Arc Curves, from Diagrams of Arc, allowing for Absorption of Crater Light in Arc. Similarity between these and Experimental Curves. Effect of Variation of Current on Total Light emitted by Arc. Very small Luminous Efficiency of all sources of Light, Even Arc. Distribution of Power supplied to Arc between xiv. TABLE OF CONTENTS. PAGE Carbon Ends and Mist. Waste of Power in Mist in Long Arcs. Conditions for Light to be Maximum for given Power developed by Generator. Influence of Cross Sections of Carbons on Light- ing Power. With Solid Carbons Light Efficiency is greater, and Arc with which Maximum Light Efficiency is obtained is Shorter the Smaller the Carbons. Low Efficiency of Commercial Arc Lamps due to Thickness of Carbons. Variation of Light Efficiency with Current. Effect of Composition of Carbons on Light Efficiency. Arcs in Series. Only Fair Method of Compar- ing Light Efficiency of Two Sources. Summary. CHAPTER XII. THE MECHANISM OF THE ARC ITS TRUE RESISTANCE HAS IT A LARGE BACKE.M.F.? THE REASON FOR THE DIFFERENT EFFECTS OF SOLID AND CORED CARBONS... 391 How Arc forms on Separating Carbons. Changing of Vapour into Carbon Mist. Resistivities of Vapour, Mist, and Flame. Source of Heat of Arc. Hollowing of Crater. Shaping of Carbons. Dependence of Area of Crater on both Current and Length of Arc. Imitation of Back E.M.F. by Vapour Film. Time-Change of Resistance of Arc. Effect of Frequency of an Added Alter- nating Current on Value and Sign of . Curve of and 5A 5A Frequency. Frequency with which Measures True Resis- oA tance of Arc. Tests for this Frequency. Two Ways in which Cores in Carbons may Affect Resistance of Arc. How Cores Affect Mean Cross Section of Mist. How they Affect Resistivity of Arc and thus Alter Shapes of P.D.-Current Curves. Influence of Cores on Value of , (1) in Change of Cross oA Section, (2) in Change of Specific Resistance Curves Con- necting with Current, for Constant Length of Arc, with Length of Arc for Constant Current, and with Frequency of Alternating Current, for both Solid and Cored Carbons. Summary. APPENDIX. 445 Apparent Area of Disc Viewed from Any Distance. Our Method of Estimating Brilliancy of a Source of Light. Assumptions Made in Photometry. Mean Spherical Candle Power and Total Light. Measurement of Either, by Means of Rousseau's Figures. Why Area of Polar Light Curve Cannot Measure Either. Candle and Gas Shadow Experiments. Supplementary List of Original Communications. LIST OF ILLUSTRATIONS. FIG. PAGE 1 Image of Arc and Carbons, Five Times Full Size ... 3 2 Section of Positive Carbon Showing Outer Crust Curling Away 5 3 Drawing of Arc and Carbons with both Carbons Solid 4 mm. 20 ampere Arc facing 6 4 Drawing of Arc and Carbons with both Carbons Solid 7 mm. 20 ampere Arc .. ... ... ... facing 6 5 Drawing of Arc and Carbons with Cored Positive and Solid Negative Carbon 7 mm. 20 ampere Arc facing 7 6 Drawing of Arc and Carbons with Cored Positive and Solid Negative Car- on 18 mm. 20 ampere Arc facing 7 7 Diagrams of Arcs of various Lengths and with various Currents, between 18 mm. Cored Positive and 15 mm. Solid Negative Carbons (W. E. Ay rton) 9 8 Diagrams of Arcs of various Lengths and with various Currents, between 13 mm. Cored Positive and 11 mm. Solid Negative Carbons (W. E. >yrton) 10 9 Diagrams of A cs of various Lengths, anrl with various Currents, between 9 mm. Cored Positive and 8 mm. Solid Negative Carbons (W. E. Ayrtou) 12 10 Diagrams o r Car ons before and after Sudden Changes of Current (W. E. Ayrton) 15 11 Diagrams of Arcs between Solid Carbons (W. E. Ayrton) ... 15 12 Diagrams of Arcs between Solid Positive and Cored Negative Carbons (W. E. Ayrton) 16 13 Horizontal Arc copied from " Davy's Elements of Chemical Philosophy" 27 14 Figure shoeing the Rotation of the Arc at- the Pole of a Magnet 29 15 Vertical Parallel Carbons showing the Position the Arc takes up near the end- (W. E. Ayrton) ... 36 16 Apparatus for Meas-iring the Resistance of the Arc (Von Lang) 43 17 Apparatus for Testing for a Back E.M.F. in the Arc (Lecher) ... 52 18 Curves showing Conditions for Arc to be "Stable (Blondel) ... 62 19 Apparatus for Testing the Conductivity of the Arc (Fleming) 70 xvi. LIST OF ILLUSTRATIONS. FIG. PAGE. 20 Apparatus for Measuring the Resistance of the Arc (Frith) ... 73 21 Apparatus for Measuring the Resistance of the Arc (Frith and Rodgers) 76 22 Curves Connecting the Instantaneous dVJdA. with the Current for a Constant P.D. (Frith and Rodgers) 79 23 Curves Connecting the Instantaneous dV/dA. with the P.D. for a Constant Current (Frith and Rodgers) ... ... ... 80 24 Apparatus for Measuring the Back E.M.F. of the Arc (Arons)... 82 25 Illustration of Experiments on Particles Shot out from Carbons (Herzfeld) 85 26 Apparatus for Testing for a Back E.M.F. in the Arc (Blondel) 88 27 Apparatus for Testing for a B*ck E.M.F. in the Arc (Granquist) ' 92 28 Hand Fed Arc Lamp 98 29 Plan of Arc Lamps, Lens, Mirror an I Diagram Screen for Magnifying the Image of the Arc ... ... ... ... 99 30 P.D. and Current Curves drawn before the Time- Variability of the P.D. was Realised (W. E. Ayrton) 101 31 Curves for Time-Change of P.D. with Constant Current and Length, after starting the Arc between Cored Positive and Solid Negative Carbons (W. E. Ayrton) 103 32 Curves for Time-Change of P.D. with Constant Current and Length, after starting the Arc between Carbons of various kinds, with ends variously shaped (W. E. Ayrton) ... ... 105 33 The same (W. E. Ayrton) 107 34 Curves showing the Influence of the Shape of the Negative Carbon on the Time-Change of P.D. (W. E. Ayrton) .. ... 109 35 Curves for Time- Change of P.D. with Solid and Cored, Flat and Normal, and Hot and Cold Carbons (W. E. Ayrton) 110 36 Curves for Time-Change of P.D. with Sudden Changes of Current, showing the Influence of a Core in- the Positive Carbon (W. E. Ayrton) ... 113 37 Curves for Time-Change of P.D. with Sudden Changes of Current, Showing the Influence of the Length of the Arc (W. E. Ayrton) 114 38 Curves connecting the P.D. with the Current for various Constant Lengths of Arc, with Solid Carbons ... ... 120 39 The same, with 18 mm. Cored and 15 mm. Solid Carbons (W. E. Ayrton) 128 40 The same with 13 mm. Cored and 11 mm. Solid Carbons (W. E. Ayrton) 129 41 The same with 9 mm. Cored and 8 mm. Solid Carbons (W. E. Ayrton) 130 42 Curves showing the Changes in the P.D. produced by Coring the Positive Carbon (W. E. Ayrton) 132 43 Hypothetical Curves of P.D. and Current, for a Constant Length of Arc, showing the Effect of Coring the Positive Carbon , 134 44 Cui ves connecting P.D. and Length of Arc for various Constant Currents. Solid Carbons 136 LIST OF ILLUSTRATIONS. X vii. FIG * PAQB 45 The same with 18 mm. Cored and 15 mm. Solid Carbons (W. E. Ayrbon) . ... 139 46 The same with 13 mm. Cored and 11 mm. Solid Carbons (W. E. Ayrton) 140 47 The same with 9 mm. Cored and 8 mm. Solid Carbons (W. E. Ayrton) 140 48 The same with both Carbons Cored (W. E. Ayrton) 142 49 Hypothetical Curves of P.D. and Length of Arc, for a Con- stant Current, showing the Effect of Coring the Positive Carbon ... ... ... .. ... 144 50 Curves connecting the Area of the Crater with the P.D. between the Carbons, for various Constant Currents 153 51 Curves connecting the Area of the Crater with the Length of the Arc, for various Constant Currents 155 52 Curves connecting the Soft Crater Ratio with the Length of the Arc, for various Constant Currents ... ... 156 53 Curves connecting the Hard Crater Ratio with the P.D. between the Carbons, for various Constant Currents 157 54 Curves connecting the Area of the Crater with the Current, for various Constant Lengths of Arc ... ... 159 55 Curves connecting the P.D. between the Carbons with the Length of the Arc, for Cored Positive and Solid Negative Carbons of various Diameters ... ... 163 56 Curves connecting the Apparent Resistance of the Arc with its Length, for various Constant Currents, with 18 mm. Cored and 15 mm. Solid Carbons ... ... 164 57 The same with 13 mm. Cored and 11 mm. Solid Carbons ... 165 58 The same with 9 mm. Cored and 8 mm. Solid Carbons ... 166 59 Curves connecting Current with Length of Arc for various Constant P.Ds 169 60 Curve connecting Current with Time for a Constant P.D. and Length of Arc 171 61 Curves connecting P.D. with Current, for various Constant Lengths of Arc, with Solid Carbons 177 62 Curves connecting Power expended in Arc with Length of Arc, for various Constant Currents, with Solid Carbons 180 63 Curves connecting Power with Current, for Lengths of Arc mm. and 7 mm., with Solid Carbons 182 64 Hyperbola connecting P.D. with Current, for a Constant Length of Arc, with Solid Carbons 187 65 Curves connecting Power with Length of Arc, for various Constant Currents, from Peukert's Experiments 194 66 Curves connecting Power with Current, for Lengths of Arc mm. and 10 mm., from Peukert's Experiments 196 67 Curves connecting Power with Length of Arc for various Constant Currents, from Cross and Shepard's Experiments... 199 68 Curves connecting Power with Current for Lengths of Arc and ^ inch, from Cross and Shepard's Experiments 200' xviii. LIST OF ILLUSTRATIONS. FIG. PAGE 69 Diagrammatic Representation of Apparatus used for Finding the P.D. between each Carbon and the" Arc 209 70 Diagrammatic Representation of various Arrangements of Main and Exploring Carbons ... .... ... ... . 213 71 Curves connecting Positive-Carbon P.D. with Current, for various Constant Lengths of Arc ... ... ... ... 215 72 Curves connecting Positive- Carbon P.D. with Length of Arc, for various Constant Currents ... ... ... ... ... 216 73 Curves connecting Negative- Carbon P.D. with Current, for various Constant Lengths of Arc ... ... ... ... 218 74 Curves connecting Negative-Carbon P.D. with Length of Arc, for various Constant Currents ... ... ... ... ... 219 75 Curves connecting Positive- Carbon Power with Length of Arc, for various Constant Currents... ... ... ... ... 220 76 Curves connecting Positive- Carbon Power with Current, for various Constant Lengths of Arc ... ... ... ... 221 77 Curve connecting Negative- Carbon Power with Current for any Length of Arc 224 78 Curves connecting Positive-Carbon P.D. plus Negative Carbon P.D. with Current, for various Constant Lengths of Arc .. 226 79 Curves used for determining graphically the Relations between the E.M.F. of the Dynamo, the outside Resistance in the Circuit, the P.D., Current, and Length of Arc with Solid Carbons 242 80 Curves connecting P.D. with Current, for various Constant Lengths of Arc, with Solid Carbons ... ... ... ... 280 81 Photographs of Arcs immediately after Hissing has begun, after Hissing has continued so me time, and when the Arc has become Silent again ... ... . ... ...facing 292 82 Diagram of a Short Hissing Arc ... ... ... ... ... 293 83 Diagrams of a Silent and a Hissing Arc ... . ... ... 294 84 Diagrams of Arcs and Carbons with Current increasing from 6 amperes, silent, to 30 amperes, hissing ... ... ... 295 85 Diagrams of Arcs and Carbons with the same Current and Length of Arc, but different sized Carbons ... ... ... 296 86 Crucible Employed for Experiments on Enclosed Arcs ... 302 87 Curves connecting P.D. with Current for a nearly Constant Length of Arc when the Arc was enclosed in a Crucible . . . 304 88 Disc Viewed from a Distance 317 89 Tracings of " Normal" Arc (Trotter) ... 318 90 Tracings of Short Arc (Trotter) 319' 91 Polar Curves of Apparent Area of Crater and Candle Power in " Normal" Arc (Trotter) 320 92 Polar Curves of Apparent Area of Crater and Candle Power in Short Arc (Trotter) 321 93 Curve connecting Apparent Area of Crater with Light of "Normal" Arc (Trotter) 322 LIST OF ILLUSTRATIONS. xix. FIG. PAGE 94 Diagrams of Arcs and Carbons for showing the Variation in the Shape of the Negative Carbon with the same Current but different Lengths of Arc... ... ... ... 324 95 Side View of Apparatus used in Measuring the Mean Spherical Candle Power of the Arc (W. E. Ay rton) 326 96 General Plan of Apparatus for Measuring the Mean Spherical Candle Power of the Arc (W. E. Ayrton) 327 97 Curves connecting Mean Spherical Candle Power with Length of Arc, for various Constant Currents (W. E. Ayrton) ... 329 98 Curves connecting Total Light emitted with Length of Arc for a Constant Current ... ... ... ... ... ... 330 99^ Apparatus employed in Measuring the Total Light emitted by 100 J the Arc (Blondel) 331 101 Curves connecting Total Light with Length of Arc for a Constant Current with Solid Carbons of various sizes (Blondel) 333 102 Curves connecting Total Light with Length of Arc, for a Constant Current, with Cored Positive and Solid Negative Carbons of various Sizes (Blondel) ... ... ... ... 334 103 Diagrams of Arcs of different Lengths, with the same Current, between the same Carbons ... ... ... 336 104 Area proportional to Total Light that would be received from the Crater if none were obstructed by the Negative Carbon . . . 338 105 Area proportional to Total Light actually received from Crater 339 106 Diagram of Arc and Carbons with Lines for finding the Quantity of Light Obscured by the Negative Carbon in any one direction ... ... ... ... ... ... ... ... 340 107 Geometrical Construction for the Area of Crater Obscured by the Negative Carbon in any one direction ... ... ... 341 108 Curves connecting Light received from Crater with Length of Arc, obtained from Diagrams in Fig. 103 ... 343 109 Photograph of Candle Flame 350 110 Section of Apparatus used for Observing the Shadow of the Arc 353 111 The Light from the Crater, the Arc Mist, and the White Spot, passing through a narrow Slit on to a White Screen 358 112 Band of Violet Light, bordering a Shadow made by intercepting the Light of the Crater of an Arc ... 359 113 Arc with Mist divided into Layers of Equal Thickness ... 361 114 Hypothetical Curves obtained from Fig. 108 by allowing for the Absorption of Crater Light by the Arc Mist 363 115 Diagrams of Arc and Carbons, showing the Effect on the Shapes of both Carbons of varying the Current with a Constant Length of Arc 365 116 Curves connecting the Mean Spherical Candle Power of the Arc with the Current, for Constant Lengths of Arc of 1 mm. and 4 mm. (W. E. Ayrton) 366 117 Curves connecting the Total Light emitted by the Arc with the Current, for a Constant P,D. of 45 volts (Blondel) 367 xx. LIST OF ILLUSTRATIONS. FIG. PAGE 118 Curves connecting the Power supplied to the Arc and the Power absorbed by the Mist with the Length of the Arc, for a Constant Current of 10 amperes ... ... ... ... 373 119 Curve showing the proportion of the whole Power supplied to the Arc that is Wasted in the Mist, with a Constant Current of 10 amperes ... ... ... ... ... ... ... 373 120 Diagrams of Arc and Carbons with the same Current and Length of Arc, but different sized Carbons ... ... ... 376 121 The same 379 122 Curves connecting Light Efficiency with Length of Arc for a Constant Current of 10 amperes with Solid Carbons (Blondel) 381 123 The same with Cored Positive and Solid Negative Carbons (Blondel) 382 124 Curves connecting Light Efficiency with Length of Arc for a Constant P.D. (Blondel) 385 125 The Shaping of the Negative Carbon with Large and Small Craters and with Long and Short Arcs ... ... ... 395 126 Hypothetical Areas of Volatilisation and Non-volatilisation in Crater 397 127 Shapes assumed by the Positive Carbon, with the same Area of Volatilisation, but with a Long Arc in the one Case and a Short Arc in the other 398 128 Diagrams of Arc and Carbons with Mist and Flame very care- fully Outlined 401 129 Curve counecting the Power Expended in the Arc Mist with the Current, for a Constant Length of Arc of 2 mm. . . 403 130 Curves showing Simultaneous Time-Changes of P.D., Current and Eesistance 405 131 Curves showing the Effect of the Frequency of an Alternating Current, Superimposed on a Direct Current Arc, on the Simultaneous Time-Changes of P.D. and Current 408 132 Curves connecting Values of with the Frequency of the Superimposed Alternating Current ... ... ... ... 412 133 Curves connecting the Mean Cross Section of the Arc Mist with the Current, for a Constant Length of Arc, with Solid- Solid, Solid-Cored, Cored-Solid, and Cored-Cored Carbons ... 420 134 Hypothetical Curves Exemplifying the Changes, in the Curve" connecting P.D. with Current for a Constant Length of Arc, caused by a Core in the Positive Carbon ... ... ... 423 135 Hypothetical Curves connecting i with the Current, for a Constant Length of Arc... ... ... ... ... .. 430 136 Hypothetical Curves connecting - - e with the Current, for a oA Constant Length of Arc 432 137 Hypothetical Curves Connecting __ with the Current, for a oA Constant Length of Arc... ,, ,, ,., ,.. 434 LIST OF ILLUSTRATIONS. xxi. FIG. PAGE 138 Hypothetical Curve of Time-Change of P.D. Accompanying a Sudden Change of Current 435 139 Hypothetical Curves Connecting with the Length of the Arc, 5A for a Constant Current ... ... ... 436 140 Hypothetical Curves Connecting with the Frequency of an Addei Alteroating Current ... ... ... ... ... 438 142 \ Figures Used in Finding the Apparent Area of a Disc ... ... I ^^ 143 | Figures Used in Finding an Area Proportional to the Mean Spheri- 144 \ cal Candle Power of an Axially Symmetrical Source of Light 453 145 Polar Light Curves of Two Similar Sources, the one having twice the Illuminating Power of the other ... ... ... 455 146 Photograph of the Shadow of a Candle Flame 457 xxiii. LIST OF TABLES. PAGE I. Current, Resistance, and E.M.F. of Arc (Schwendler) ... 37 II. Areas of Crater with Different Currents ... ... ... 39 III. P.Ds. with Silent and Hissing Arcs (Niaudet) 40 IV. P.D. Current and Length of Arc (Nebel) 48 V. P.Ds. for Different Conditions of the Arc (Lecher) ... 53 VI. P.Ds. with Constant Current and Varying Lengths of Arc (Luggin) 55 VII. P.D. between Carbons with and without a Sprinkling of Soda (Luggin) 56 VIII. Current Density and Area of Tip of Positive Carbon (Luggin) ... ... ... ... 61 IX. Experiments to Find Back E.M.F. of Arc (Blondel) ... 90 X. Experiments to Find Back E.M.F. of Arc (Granquist) ... 93 XI. P.D. for Normal 5mm. Arc with Various Constant Currents (Solid Carbons 11/9) 121 XII. P.D. and Current with Various Constant Lengths of Arc (Solid Carbons 11/9) 122 XIII. Same as above (Cored Positive and Solid Negative Carbons 18/15) ( W. E. Ayrton) 125 XIV. Same as above (Carbons 13/11) 126 XV. Same as above (Carbons 9/8) 127 XVI. Diameter of Crater, Square of Diameter, P.D., and Current for Various Lengths of Arc 151 XVII. Diameters of Crater, Observed and Calculated, for Various Currents and Lengths of Arc ... ... ... ... 154 XVIII. Crater Ratios for Various Currents and Lengths of Arc ... 156 XIX. Depth of Crater with Different Currents and Lengths of Arc 160 XX. Influence of Diameters of Carbons (Positive Cored) on P.D. 162 XXI. Comparison of Observed and Calculated P.Ds. for Different Currents and Lengths of Arc (Solid Carbons 11/9) ... 185 XXII. Edlund's Results referred to General Equation for P.D., Current and Length of Arc 190 xxiv. LIST OF TABLES. PAGE XXIII. Frolich's Results referred to General Equation for P.D., Current, and Length of Arc ... ... ... ... 192 XXIV. Peukert's Results referred to the same Equation ... ... 195 XXV. Cross and Shepard's Results referred to the same Equation 201 XXVI. Duncan Rowland and Todd's Results referred to the same Equation 204 XXVII. Positive Carbon P.Ds. for Various Currents and Lengths of Arc (Solid Carbons 11/9) 214 XXVIII. Negative Carbon P.Ds. for Various Currents and Lengths of Arc (Solid Carbons 11/9) 217 XXIX. Calculated Values of Positive Carbon P.Ds. (Solid Carbons 11/9) 223 XXX. Calculated Values of Negative Carbon P.Ds. (Solid Carbons 11/9) 225 XXXI. Sum of Positive and Negative Carbon P.Ds., for Various Currents and Lengths of Arc (Solid Carbons 11/9) ... 227 XXXII. Calculated Values of Sum of Positive and Negative Carbon P.Ds. (Solid Carbons 11/9) 227 XXXIII. P.D. between Carbons with Third Carbon in Arc near Positive Carbon (Solid Carbons 11/9) 229 XXXIV. P.D. between Carbons with Third Carbon in Arc near Negative Carbon (Solid Carbons 11/9) ..229 XXXV. Mean P.D. between Carbons with Third Carbon in Arc (Solid Carbons 11/9) 230 XXXVI. Calculated Values of P.D. between Carbons with Third Carbon in Arc (Solid Carbons 11/9) 231 XXXVII. Positive Carbon P.D. plus Vapour P.D. (Solid Carbons 11/9) ... 233 XXXVIII. Negative Carbon P.D. plus Vapour P.D. (Solid Carbons 11/9) 234 XXXIX. Comparison, with Solid and Cored Carbons, of P.D. between Carbons with Third Carbon in Arc 235 XL. Comparison, with Solid and Cored Carbons, of Positive Carbon P.Ds 236 XLI. Comparison, with Solid and Cored Carbons, of Negative Carbon P.Ds 237 XLII. Conditions to obtain Maximum Power-Efficiency with E.M.F., P.D., Current, Length, and Series Resistance fixed, in Turn (Solid Carbons 11/9) 270 XLIII. P.D. between Carbons at Hissing Points (Solid Carbons 11/9) 283 XLIV. Currents at Hissing Points (Solid Carbons 11/9) 283 XLV. Comparison of Calculated and Observed Values of P.Ds. at Hissing Points (Solid Carbons 11/9) 285 XL VI. Total P.Ds. and Positive Carbon P.Ds. at Hissing Points, and with Hissing Arcs (Solid Carbons 11/9) 287 XL VI I. Diminution of Total and of Positive Carbon P.Ds. Accom- panying Hissing (Solid Carbons 11/9) 287 LIST OF TABLES. xxv. PAGE XLVIII. P.D. and Length of Arc for Hissing Arcs (Cored Positive and Solid Negative Carbons) ... ... 291 XLIX. Effect of Blowing Hydrogen against Crater of Arc ... 306 L. Mean Spherical Candle Power of Arcs of Different Lengths with Constant Currents (W. E. Ayrton) 328 LI. Crater Light with and without Absorption by Arc, for Arcs of Various Lengths, with Constant Current . 362 LI I. Data of some Commercial Arc Lamps . 383 LIII. Cross Section of Arc Mist, Current, P.D., and Resistance of, and Power Expended in Mist (Solid Carbons 11/9) ... 402 LIV. Currents and P.Ds. with Small Alternating Current Superimposed on 10 Ampere Arc (Solid Carbons 11/9) 415 LV. Mean Cross Section of Mist for Different Currents and Lengths of Arc with Various Carbons... ... ... 419 LVI. Cross Section of Mist Close to Crater for Different Currents and Lengths of Arc with Various Carbons ... ... 421 LVII. Ratios of Cross Section of Mist with one Current to Cross Section with Smaller Current ... .,. 426 LVIII. Ratios of Cross Section of Mist Close to Crater with one Current to Cross Section with Smaller Current ... 426 List of Original Communications Concerning the Arc .... ... 94 Supplementary List ... m 458 EBBATA, Page 13, line 1, for Fig. 9 read Fig. 7. Page 14, line 3, for 5 read 6. Page 50, line IJor Fig. 13 read Fig. 16. Page 51, line 8 from end, for back E.M.F. of the arc read P.D. between the carbons. Page 62, line 6 from end, for 1890 read 1891. Page 64, line 5 from end, for Capt. Abney read Sir W. de W. Abney. Page 64, line 3 from end, for Mr. Crookes read Sir. W. Crookes. Page 88, line 11, for air read arc. Page 95, line 7 from end, for p. 2 read p. 227. Page 207, line 3, for Twelve read Fourteen. CHAPTER I. THE APPEARANCE OF THE ARC. SINCE the discovery of the electric arc early in the present century, Nature has been subjected to a series of questions with the object of extracting from her a statement of the mysterious laws that govern it. These questions which we call experiments she has, so far, answered but sparingly. They have been repeated again and again, but, even when replies have been vouchsafed, they have been couched in such ambiguous terms that one experimenter has interpreted them in one way, and another in another, and we are still far from having a clear understanding of the laws of the arc. A certain amount of knowledge has, however, been gained, and it is proposed in the present work to deal with some of the facts that have been acquired concerning direct-current arcs, maintained between carbon rods, the arc being not longer than the diameter of the positive carbon, and the potential difference between the rods being not greater than, say, 100 volts. It is proposed, in fact, to deal only with such direct- current arcs as are used in the lighting of our streets, and to leave on one side alternate-current arcs, very long arcs main- tained with a large potential difference between the carbons, and arcs maintained between metals. The arc is so bright that, if looked at with the naked eye, it appears to be simply a dazzlingly bright spot with needle-like rays diverging from it in all directions, but by projecting its image on to a screen its real shape and colour may be easily observed if the image is magnified, so much the better. In arcs maintained between vertical carbon rods, with the positive carbon uppermost, both shape and colour vary accord- ing to the length of the arc and the current flowing, but certain characteristics are common to all. In all, the end of A 2 THE ELECTRIC ARC. the positive carbon is more or less pointed, with a depression at the tip called the crater. This depression is shallower, the longer the arc, and is practically non-existent with arcs of lengths approaching the diameter of the positive carbon. The end of the negative carbon is also pointed, but instead of a depression it often has a sort of little hillock on the tip. The tips of both carbons are white hot, and in the space between them there is a faint purple light, outlined by a deep shadow. At a very early stage in the experiments made by the students of the Central Technical College, under Prof. Ayrton's direction, it was found that altering either the current or the length of the arc caused a change in the shapes of the carbons and visible arc, which in some cases was very considerable. It was therefore thought advisable to obtain a record of these changes under all circumstances, and diagrams of the carbons and arc were taken, when the potential difference had acquired its steady value, for all the currents and lengths of arc observed. The diagrams were obtained by placing a piece of squared paper over the screen on which the enlarged image of the arc was projected, and drawing the complete outlines of the carbons and image. The carbons are always easy enough to draw for they are very definite, but the exact curve which outlines the purple image of the arc is much more difficult to obtain, for this image melts off very gradually into the surrounding darkness. Fig. 1 is a reproduction of one of the diagrams half of the original size, and since the original diagram enlarged the carbons ten times, this reproduction shows them Jive times full size It may be observed that there is a white-hot crater at the end of the positive carbon, and a white-hot tip to the negative, and that the area of the crater in the positive is much larger than the area of the white-hot tip of the negative. That this glowing tip of the negative carbon gives out a fair amount of light may be easily seen by observing the beam of light from an arc after it has passed through a lens. This beam divides itself into two distinct parts, separated by a dark space, so that it looks like two beams, one coming from the crater of the positive, the other from the bright spot on the negative carbon. If a piece of paper be placed in the dark space between the two beams, it will have a faint violet Dull Ydllo Dar Sh Vihit Vic let Red. Y'llow \ : ts. FIG. 1. Image of Carbons and Arc 5 times full size. Current, 10 amperes. Length of Arc, 3mm. P.O. steady at 46 -5 volts. 4 THE ELECTRIC ARC. light on it, but this light is evidently not sufficient to make the dust particles in the air visible. The area of the bright spot on the tip of the negative carbon increases with the current, but at a much slower rate than the area of the crater in the positive, so that the ratio of the area of the crater to the area of the negative bright spot increases rapidly as the current is increased, with silent arcs. The part marked "bright spots" on the negative carbon represents a circlet of seething balls, which, whatever they may be, always appear at the junction of the light and dark parts of the negative carbon. Above them, as far as the line which is marked " yellow," the carbon presents a granu- lated appearance, being covered with very small boiling balls, and the whole being of a reddish yellow colour. Then comes the yellow-hot part, marked " yellow," which is quite smooth, and finally the white-hot tip. The positive carbon has also its smooth yellow-hot part marked " yellow," and its band of granulated darker yellow part above that, and higher still its circlet of seething balls larger than those on the negative. The outlines of these balls are indicated (Fig. 1) in the highest wavy line, but they cannot generally be seen very distinctly, because no light is thrown on to them to be reflected back again, in the same way as the light from the crater is cast on to the negative carbon. Looking at the arc itself through smoked glass, instead of at the image, it is seen that these balls are really the frayed ends of an outer crust of the carbon which is peeling off. It is as if the inner part of the carbon, being much hotter than this outer crust, caused it to expand and split, forming a sort of fringe hanging down over the inner hotter part from which it has broken away. Between this crust which crumbles at a touch when cold and the body of the carbon there is a space of from Jmm. to 1mm. to the height of 5mm. or more, from which when the arc is burning sparks fly out, drop down to the edge of the crust, and then fly out- wards and upwards, probably carried along by the strong upward draught of the column of hot carbon and air. It is possible that they finally settle on the positive carbon, for after the arc is extinguished this carbon is found to have numerous small particles of carbon on it arranged fairly THE APPEARANCE OF THE ARC. 5 symmetrically. The tips of the strips of carbon that form the outer crust apparently get burnt by the hot volatile carbon into a semi-globular shape, and they boil and bubble under the action of this heat just as a lump of sugar does when held in a candle flame, and probably the action is really very much the same in both cases. Fig. 2 is a drawing of a section of a positive carbon with its outer crust, A, showing the way in which this outer crust bulges out and leaves a space between itself and the inner part of the carbon, B. FIG. 2. Section of Positive Carbon with the Outer Crust curling away from it. Between the part of the arc marked " violet " in Fig. 1 and that marked "green" there is a dark space, which is scarcely perceptible with small currents and short arcs, but becomes very wide and well marked with large currents and long arcs. The " green " line shows the extreme edge of the luminous part of the arc, or, at least, of that part which is bright enough to show light on the image. Figs. 3 to 6 show clearly the outlines of the purple and green parts of the arc, and of the shadow between them, under different conditions. These figures I obtained by tracing the enlarged outlines of the carbons and arc in the way already described; very 6 THE ELECTRIC AEG. special attention being given to the outlines of the purple part of the arc, the shadow, and the green outside part. The outlines were then shaded, so as to give as nearly as possible the values of the light given out by each part. Thus the most light is given out by the crater of the positive carbon, and by the tip of the negative carbon ; therefore these were left white. The shadows between the purple and green parts of the arc are somewhat more abrupt than they really were, but their shapes are, I believe, correct. Unless the axes of the two carbons are absolutely in line, the arc is always a little to one side or the other, and that is the reason that the arc in all these four figures is slightly out of the centre ; it is almost impossible to get it perfectly central. In Fig. 4 the outlines of the balls of boiling carbon on the positive as well as on the negative carbon are shown. In Figs. 3 and 5 they could only be seen on the negative carbon, and in Fig. 6 the arc was so long that the screen was not large enough to show the boiling balls on either of the carbons. The current used for the whole four figures was 20 amperes, the carbons were 18mm. positive and 15mm. negative. In Fig. 3 the length of arc was 4mm., and the carbons used were both solid. It may be seen that the central purple part of the arc is of the form of an oblate spheroid, broken in upon by the tips of the carbons. Another diagram, made at the same time, of an arc of the same length and with the same current, but with the positive carbon cored, showed a central part of much the same shape, but of smaller area, smaller, in fact, not only in width, but in length, because although the distance between the tip of the negative carbon and the plane through the edge of the crater was in each case 4mm., the central part surrounded a much greater length of the point of the negative with the solid positive carbon than with the cored. The green part of the arc also started much higher up the negative with the cored than with the solid positive carbon, and touched the positive carbon 4mm. from its tip, whereas the green part could be seen at a distance of 14'5mm. up the solid positive carbon (Fig. 3). Thus, the whole visible part of the arc is much larger with a solid than with a cored positive carbon with an arc of 4mm. and a current of 20 amperes, but the general form of the arc is very much the same. FIG. 3. Carbons : Positive, 18mm. solid ; Negative, 15mm. solid. Current, 20 amperes. P.D. between Carbons, 48 volts. Length of Arc, 4mm ?' i / FIG. 4.- Carbons : Positive, 18mm. solid ; Negative, 15mm. solid. Current, 20 amperes. P.D. between Carbons, r>G volts. Length of Arc, 7mm. FIG. 5. Carbons : Positive, 18mra. cored ; Negative, 15mm. solid. Current, 20 amperes. P.D. between Carbons, 51 volts. Length of Arc, 7mm. 4 FIG. 6. Carbons : Positive, 18mm cored ; Negative, 15mm. solid. Current 20 amperes. P.O. between Carbons, 68 volts. Length of Arc, 18mm . THE APPEARANCE OF THE ARC. 7 In Figs. 4 and 5 the two arcs are of the same length, 7mm., the current 20 amperes; but for Fig. 4 the positive carbon was solid, and for Fig. 5 it was cored. Here, again, both the central purple part and the green portion surround the negative carbon to a greater distance when the positive carbon is solid than when it is cored ; again, also, both the central portion and the whole visible arc are larger with the solid than with the cored positive carbon. But in these two figures the form of the central part is also different. With the cored carbon it is gourd-shaped, with the solid, pear-shaped. With the cored carbon the arc has a dark shadow dividing it into two unequal parts, with the solid carbon this shadow is entirely absent. The tip of the positive carbon has a longer, and the tip of the negative a shorter point with the cored than with the solid carbon, which may be due to a lower temperature of the crater in the cored carbon, for, as will be shown later (page 14), greater heat is indicated by a more pointed negative and a less pointed positive carbon. The balls on the positive carbon in Fig. 4 were not really luminous the whole time I was drawing that figure, but every now and then there was a little hiss caused by some imper- fection in the carbon, which lighted them up, and during one of those periods I drew them. In Fig. 6 the positive carbon was cored, and the arc was 18mm. in length, the current still 20 amperes. In this arc the gourd shape is much accentuated the central part looks almost like two air balls, the one next the positive carbon placed horizontally, the other placed vertically below it, and touching the negative carbon. The vertical ball has inside it a small ball touching the negative. All three balls were of different shades of purple, the large one near the negative carbon was palest, the small one was darker, and the one near the positive was darkest of all. The shade of the purple part of the arc was quite different according as solid or cored positive carbons were used, being much bluer with solid than with cored carbons. I tried to obtain an arc of 18mm. with both carbons solid, in order to compare the two diagrams, but found it impossible to maintain an arc of more than 14mm. with two 18mm. and 15mm. solid carbons. Every time the length of the arc was 8 THE ELECTRIC ARC. increased beyond this the arc went out, because, as will be shown later, the E.M.F. of the dynamo was insufficient to maintain a longer arc with a current of 20 amperes flowing when both carbons were uncored. The shape of the 14mm. arc showed no tendency towards the double ball form observable with the cored carbon; it retained the pear shape noticed in Fig. 4. I have, however, found a tendency to assume the double ball form with arcs maintained between solid carbons when the current was very small ; but, if the length of the arc is the same in both cases, the current has to be much smaller to produce this form when the positive carbon is solid than when it is cored. Thus it is clear that when the current is kept constant, altering the length of the arc, alters both its size and shape ; and the use of a cored positive carbon, instead of a solid, changes the size, the colour, and, in long arcs, the form of the visible part of the arc. The diagrams in Figs. 7 to 12 are reproductions of some of those made by Prof. Ayrton's students. They show very accurately the shapes of the ends of the carbons under the given conditions, but, as in Fig. 1, the dotted outlines of the arc must be taken to be only approximately correct. They show, for instance, that, with a given length of arc, the diameter of the visible part of the arc is smaller, the smaller the current, but not with absolute accuracy exactly how much smaller. These diagrams have been reduced from ten times the full size of the carbons to two-thirds full size, and arranged in order of the sizes of the carbons, the lengths of the arc, and the currents. Figures in the same horizontal row are for the same length of arc with different currents, and figures in the same vertical column are for the same current with different lengths of arc. We will first examine what is the effect on the shape of the negative carbon of changing (1) the current strength, and (2) the length of the arc ; and then we will see what effect these same changes have on the shape of the positive carbon. In all the figures with a short arc, say 0'5mm. (Fig. 7), the negative carbon is quite pointed, even with a small current, and it becomes more and more pointed as the current becomes larger and larger. With a 1 mm. arc the negative is less pointed, Amperes, 5 Amperes Amperes 130 Ampere" p*n n w A FIG. 7. -Carbons, Positive (upper) 18mm. cored. Negative (lower) 15mm. soHd. 10 THE ELECTEIC ARC. both with small and large currents, than with a O'Smm. arc, and as the arc gets longer the negative becomes blunter and blunter although in every case it is more pointed with a large current than with a small one for the same length of arc. At last, when the arc is 6mm. long, the negative is quite blunt, even 2 Amperes 6 Amperes. 10 Amperes. 16 Amperes. 21 Amperes. 28 Amperes u iU E @ff7=& p y n FIG. 8. Carbons, Positive (upper) 13ram. cored. Negative (lower) llmm solid. when a current as great as 20 amperes is flowing. Thus, the tip of the negative is more pointed (1) The shorter the arc, (2) The larger the current. In order to understand the causes of these phenomena, we must examine the shapes of the negative tips a little more closely. THE APPEARANCE OF THE ARC. 11 Comparing the 6-ampere 0'5mm. arc with the 6-ampere 3mm. arc in Fig. 7, one sees that the former is like the latter, with a sort of extra point added; comparing the 30-ampere arcs for the same two lengths, the same thing is observable, only it is much more pronounced. This sort of extra point is, in fact, found on all the negative carbons when the arc is short, whatever the current, and it is not found on any when the arc is long. This point must, therefore, depend upon the carbons being near together, and is caused, I think, solely by carbon deposited on the negative tip from the crater of the positive carbon. As the arc is lengthened, less and less of the carbon shot out by the positive reaches the tip of the negative carbon, and this little extra tip becomes smaller and smaller, and finally disappears. When the distance between the carbons is great and the current small, the arc often plays about the edges of the carbons, sometimes seeming to travel round and round them, sometimes remaining stationary in one place for a short time, and then going to another, and so on, but always trying to make itself as long as possible. But in some cases, however the positive end of the arc may move, the negative end appears to remain in the same place, so that the negative bright spot remains fixed in position, and when this is so, on extinguishing the arc, it is found that there is a small crater at the end of the negative carbon. It is possible that this crater would always exist in the negative carbon were it not that when the arc is shorter the crater is constantly filled up by the carbon deposited on it from the positive carbon. When the arc is very short, and the current large enough to cause hissing, the deposition takes place so rapidly as to cause a " mushroom " to form, such as may be seen in the 25-ampere 1mm. arc in Fig. 9. When the arc is short, even when it is silent, the deposition is still often rapid enough to cause the negative carbon to grow longer instead of shorter, and this fact alone would seem to prove that the extra tip noticed on the negative carbon with short arcs is caused by carbon deposited on it from the crater. It is true that with large currents the tip of the negative carbon is somewhat pointed, even when the arc is not very 12 THE ELECT EIC ARC. 3 Amperes. 6 Amperes. 12 Amperes 16 Amperes. 26 Amperes. 30 Amperes S T1 A u IS u FIG. 9. Carbons, Positive (upper) 9mm. cored. Negative (lower) 8mm. solid- THE APPEARANCE OF THE ARC. 13 short, as in the 30-ampere 3mm. arc in Fig. H, but it seems to be pointed in a different way. The end of the carbon has no little extra tip on it, but becomes more nearly cone shaped, and this sort of pointing is attributable, I think, to quite a different cause namely, the burning away of the carbon. Most of the heating of the negative carbon takes place from the out- side, and is caused partly by radiation from the crater and partly by the volatile carbon giving up its heat to it. When the current is small the heat is comparatively small ; there- fore only a thin layer and a short length of the negative carbon is made hot enough to burn away, and consequently the point, which is the result of the burning away, is short and blunt. With large currents, however, the heat, being greater, reaches farther, both through and down the negative carbon, and the resulting tip is longer and more slender. It is more or less conical, because the parts farther away from the positive carbon get less heat, and, therefore, a thinner layer of them is burnt away. Thus with short arcs there are two distinct causes tending to give the tip of the negative carbon its special shape, whereas with long arcs one of these causes is nearly or quite inoperative, hence the difference of character of the shapes of the negative carbons in the two cases. It is much more difficult to find out what happens to the posi- tive carbon than to the negative when the arc is lengthened or the current increased, because that carbon is very rarely luminous over the whole length of its tapering part. As has already been pointed out (page 4), the negative carbon is always bathed in the light from the positive, and, therefore, its shape is very easily discerned; but the positive sends all its own light away from it, and can receive little, if any, from the negative. But even so, by comparing the carbons in those cases in which it has been possible to trace the positive carbon to its unburnt part, it may be perceived that it also tapers more with a short arc than with a long one when the same current is flowing, and has a longer, but less pointed, tapering part with a large current than with a small one. For instance, take the 6-arnpere 0'5mm. arc and the G-ampere 5rnm. arc in Fig. 7, evidently the positive carbon 14 THE ELECTEIC ARC. tapers more in the former than in the latter, and in the 5mm. arcs in the same figure the positive carbon has a longer tapering part with 25 amperes than with IT amperes. Also it will be found that wherever the craters show, the diameter of the crater is greater with a larger current than with a smaller one for the same length of arc and greater with a longer arc than with a shorter one when the same current is flowing. Apparently what happens is this. The positive carbon is consumed in two ways (1) by being shot out from the crater either in the form of vapour or of small particles, (2) by burn- ing in combination with air. It is not probable that volatilisa tion, which requires an enormous temperature, can take place, if it takes place at all, anywhere except at the surface of the crater, and perhaps at the parts of the tip immediately surround- ing that surface ; therefore all the shaping of the positive carbon, except the formation of the crater, must depend upon its burning in combination with air. At the extreme tip the burning will take place most rapidly, because, owing to the immediate vicinity of the crater, the surface carbon will be hotter there than anywhere else, and the larger the crater the more rapidly the tip will burn away. Thus, instead of becoming more pointed as the current increases, the positive carbon actually becomes less pointed, because the tip is con- sumed so much faster than the sides. Although it is less slender, the point is longer, however, because the increased amount of volatile carbon extends farther up the sides, and thus burns away a longer portion of the carbon. When the arc is short, the volatile carbon, not finding room between the tips, spreads out farther, and so also spreads farther along the surfaces of the carbons and causes them to burn away to a greater distance than when the arc is long. In fact, a given amount of volatile carbon must take up a given space with a given pressure all round it. If it can get this space be tween the carbons, it takes it ; if not, it extends itself sideways and longways, and hence the ends of both the carbons have longer points with short arcs than with long ones, when the current is the same for each length of arc. Fig. 10 shows very well the alteration that takes place in the shapes of the carbons when the current is suddenly changed from a higher to a lower, and from a lower to a THE APPEARANCE OF THE ARC. 1& higher value. The left-hand figure shows particularly well the alteration in the negative carbon. In this case, after the carbons had been formed by a current of 30 amperes, the current was suddenly changed to one of 4 amperes, and three minutes afterwards the dotted line diagram was taken, showing th& negative carbon with a long tapering end. But with the smaller current the volatile carbon did not extend down nearly as far as before; consequently, as the tip of the carbon was gradually burnt away, the tapering of new parts of thi& FIG. 10. Carbons: Positive (upper) 13mm. cored. Negative (lower) llmm. solid. Length of Arc 4mm. A, Current suddenly changed from' 30 amperes to 4 amperes. Dotted lines show the shapes of the Carbons. 3 minutes after the change. Continuous lines show their shapes 25 minutes after. B, Current suddenly changed from 10 amperes to 30 amperes. negative carbon was not kept up. Hence, in 25 minutes after the current had been reduced from 30 to 4 amperes, the end of the negative carbon had become blunt, as shown by the continuous outside line. The small piece at the top of th& 105 Amp. 3 Amp 14 Amp. FIG. 11. A, Carbons : Positive (upper) 13mm. solid. Negative (lower) llmm. solid. Length of Arc, Omm. B and C, Carbons : Positive (upper) 9mm. solid. Negative (lower) 8mm. solid. Length of Arc, 4mm. negative carbon, which is of much smaller diameter than the remainder, indicates how far down the burning action of the amount of volatile carbon given off by the smaller current extended. Fig. 1 1 shows the arc with solid carbons. In B a current of 3 amperes was flowing through an arc of 4mm. Com- 16 THE ELECTRIC AEG. paring this with the arc of the same length, and with the same current in Fig. 9, for which the carbons were of the same size, the only thing to notice is that, as in Figs. 4 and 5, the visible arc, as shown by the dotted lines, is larger with a solid than with a cored positive carbon. Experience has shown that this is quite correct. In every case in which I have been able to compare the sizes of the arcs obtained with solid and cored positive carbons under similar conditions, I have found the area of the visible part to be larger when the carbons were both solid. V A 4 Amperes. 6 Amperes. 10 Amperes. - 16 Amneres A 24 Amperes.j FIG. 12. Carbons : Positive (upper) 13mm. solid. Negative (lower) llmm. cored. Length of Arc, 4mm. In Fig. 12 the positive carbons were solid and the negatives cored, with the result that the latter were burnt away farther down than they would have been if the cases had been reversed, and the negative carbons had craters in them. SUMMARY. When a direct-current silent arc is maintained between vertical carbon rods, the positive carbon being uppermost I. The tip of the positive carbon is white hot, and the tip of the negative has a white-hot spot on it. II. A white-hot crater forms in the end of the positive carbon, and a more or less blunt point forms on the end of the negative. III. The space between the two is filled by a violet light, the shape of which is defined by a shadow, which in its turn is bounded at its sides by a green light. IV. The ends of both carbons are tapered, and the lengths of the tapering parts are increased both by increasing the current and by shortening the arc. V. The diameter of the crater increases as the current increases, and also as the length of the arc increases. THE APPEARANCE OF THE ARC. 17 VI. With uncored carbons the violet part of the arc is bluer, and all parts of the arc are larger than with cored carbons. VII. With uncored carbons the violet part of the arc is of the form of an oblate spheroid when the arc is short, pear- shaped when it is long, and gourd-shaped when it is long and the current is very small. VIII. With cored carbons the violet part is of the form of an oblate spheroid when the arc is short, gourd-shaped when it is long, and sometimes almost of the shape of a figure of 8 when the arc is very long for the current flowing. IX. When the negative carbon is cored, a crater is formed in its tip exactly as if it were a positive carbon. CHAPTER II. A SHORT HISTORY OF THE ARC. ON March 20, 1800, Volta wrote his first letter announcing the discovery of his pile. The news was received by the scientific world with an enthusiasm only to be paralleled by that which was aroused at the end of 1895 by the discovery of the X-rays by Rontgen. New possibilities were opened up, and none could tell whither they might lead. A sort of experimental fever seized upon mankind, or at least upon the scientific part of it, and Paper after Paper was written describing new and inte- resting results obtained with the pile. So numerous were these Papers in the course of the next year that in the middle of 1801 a certain Dr. Benzenberg wrote to the editor of Gil- bert's Annalen : " Could not the Annalen, in consideration of its object, be a little more varied? Galvanism, interesting as it is, is still only a very small part of physics. We can appa- rently only expect any real advance in knowledge from such work as is carried oat on a large scale, and not from each experimenter, whose slight knowledge and small apparatus allow him to discover only what ten others have already found out before him." The first question to which an answer was sought by all these numerous observers was, What is the nature of the new current 1 ? Is it a "galvanic" current? is it "common elec- tricity " ? or is it neither ? Odd as it may now seem, many Papers were written to prove that the voltaic current had nothing in common with either galvanism or common i.e., f fictional electricity. The early experiments may be divided into three classes, viz. : (1) Those which dealt with the effect of the current on living things. (2) Those which produced chemical decompo- c2 20 THE ELECTRIC ABC. sition of inorganic matter, particularly of water. (3) Those which dealt with the heating power of the current, more par ticularly with the sparks produced by making or breaking a circuit. These last experiments led directly to the discovery of the arc, and are, therefore, the only ones with which we ar& immediately concerned. One of the most ordinary ways of using frictional electricity was to produce sparks, and therefore one of the most obvious- methods of showing that the voltaic current was of the same nature as "common electricity" was to make a spark by bringing together two conductors attached to the terminals of a battery. Most of the early observers were able to do this ; but Sir Humphry Davy, towards the end of October, 1800, was the first to try tha effect of using as conductors two pieces of well-burned charcoal, a substance which Priestley had already shown to be a good conductor of electricity.* In speaking of the result of using charcoal Davy said : " I have found that this substance possesses the same pro- perties as metallic bodies in producing the shock and spark when made a medium of communication between the ends of the galvanic pile of Signer Volta." l Later, in a lecture before the Royal Institution, given in 1801, Sir Humphry mentioned that the spark passing between two pieces of well-burned charcoal was larger than that passing between brass knobs, " and of a vivid whiteness ; an evident combustion was produced, the charcoal remained red hot for some time after the contact, and threw off bright coruscations." 8 This is evidently the description, not of an arc, but of a spark. For the essence of an arc is that it should be continuous, and that the poles should not be in contact after it has once started. The spark produced by Sir Humphry Davy was plainly not continuous ; and although the carbons remained red hot for some time after contact, there can have been no arc joining them, or so close an observer would have mentioned it. * Priestley's " History of Electricity," p. 598. 1 To avoid the continual use of footnotes, the titles of the Communica- tions referred to in the text, and of others of interest on the subject, are arranged in chronological order at the end of the Chapter. The numbers in the text refer to the numbers in this list. A SHORT HISTORY OF TEE ARC. 21 la another lecture, delivered at the Royal Institution in 1802, in which he spoke of trying the effect of the electrical ignition of dry charcoal upon muriatic acid gas confined over mercury, Davy said, "The charcoal was made white hot by successive contacts made for nearly two hours." 9 Hence it is quite certain, not only that he knew nothing about the arc at that time, but that the battery he used was incap- able of maintaining an arc, otherwise the successive contacts would have been unnecessary. In reading the accounts of the first experiments made upon the sparks produced by batteries, it seems as if the arc could hardly fail to be discovered very soon ; as if in each case the next experiment must be the one that will produce a veritable arc. But this leaves out of account the resistance of the batteries used. The first batteries were mostly made of coins, such as the half-crown in England, and the double louis d'or in France and Italy, divided from pieces of zinc of the same size and shape by discs of cardboard soaked in dilute acid. The resistance of such a battery would be very great compared with what it should be in order to maintain an arc, and the pissing of a spark would so lower the P.D. between the terminals that no other spark could pass till the battery had somewhat recovered. In fact, these batteries, having a high E.M.F. and great resistance, especially when they consisted of many pairs of plates, were exactly adapted to imitate the action of a frictional machine, and therefore to show that the voltaic current was an electric current which was all that their devisers attempted at first to prove. Cruickshanks very early discarded the cardboard discs, and arranged his pairs of plates in troughs containing dilute acid ; and English experimenters immediately recognised the advan- tage of this arrangement. Most foreigners, however, continued for a long time to use the more primitive form of battery, and hence, although they made very numerous experiments upon the sparks produced by batteries both with charcoal and with metal terminals, their sparks probably remained sparks, and did not develop into arcs. The diminution in the resistance of the battery caused -by the use of larger plates was discovered early in 1801 by Fourcroy, Vauquelin and Thenard, who tried the effect of 22 THE ELECTRIC ARC. plates of different sizes. With eight pairs of plates eight inches in diameter they found that they could produce sparks brighter than with 120 pairs of smaller plates. Pfaff of Kiel says, in describing these experiments, " The rays streamed on all sides several lines wide, thej crackling was very sharp, and in oxygen the wire burnt with a vivid flame." 5 Hence, the experimenters deduced the fact that batteries with large plates were the best to use for producing sparks and observing the heating effect of the current. For some time after 1801 Davy and the other English observers confined themselves principally to experimenting upon the chemical effects of the current in decomposing substances which had proved refractory until this powerful agent was discovered. On the Continent, however, it was otherwise ; the spark had its full share of attention for its own sake. In France Fourcroy, Yauquelin and Thenard, and in Germany and Austria Hitter, Tromsdorff, Gilbert and Pfaff, all experi- mented with it, and melted and burnt gold and silver leaf and thin wires by means of it, causing flames to arise between the two poles. Hence it is impossible to say when and by whom the arc was really discovered. For the arc, after all, is but a spark, which continues after the poles are separated, and which melts and burns or volatilises the substance of the poles. These experimenters probably did not see any great distinction between a continuous and rapidly following shower of sparks and a single spark which continued. They never mentioned the time of duration of their sparks, and they were so much accustomed to sparks passing between the two poles of a frictional machine without actual contact taking place, that it is very possible that a spark continuing to exist after the poles had been separated would appear quite natural to them. The following abstracts and extracts will suffice to show the impossibility of judging when and by whom the arc was really discovered. In 1801 Fourcroy, Vauquelin and Thenard, with a battery of plates a foot square, " ignited wires immediately, and in oxygen they burnt with a very vivid light." 10 In the same year Hitter, of Jena, wrote to Gilbert, the Editor of the Annalen, that in trying to observe which end of a zinc-silver battery evolved the greater heat, he found that, A SHORT HISTORY OF THE ARC. 23 when a silver leaf was attached to the zinc end and well burnt clean charcoal to the silver end, the silver could be completely burnt away by making contact between it and the charcoal ; while, if the position of the silver and charcoal were reversed, the silver did not burn, but there appeared on the charcoal "yellow, more than instantaneous sparks, which were not seen in the other experiment, quite sharp edges of the charcoal appeared to become blunt, in short, everything pointed to a combustion of the charcoal." 6 (The italics are Hitter's.) In the same letter Ritter mentioned that when he had iron wires on each side of the battery, and a spark passed, they some- times became melted together, and he had to use some force to separate them. He also said, " I have spoken above of the big spark that the battery of 224 plates gave at the closing of the silver wire with the zinc plate above it. But also on breaking the circuit it gave sparks. ... On quickly drawing away the iron wire attached to the silver plate in a vertical direction from the surface of the zinc plate, a small red spark appeared, which seemed to come with more certainty when the circuit had been closed for some time before it was opened." In 1802 was published the following account of experiments made in April of the same year by Prof. Tromsdorff, at Erfurth. A leaf of fine gold, after having been fixed to the zinc end of the pile, ignited and burnt with a crackling noise when the wire of the copper side was brought in contact with it. " Other metals burnt with flames of different colours. . . . . To prove that the ascension of the metals is a true oxidation, the experiments may be performed in a hollow glass sphere ; the oxide will adhere to the sides of the glass, and may be collected." n The next account, also in 1802, is anonymous: "Two carbon rods, which were attached as conductors to a battery of 26 pairs, were brought into contact in a receptacle full of oxygen. They caught fire and burnt." 12 In 1803 Mr. Pepys, an Englishman, with a battery of 60 pairs of zinc and copper plates, disposed in two troughs, after the plan suggested by Cruickshanks, found that " carbons of boxwood not only ignited at their point of contact, but glowed red for a distance of quite two inches, and continued to do so for some time." 13 24 THE ELECTRIC ARC. In 1804 Cuthbertson, another Englishman, wrote "charcoal was deflagrated and ignited for about one inch by a battery." u From 1804 till 1807 very little that was fresh was done. The old experiments were repeated by many observers, but no advance was made. In 1807 Cuthbertson wrote more fully on the subject in his book on " Practical Electricity and Galvan- ism," quoted by Prof. Silvanus Thompson in his Cantor Lectures of 1895 : " Experiment 209, Deflagration of Charcoal by Galvanic Action. -The charcoal for this experiment must be made of some very close grained wood, such as boxwood or lignum vitse, well charred, cut into pieces about an inch long, one end being scraped to a point, and the other so that it can be held by a port-crayon fixed to the end of one of the directors ; then, approaching the point of charcoal to the end of the other director, light will either appear or the charcoal will be set on fire. The particular management required should be obtained by trials. The light, when properly managed, exceeds any other artificial light ever yet produced." 15 In his Bakerian Lecture delivered on November 16tb, 1809, Davy said that when a current was sent by 1,000 double plates each four inches square through potassium vapour between platinum electrodes, over nitrogen gas, a vivid white flame arose. " It was a most brilliant flame, of from half an inch to one and a quarter inches in length." ir In the library of the Royal Institution are two large thick volumes of manuscript notes, bound in leather, and carefully paged. These are Sir Humphry Davy's laboratory notes for the years 1805 to 1812. Faraday, who paged them, wrote a short note at the beginning of each volume, saying that Davy had a way, before he went to live at the Royal Institution, of tearing out pages from his note books, and taking them home with him to think over ; but that these two volumes being complete, he, Faraday, had paged them. Finding that there was no more direct mention of the arc than the above in any of Sir Humphry Davy's published works, nor in the Philosophical Transactions of the Royal Society, nor in the Philosophical Magazine before 1812, I searched through these two volumes for any record of the first discovery of the arc, and found the following two passages which I am kindly permitted to publish. A SHORT HISTORY OF THE ARC. 25 " April 20, 1808. " A given quantity of muriatic acid gas was acted upon by dry charcoal ; there was a continued vivid light in the galvanic circuit." "August 23, 1809. " AN EXPERIMENT TO ASCERTAIN WHETHER ANY HEAT SENSIBLE TO THE THERMOMETER IS PRODUCED BY THE ELECTRIC FLAME IN VACUO. "The jar which contained the apparatus consisted of a concave-plated mirror, so situated as to collect the light radiating from the charcoal, and to concentrate them (sic) on the bulb of a mercurial thermometer, which, together with the wires holding the two pieces of charcoal, passed through a collar of leather. No heat was apparently produced by the light excited in vacuo. The air being introduced, immediately the column of mercury rose. The light in vacuo was in part of a beautiful blue colour, and attended with bright red scintil- lations." 16 The " vivid light " referred to in the first of these extracts is plainly an arc ; but in the second, the words " electric flame " leave no room for doubt, not only that Davy was using an arc, but that it was no new phenomenon to him. When was the arc discovered then, and by whom ? Was it not simply evolved through experiments on sparks and on the burning of metals, so gradually that no one realised it as a separate phenomenon until, with the large battery subscribed for by the members of the Royal Institution, Davy made a very long horizontal arc which formed a true arch, and therefore appealed to the imagination as something new ? Even then, however, it was chiefly considered interesting as showing the immense power of the battery, as will be seen from the following accounts, the first of which, taken from the Monthly Maya.zine, a sort of popular journal of art, science, and literature, is, I believe, the first definite published account of the arc. The second is from Davy's " Elements of Chemical Philosophy," published in 1812. "At the concluding lecture for the season at the Koyal Institution the large voltaic apparatus, consisting of 2,000 double plates, four inches square, was put in action for the first time. The effects of this combination, the largest that has been constructed, were of a very brilliant kind. The spark, the 26 THE ELECTRIC ARC. light of which was so intense as to resemble that of the sun, struck through some lines of air, and produced a discharge through heated air nearly three inches in length, and of a dazzling splendour. Several bodies which had not been fused before were fused by this flame Charcoal was made to evaporate, and plumbago appeared to fuse in vacuo. Charcoal was ignited to intense whiteness by it in oxymuriatic acid, and volatilised by it, but without being decomposed." 19 Here is Davy's own account : " The most powerful combination that exists in which number of alternations is combined with extent of surface, is that constructed by the subscriptions of a few zealous cultivators and patrons of science, in the laboratory of the Royal Institution. It consists of two hundred instruments, connected together in regular order, each composed of ten double plates arranged in cells of porcelain, and containing in each plate thirty-two square inches, so that the whole number of double plates is 2,000, and the whole sur- face 128,000 square inches. This battery, when the cells were filled with one part of nitric acid and one part of sulphuric acid, afforded a series of brilliant and impressive effects. When pieces of charcoal, about an inch long and one- sixth of an inch in diameter, were brought near each other (within the thirtieth or fortieth part of an inch), a bright spark was produced, and more than half the volume of the charcoal became ignited to whiteness, and by withdrawing the points from each other a constant discharge took place through the heated air, in a space at least equal to four inches, producing a most brilliant ascending arch of light, broad and conical in form in the middle. "When any substance was introduced into this arch, it instantly became ignited ; platina melted as readily in it as wax in the flame of a common candle quartz, the sapphire, magnesia, lime, all entered into fusion; fragments of diamond, and points of charcoal and plumbago, rapidly disappeared and seemed to evaporate in it, even when the connection was made in a receiver exhausted by the air pump ; but there was no evidence of their having previously undergone fusion. " When the communication between the points positively and negatively electrified was made in air rarefied in the receiver of A SHORT HISTORY OF THE ARC. 27 the air pump, the distance at which the discharge took place increased as the exhaustion was made, and when the atmos- phere in the vessel supported only one-fourth of an inch of mercury in the barometrical gauge, the sparks passed through a space of nearly half an inch ; and, by withdrawing the points from each other, the discharge was made through six or seven inches, producing a most beautiful coruscation of purple light, the charcoal became intensely ignited, and some platinum wire attached to it fused with brilliant scintillations, and fell in large globules upon the plate of the pumps. All the phenomena of chemical decomposition were produced with intense rapidity by this combination. When the points of charcoal were brought near each other in non-conducting fluids, such as oils, ether, and oxymuriatic compounds, brilliant sparks occurred, and elastic matter was rapidly generated ; and such was the intensity of the electricity that sparks were produced even in good imperfect conductors, such as the nitric and sulphuric acids." 20 FIG. 13. Horizontal Arc, copied from the figure in " Davy's Elements of Chemical Philosophy." This very definite and beautiful description of the arc leaves no doubt that Sir Humphry Davy was the first to show the long horizontal arch of flame that gives the arc its name; although the question whether or not he was the first person to obtain an arc of any shape and size will probably remain for ever a mystery. After 1812 no important work on the arc w-.s done till 1820, when Arago suggested that it would probably behave like a flexible conductor, and both attract a magnet and be attracted by it. He thought a very powerful battery was needed to pro- duce such an arc as would show the deflection; and not having one himself, he suggested that someone who had should try the experiment. 21 Meanwhile Davy, working on the same lines, had come to the same conclusion; and without having seen Arago's suggestion, which, however, had been published before 28 THE ELECTRIC ARC. he made the experiment, he tried the effect of an arc and a magnet on one another, and found that they deflected one another, just as Arago and he had predicted. It was on this occasion that he gave the name of arc to the electric flame. 22 In 1821 Dr. Robert Hare, a Professor in the University of Pennsylvania, published an account of his "Galvanic Deflagrator," an improved form of battery, with which he found that he could get much finer heating effects than with the older forms. His notions were peculiar, for he thought that "the fluid extricated by Volta's pile"ivas "a compound of caloric and electricity," both of which were material fluids. He remarked that "the igneous fluid appeared to proceed from the positive side," which later observers construed into his having been the first to notice that material was carried from the positive to the negative pole. He also said that, when the positive pole was of charcoal and the negative of steel, the light was the most vivid that he had ever seen, and the charcoal assumed a pasty consistence as if in a state approaching to fusion. He was the first to suggest that the charcoal could retain this state with- out combining with the air, and burning away, "because of the volatilisation of the carbon forming about it a circumam- bient air." 23 Silliman himself, the editor of the Journal, next obtained a deflagrator and made some very notable discoveries. It is a little difficult at first to follow the course of his observations, for the poles of his deflagrator appear to have got mixed up ; but he explained this in a subsequent number of the Journal, and even if he had not done so, in the light of our present knowledge there would have been no real possibility of mistake. He first observed what must have been a hissing arc, for he described very clearly the formation of a mushroom at the end of the negative charcoal, and pointed out that the negative charcoal grew in length during the process, and that, therefore, particles must be shot out from the positive charcoal on to it. To confirm this observation he described and named the crater in the positive pole, and observed that, as he moved the nega- tive over the surface of the positive pole, it produced a crater- shaped cavity over every place where it rested. The first notice of the peculiar smell of the arc is also due to him. " I should observe that during the ignition of the charcoal points, A SHORT HISTORY OF THE ARC. 29 there is a peculiar odour somewhat resembling electricity." He examined the negative charcoal after the arc was extin- guished, and found that it appeared to have been fused by the heat. 24 He described the boiling bubbles that appear on both carbons while the arc is burning, examined some of these when cold, and came to the conclusion that they consisted of melted carbon. He examined under the microscrope a mushroom formed between charcoal as the positive pole and plumbago as the negative, and found " a congeries of aggregated spheres with every mark of perfect fusion and with a perfect metallic lustre.'* These spheres were of many colours, and some were black and some white. The coloured ones were attracted by a magnet, proving that they contained iron. The black ones he considered to be melted carbon. 25 Later he fused two carbons together by allowing them to touch while an arc was burning between them ; but his experiments were, unfortunately, stopped by ill health, and were never resumed. 26 A great gap now appears in the history of the arc, and there is nothing noteworthy to record till 1838, when Gassiot showed that the temperature of the positive electrode was much greater than that of the negative. Eitter had already shown this for a spark, unless, perchance, he had an arc, which is possible ; but Gassiot showed that, of two wires of the same substance and diameter, that which formed the positive pole of a horizontal arc was melted so far along as to bend down,, while the negative remained perfectly stiff. 27 In the same year, FIQ t 14. Rotation of the Arc at the Pole of a Magnet. (Copied from the Transactions of the London Electrical Society.) in conjunction with Walker, Sturgeon, and Mason, he also first observed the rotation of the arc at the pole of a magnet. 30 THE ELECTRIC ARC. They found that if they completed the circuit of a powerful battery through the pole of a magnet, so that an arc was main- tained between a wire from the positive terminal of the battery and this pole, then the arc would rotate clockwise if the pole were north-seeking, and counter-clockwise if it were south-seeking. 28 Daniell, the inventor of the cell which bears his name, made many experiments with large batteries. Using charcoal for the positive and platinum for the negative pole of an arc, he found that the platinum became coated with carbon, which was beautifully moulded to its shape ; while, if he used platinum for the positive pole and charcoal for the negative, the latter became covered with little globules of platinum after the arc was extinguished. This confirmed Silliman's discovery that the material of the positive pole was shot out on to the negative. Finding that with his battery the arc would not start without actual contact of the poles, Daniell tried sending a spark from a Leyden jar between the poles when they were apart, and succeeded in igniting the arc by this means. 29 In 1840 Grove made some very notable experiments to determine whether the amount of matter separated from the poles by a given quantity of electricity was constant for a given material. He came to the conclusion that it was, and that " the all-important law of Faraday is capable of much exten- sion." The law he alluded to was, of course, the law of elec- trolysis, and shows that he considered the action of the arc to be purely electrolytic. Indeed, in the Paper in which he described these experiments he said, "The passage of the current is, as proved in these experiments, materially modified by the nature of the elastic medium through which it passes, .and is greatly aided when such medium is capable of uniting chemically with the electrodes. In pure hydrogen I have never yet been able to maintain a continuous arc, except with char- coal, which forms carburetted hydrogen." Grove tried using the carbon from gas retorts, but found that charcoal gave a larger and more diffuse flame. He described the three requi- sites for a brilliant discharge in an oxydating medium as being oxydability, volatility, and looseness of aggregation of the , particles. 80 A SHORT HISTORY OF THE ARC. 31 To Becquerel is due the honour of having discovered that the electric light had the same chemical effect on the salts of silver as sunlight, 31 and De la Rive first used this power of the arc to obtain a daguerrotype, a faint one it is true, of a bust. 32 In the same year Mackrell obtained an arc between two fine iron wires in dilute sulphuric acid, and he found that, if he used a positive pole of iron and a negative one of charcoal, if the iron were put into the acid first the charcoal became brilliant, but if the charcoal were immersed first, no such result took place. 34 Casselmann, in 1844, first described the shape of a long arc, as two cones with their bases in contact with the carbons, and their points touching one another. He allowed the arc to burn away till it became extinguished, under different conditions, and found that with the same battery a longer arc could be maintained between charcoal electrodes than between electrodes of carbon prepared as the plates of a Bunsen battery are pre- pared. Between these carbons also the arc hissed, but if they were heated red hot beforehand, and steeped in solutions of such volatile substances as sodium or potassium, the arc burnt quietly and steadily, and would grow to a greater length before it became extinguished. 35 In 1845 a very curious discovery was made by Neef, who wished to find out at which part of the arc the light first appeared. In order to eliminate any secondary heating effect produced by the combination of the hot positive pole with the oxygen of the air, he used platinum poles a plane for the positive and the point of a cone for the negative. Between these he struck an arc with a very small current by means of a spark from a Ley den jar. He then observed the effect with a microscope, and found that the light started at the negative pole, with no perceptible heat. The results he considered he obtained were the following : (1) The light always appears first at the negative pole, and this first light is independent of combustion. (2) The source of the heat is the positive pole, and this heat is originally dark heat. (3) The light and heat do not, at first, mingle, but only when they have attained a certain intensity ; from this fusion the phenomena of combustion and the flame are produced. 32 THE ELECTEIG ARC. He was the first to suggest that the carbon which was fused and shot off from the positive pole was condensed at the negative pole to the specific gravity of crystallisable gra- phite. 37 De la Rive, after having made the first daguerreotype with the arc, made a series of experiments as to the longest arc that could be maintained by a given battery when the poles were of various substances. He used a voltameter to measure the current, and found that the current that was flowing when the arc became extinguished was the same for all substances, but that the length of the arc varied with the substance. He noticed that when he had a slab of carbon for the negative pole and a pointed carbon rod for the positive, the deposit from the positive took a regular form. Also the longest arc was only half as long with this arrangement as it was when the positions of the slab and the rod were reversed. When the poles were of magnetised iron the longest arc was much shorter than when the iron poles were unmagnetised. 38 In the same year Van Breda, experimenting on the arc in vacuo, found that with copper poles, when he placed a slip of iron in the arc between them, the copper of both poles became covered with iron, and there were traces of copper on the iron slip. On weighing both electrodes and the iron slip, he found that the electrodes had each gained in weight, and the iron lost, but that taking all three together there had been a loss of weight. With one electrode of iron and one of coke, the iron lost more weight than the coke, whether it was at the positive or negative pole. 39 Matteucci made some very accurate and important experi- ments on the amount of matter lost by each electrode in a given time. Like Van Breda, he came to the conclusion that matter was shot out by both poles, and he pointed out that the two sets of particles, being in opposite electric states, must attract one another. He found that the difference of tempera- ture between the poles was greater the smaller the conductivity of the electrodes, and that the amount of matter lost by each depended upon its temperature, its oxydability, and the vola- tility and fusibility of the products of oxydation. Both poles lost more in air than in a vacuum in a given time. With coke electrodes he estimated that the proportion of the loss at the A SHORT HISTORY OF THE ARC. 33 positive pole to that at the negative varied between 2 to 1 and 5 to 1, according to the length of the arc. 40 Quet, placing a vertical carbon arc perpendicular to the common axis of the coils of an electromagnet, found that the arc shot out horizontally, like the flame of a blow-pipe, and that, unless the carbons were very close together, the arc became extinguished with a loud noise. 41 Several electric blow- pipes on this principle have since been invented. In 1852 Grove made a most interesting experiment, which showed that a liquid could act as one pole of an arc. He attached fine platinum wires to the terminals of a battery of 500 cells, dipped the ends of both wires into distilled water, and then gradually withdrew the negative wire till it was a quarter of an inch above the surface of the water. " A cone of blue flame was now perceptible, the water forming its base, and the point of the wire its apex. The wire rapidly fused, and became so brilliant that the cone of flame could no longer be perceived, and the globule of fused platinum was apparently suspended in air, and hanging from the wire ; it appeared sustained by a repulsive action, like a cork ball on a jet d'eau, and threw out scintillations in a direction away from the water. The surface of the water at the base of the cone was depressed and divided into little concave cups, which were in a continual agitation." When the conditions were reversed, so that the negative wire was immersed and the positive out of the water, the effect was the same, but not so marked. The cone was smaller, and its base was much narrower in proportion to its height. 42 The first accurate quantitative experiments on the arc were made by Edlund in 1867. In spite of the disadvantages under which he laboured for he had no dynamo, and at that time there were no recognised units of current, P.D., or resistance Edlund discovered one of the fundamental conditions of the arc, namely, that with a constant current the apparent resistance is equal to a constant resistance, plus a resistance which varies directly with the length of the arc. Edlund's method of experimenting was as follows : He used a battery to send a current through an arc of definite length, then, putting out the arc and pressing the carbons tightly together, he measured the distance by which he had to separate the plates in a copper voltameter so as to bring the current to 21 34 THE ELECTRIC ARC. the same value as before. Doing this for various lengths of arc he found that, as long as the current was kept constant, the length of the copper voltameter which represented the arc could be expressed by a constant length plus a length which varied directly with that of the arc. Hence, putting his result in the form of an equation, he found out that where r is the apparent resistance of the arc, I its length, and a and b constants for a constant current. When, however, the current was varied, he found that a and b both diminished as the current increased, so that the apparent resistance of the arc for a given length was smaller the greater the current. The numbers which he obtained for a justified him, he considered, in concluding that a varied inversely as the current, but those for b were too small to enable him to arrive at the law connecting b with the current. Edlund started his experiments with the idea that there was a back E.M.F. in the arc caused by the disintegration of the carbon particles, and therefore, having obtained several values of a and b with different currents, he calculated the back E.M.F. in the arc when each of those currents was flowing. From these calculations he concluded that the back E.M.F. in the arc had a constant value equal to that of about 23 Bunsen's cells, for all the currents he used, and that the true resistance of the arc was directly proportional to its length, increasing, however, as the current decreased. He next considered the question theoretically, and gave what he regarded as a proof that the back E.M.F. in the arc must be independent of the current, and also that the work performed in the arc by the current was proportional to the current as long as the E.M.F. of the battery remained constant. He then made a new series of experiments to determine whether the back E.M.F. depended upon the E.M.F. of the battery used to produce the current, and decided that it did not. 44 Edlund's next series of experiments was undertaken to find out whether the back E.M.F. was constant with smaller A SHORT HISTORY OF THE ARC. 35 currents than had been employed in the first series. The deflec- tions produced by the currents in the tangent galvanometer used were not published in this case, as they had been before; but Edlund considered that his results showed that, in the case of small currents, the back KM.F. diminished as the current was decreased. He used copper, brass, and silver pole points for these experiments, as well as carbon. 45 Edlund's third series of experiments was very striking. He found that, when an arc was produced with a somewhat large current between carbon poles, the arc continued for a short time after the circuit was broken, so that, if the circuit were closed again fairly quickly after the break had been made, the arc was not put out. But, on the other hand, when silver poles were used, the arc did not continue for even one-eightieth of a second after the circuit was broken. From this he concluded that if carbon poles were used, and if immediately after breaking the circuit the carbons were switched on to a galvanometer, a momentary current would be sent by the arc through the gal variometer, and the existence of the back E.M.F. in the arc would thus be made certain. A series of experiments carried out in this way, with and without a battery being switched with the arc into the galvanometer circuit, led Edlund to conclude that the back E.M.F. existing in the arc after the main circuit had been broken could not be less than that of from 10 to 15 Bunsen's cells. Further, from' the momentary current being increased when the negative carbon was warmed by a Bunsen's burner, and not diminished as might have been expected had the back E.M.F. been a thermo- electric one (set up by the positive carbon being hotter than the negative), he concluded that the back E.M.F. in the arc was not due to thermo-electric action. 46 In 1876 the Jablochkoff candle came into use. It consisted of two upright parallel carbon rods, separated from one another by a layer of solid insulating material, which burnt away at about the same rate as the carbons. This solid material was supposed to be necessary to keep the arc from running down the carbons and burning anywhere but at the tips. When, later, it was discovered that the arc still remained at the ends of the carbon, even when there was nothing but air between them, this was attributed to the action of the upward P2 36 THE ELECTEIC AEG. current of hot air and vapour. In 1878, however, Prof. Ayrtort gave the true explanation, and proved that the hot-air theory could not be correct, by showing that the arc remained at the ends of the carbons, even when they were held upside down. He pointed out that in remaining always at the ends of the carbons the arc was simply following Ampere's law concerning the tendency of a circuit in which a current is flowing to enlarge itself, on account of the repulsive action of the current in one part of the circuit on the current in another part at right angles to it. Prof. Ayrton's own explanation will make this clearer. " The figure below, in which the continuous arrows indicate the directions of the currents, and the dotted arrows the line of action of the repulsive forces, show this action clearly. The carbons are placed further apart in the figure than they are in reality, merely for convenience of drawing. The two forces are r\ ARC r\ MACHINE FIG. 15. oblique to the carbons ; but the resultant is parallel to them,, and will always be away from those ends of the carbons which are connected with the magneto-electric machine, no matter how often the whole current be reversed." 49 This explanation also applies to the form taken by a hori- zontal arc, and shows that the upward direction of Sir Hum- phry Davy's long arc (see Fig. 13, p. 27) depended principally on the position of the poles relatively to the remainder of the circuit. The same cause makes the vertical arc, when it is- long and the current is small, take up a position between the points of the carbon which are farthest from each other, and thus make itself as long as possible. Mr. Schwendler, during the course of an investigation or* " The Electric Light," carried out in 1878 for the Board of A SHORT HISTORY OF THE ARC. 37 Directors of the East Indian Railway Company, gave the following conclusions in a precis of his report : " There appears to be no doubt that an appreciable E.M.F. in the arc is established, which acts in opposition to the E.M.F. of the dynamo machine. This E.M.F. of the arc increases with the current passing through the arc. The resistance of the arc for constant length is also a function of the current passing through it, i.e., the resistance of the arc decreases with the current (see the following table)." Table I. (Schwendler). Current in Resistance of the arc E.M.F. of the arc webers. in Siemens units. in volts. 28-81 0-91 2-02 23-87 1-72 1-91 16-27 1-97 186 Mr. Schwendler said, further, that he considered it highly probable that the resistance of an arc of constant length was inversely proportional to the current. No details were given in this precis regarding the way in which the E.M.F. of the arc was measured. 50 In 1879 Messrs. De la Rue and Hugo Miiller, while experi- menting on the discharge in vacuum tubes, came to the con- clusion that " the stratified discharge in a vacuum tube is simply a magnified form of arc." In order to test this theory they made a series of experiments on discharges in various gases at various pressures, with the poles at various distances from one another, and of different shapes. The poles were -fixed in a bell jar that could be filled with the different gases and exhausted ; a suitable arrangement was made for altering the distance between the poles, and the gases used were air, hydrogen and carbonic acid. In air the pressures varied from 2 '6mm. to 761mm., the dis- tances varied between 0'54in. and 6 4in., the current ranged from 0-01390 to 0-04474 webers, and the number of chloride of silver cells used varied from 10,940 to 11,000. The sub- stance of the electrodes was only definitely mentioned in one case, when it was brass. Many beautiful engravings, showing the appearance of the discharge under different circumstances, 38 THE ELECTRIC ARC. were published ; from these it appeared that in air the light usually divided itself into at least two and sometimes more parts, with dark spaces between them. In hydrogen, in some cases, the discharge showed a very- definite stratification. In carbonic acid, when the pressure was very small, there was very little evidence of stratification ; but in both gases the discharge was divided, as in air, into light and dark parts. Mr. Seaton, one of the assistants of Messrs. De la Rue and Miiller, first noticed a very interesting circumstance connected with the discharge. Whenever contact was first made the pressure in the bell jar increased far more than could be accounted for by the rise of temperature of the enclosed gas. The moment contact was broken the pressure fell almost to what it had been before contact was made, the slight increase being due to rise of temperature. It was found by experiment that the increase of pressure took place at both terminals equally. The experimenters considered it to be accounted for by u ihe projection of the gas-molecules by electrificatioi> against the walls of the glass vessel, producing thereby effects of pressure, which, however, are distinct from the molecular motion induced by heat." The parts of the Paper which concern the arc are summed up in the following manner : "When the discharge takes place there is a sudden dilata- tion of the medium, in addition to and distinct from that caused by heat. This dilatation ceases instantaneously when the discharge ceases. " The electric arc and the stratified discharge in vacuum, tubes are modifications of the same phenomenon." 53 In the same year Rossetti found, from a large number of experiments, that the maximum temperature of the positive pole was 3,900C., and that of the negative about 3,150C. The temperature of the arc itself he found to be about 4,800C. whatever the intensity of the current flowing. The method of experimenting was not given. 54 In the following year, 1880, the first measurements of the diameter of the crater of the positive carbon were made by Mr. J. D. F. Andrews, who was also the first to remark that, in order that a definite result might be obtained with each current A SHORT HISTORY OF THE ARC. 39 and length of arc employed, the arc should be allowed to burn steadily and quietly for at least half an hour before any measurements were taken. He measured the diameter of the crater, when cold, with a rule divided into lOOths of an inch, and, neglecting its depth, which was very small with the length of arc he used ( T Vn.), he found the area from the diameter. He considered that his experiments showed that the area of the crater was " directly proportional to the quantity of current producing it." In proof of this he gave the following table : Table II. (Andrews). Comparison of Observed Currents and Currents calculated on the Assumption that Area of Crater is directly proportional to Current. Diameters of craters, in inches. Areas of craters, in inches. Quantities of cur. in webers measured. Quantities of current in webers cal. from craters. 0140 0-156 0-186 0-203 0-266 0-326 0-453 0-0196 0-0243 0-0272 0-0324 0-0556 0-0825 0-1602 9 12 29 42 81 9-9 12-4 13-8 16-5 28-3 42-0 81-6 The diameters of the carbons used were not given. Mr. Andrews remarked that when the arc hissed the end of the positive carbon was covered with a number of small craters, showing that it moved about, and that a number of very small arcs appeared to try to spread over the end of the positive car- bon, each detonating the air, and thus causing a hissing noise. 55 Le Roux considered that the great fall of potential at the positive carbon was caused by a back E.M.F., the result of a thermo-electric effect. His idea was that the carbon of the positive electrode was electro-positive to the vapour of the arc in a degree which increased as the temperature increased. He found that with a high resistance galvanometer in the arc circuit he could detect the back E.M.F. 0'2sec. after he had stopped the arc by hand. 57 Niaudet in 1881 first noticed that the hissing of the arc was accompanied by a sudden fall of P.D., and gave the following table of observations that he had made : 40 THE ELECTRIC ARC. Table III. (Niaudet). Currents and P.D. with Silent and Hissinq Arcs. 58 Current in webers. P.D. (presumably in volts). 34 36 34 43 38-1 54-3 43 49 41-4 49 Silent Hissing Silent Hissing Silent In a Paper on " The Resistance of the Electric Arc " Profs. Ayrton and Perry in 1882 described experiments made with Grove's cells to test the accuracy of Mr. Schwendler's conclusions concerning the back E.M.F. and the resistance of the arc, and they found that, when carbons 0'24in. in diameter were used and the length of the arc kept constant, the current could be varied from about 5 to 15 amperes without much change being produced in the P.D. between the carbons. They also used a Brush machine to produce an arc up to l'25in. in length, and gave as the equation connecting V, the P.D. between the carbons in volts, and a, the length of the arc in inches V = 63 + 55a-63xlO- 10a , and this equation they regarded as being true for currents between 5-5 and 1CK amperes with the carbons employed. 59 In 1882 Prof. Dewar made some very interesting experi- ments on the internal pressure of the arc. He used a horizontal arc maintained between carbon tubes, each of which was attached to a manometer. With a steady silent arc the mano- meter attached to the positive carbon showed a fixed increase of pressure of about 1mm. to 2mm. of vertical water pressure, while at the negative carbon there was a slight diminution of pressure. The same results were obtained when the arc and ends of the carbons were enclosed in a block of magnesia to equalise the temperature of the poles, and also when the mano- meters were filled with carbonic oxide or nitrogen instead of with air. When the arc hissed, it often no longer covered the ends of the carbons, so that the manometers showed no pressure ; but when this did not happen, the positive carbon showed a dimi- nution and the negative an increase of pressure with a hissing arc. A SHORT HISTOIiY OF THE AUG. 41 From these experiments Prof. Dawar concluded that the arc acted as if it had a surface tension. 60 In 1883 Frolich, desiring to find out whether Edlund's equa- tion r = a + bl were true for the larger currents that could be obtained with dynamos, used the results of experiments made for the purpose of testing the dynamos constructed by Messrs. Siemens and Halske, by various people at various times, to obtain an equation connecting the P.D. between the carbons with the length of the arc. In the table given in his Paper the P.D.s corresponding with different currents for the same length of arc showed wide variations, yet he took it for granted that the P.D. was really independent of the current, and so he deduced the equation as the relation that would connect the P.D. between the carbons with the length of the arc, where a and b were the same, whatever the current, if there were no errors of observation in the experiments. Frolich found what he considered to be the numerical values of a and 5, and so he put his equation connecting V. the P.D. in volts between the carbons with I the length of the arc in millimetres in the form From this formula he calculated what he considered ought to have been the P.D.s for the various currents and lengths of arc with any current from 1 to 100 amperes, in the 47 measure- ments the results of which he quoted; and the differences between the results given by his formula and by experiment he put down to errors of observation. By dividing by A, the current in amperes, Frolich's formula became 39 1-81 and this he considered was the formula which gave r the appa- rent resistance in ohms of an arc I millimetres long produced by a current of A amperes. He used the latter formula to calculate a table of 273 apparent resistances of arcs, varying from Omm. to 20mm. in length, and produced by currents of 1, 5, 10, 15, I to points J j Ordinary Vertical,positive carbon above negative Lower cooled to tip by mer- ) positive cury bath in water jacket J negative less than 35 47 46 43 41 The carbons enveloped in mercury developed mushrooms, and the arc was very unsteady during the last experiment. Lecher considered the results to prove that the P.D. between the sarbons depended on their temperatures. He thought hissing was caused by the discharge springing to and fro to cooler places as the previous places became too hot, and thus setting up a vibration which produced sound. Lecher used an exploring carbon of l'2mm. diameter to find the P.D. between each of the carbons and the arc. By placing the exploring carbon vertically midway between the carbons of a horizontal arc, he obtained 35 volts as the P.D. between the positive carbon and the exploring carbon, and 10 volts as the P.D. between the exploring carbon and the negative. He found that the exploring carbon could be some little distance out of the visible arc without the P.D. between it and either of the other carbons being materially altered. 54 THE ELECTRIC ARC. Using a Ruhmkorff coil and a condenser, he found that the* silent arc was not discontinuous, but that the hissing arc was. 7s Uppenborn also explored the arc with a carbon rod, having tried copper and platinum wires embedded in clay, steatite, and glass tubes, to no purpose. He found that with arcs of from 6mm. to 16mm. in length, the P.D. between the positive carbon and the exploring carbon placed near it, varied from 38 volts to 32'5 volts, while he found only 5 volts P.D. between the negative carbon and the exploring carbon placed near it. He gave a very good description of the shape of the arc. 76 Luggin, in a long and very interesting paper, discussed the Wheatstone's bridge methods previously used for measuring the resistance of the arc, all of which he considered were open to criticism. He pointed out that, whereas when a small increase of E.M.F. was applied to an ordinary conductor through which a current was flowing, the P.D. at its ends increased, and therefore the variation of P.D. had a positive sign ; in the arc, on the contrary, an increase of current was attended by a diminution of the P.D. between the ends of the carbons, and consequently the variation of the P.D., caused by an increase of the E.M.F., must have a negative sign. Having shown the connection between the resistances in an ordinary Wheatstone's bridge, and having mentioned that the relation remained the same even if there were constant E.M.F.'s in all the arms, he continued thus : " If now an arc were started in the arm a, while in all the other resistances the bridge remained unaltered, then the P.D. at the ends of a would be less than before, and we should have to conclude from the diminished P.D. that the resistance w^ had become less, and that the arc had a negative resistance." Luggin himself used a method somewhat similar to Von Lang's for finding the resistance of the arc. In one of the arms of a Wheatstone's bridge he placed an arc, in the second a comparing resistance of 2 ohms, and in the third and fourth liquid resistances amounting together to 300 ohms. In one of the diagonals was a battery of accumulators and a rheostat to regulate the current, which was shunted by a liquid resis- tance of 600 ohms and an electrically-driven tuning-fork. In the second diagonal, a condenser and telephone were in series, A SHORT HISTORY OF THE ARC 65 the former being used to protect the telephone from the direct current, and to take such a quantity of electricity from the alternating current as to allow the telephone to be sufficiently sensitive. Luggin attributed the fall of P.D. between the carbons that took place when the current was increased to a diminution in the resistance of the gaseous medium caused by its rise of temperature. He pointed out that this change could not be an instantaneous one, and that therefore if the current were alternated with sufficient rapidity the P.D. would rise and fall with the current, " and the arc would show a positive resistance." He considered that the reason that Arons found a positive resistance in the arc was that the alternating current he impressed on the direct current in his arc alternated very rapidly, and he was quite unable to understand why Frolich did not find a negative resistance. To find the variation in the P.D. between the carbons when the length of the arc was varied and the current kept constant, Luggin used two Siemens carbons 10mm. in diameter, the positive cored and the negative uncored. For each figure he took the mean of three or four sets of observations. The fol- lowing table gives the results of his experiments with a current of 7 amperes. The length of the arc is given in scale divi- sions, each of which was O434mm. He found that the formula V = 40-04 + l-774 I, where V was the P.D. between the carbons in volts and I the length of the arc in scale divisions, fitted his observations extremely well, as will be seen from the following table. Table VI. (Luggin.} Current 7 amperes. Positive Carbon Cored, Negative Uncored. L V (volts) observed. V (volts) calculated. Difference. i 41-6 41-81 -0-21 2 43-3 43-59 -0-29 3 45-4 45-36 + 0-04 4 47-6 47-14 + 0-46 5 49-3 48-91 + 0-39 6 50-8 50-68 + 0-12 7 52-3 52-46 -0-16 8 53-9 54-23 -0-33 56 THE ELECTRIC ARC. Luggin tried using a horizontal disc of carbon 15cm. in dia- meter as one of the electrodes of an upright arc, and a carbon rod for the other. When the disc was placed under the rod and used as the negative electrode, it was found that even a very slow rotation of the disc extinguished the arc, however strong the current. When, however, the disc was placed above the rod and used as the positive electrode, it could be rotated fairly quickly even with a current of only 7 amperes, and with currents of from 27 to 33 amperes it could be rotated very fast indeed without the arc becoming extinguished. With slow rotations the disc was pitted with small craters, but with the faster ones these craters ran into one another. When the arc hissed, while the disc was still, the P.O. between the carbons sank as usual 10 or 11 volts, but if, while the hissing continued the disc was set in rotation, the P.D. sank from 3 to 5 volts lower still. He next experimented with iron electrodes, and finally he used an exploring carbon to find the difference in volts between the fall of potential between the positive carbon and any point in the arc, and the fall of potential between that same point and the negative carbon. This difference is denoted by E in the following table, while V denotes the P.D. between the carbons in volts, and I the length of the arc in mm. Siemens carbons were used, and a current of 6 '8 amperes for the first set of results, and one of 8 4 9 amperes for the second. Results (I.) were obtained with ordinary Siemens carbons. Results (II.) with carbons sprinkled with soda. Table VII. (Luggin.) (I.) (II.) V E V E I 39-8 25-9 17-9 0-43 2-9 42-5 27-1 19-4 1-76 3-0 46-3 26'9 20-0 0-69 3-9 48-7 32-2 21-4 3-77 4-0 49-3 31-0 22-6 2-89 5-0 51-7 33-3 28-0 7-00 6-8 52-7 32-9 57-7 34-6 From the immense diminution in E in (II.), caused by sprink- ling the carbons with soda, so much greater than the corres- A SHOUT HISTORY OF THE ARC. 57 ponding diminution in V, Luggin concluded that there was an enormous leap of potential at the positive pole, which was almost neutralised by sprinking the carbons with soda. This onesidedness diminished as the length of the arc diminished, and he mentioned that once, with the ordinary Siemens carbons, when the point of the negative carbon was entirely surrounded by the crater, V was 35 '5 volts and E was as low as 18-8 volts. 77 Dabs, in 1888, found that if two carbon plates were placed one above the other with a distance of 1mm. between them, and a blowpipe flame was directed on to the lower, so as to carry carbon particles to the upper, a galvanometer connected with the plates showed a weak current flowing against the blast. Also that if a carbon plate were heated on an oxyhydrogen flame and laid on a cold carbon plate, a current flowed from the cold to the hot plate. With copper plates the effect was less, and was nil with iron. Dubs regarded the effect as analogous with the back E.M.F. in the arc, and considered that that depended, at any rate in part, on the mechanical action of the current. 79 In 1889, Luggin followed up his previous researches by a long and close investigation of the arc with exploring carbons. Some parts of the Paper in which he gave the results of these investigations it is impossible to follow ; for not only is the German very involved, but there is a complete dearth of Figures, and the explanations given are too scanty to enable the reader to construct these for himself. This is all the greater pity, as Luggin's work, where it can be understood, is both original and suggestive. The first experiments were undertaken to find out how the potential varied in different parts of the same cross-section of an arc 8mm. in length. Siemens carbons, 12mm. in diameter, were used for the electrodes, and Carre carbons, 1mm. to 2mm. in diameter, for exploring. These always burnt to a point in the arc. The results differed according as the positive carbon was solid or cored. When it was solid, it was found that when one exploring carbon just touched the purple core of the arc and another just dipped into the outer flame, both in the lowest cross-section of the arc, the potential of the inner carbon was three volts lower than that of the outer one. 58 THE ELECTRIC ARC. For higher cross-sections of the arc the case was reversed, the inner carbon having a potential two volts higher than the outer in the cross-section midway between the electrodes. When the point of one carbon was placed at the centre of the purple core, and that of the other touched the outer flame in the same cross-section, the potential of the inner carbon was higher than that of the outer. When the positive carbon was cored, very little difference was found between the potentials of the inner and outer portions of the same cross-section of the arc, which led Luggin to doubt if the differences found with solid carbons had not been caused by the exploring carbon itself. Luggin found that a thick exploring carbon disturbed the arc considerably, and that it seemed to repel it. Its insertion also raised the P.D. between the carbons, and sometimes made the arc hiss and sing. Putting a thick exploring carbon about 2mm. from the positive electrode caused two arcs to form, one between the positive and the exploring carbon, and the other between the exploring carbon and the negative. An exploring carbon of l'3mm. diameter was placed with its point immediately under the crater (carbons both solid, 12mm. in diameter), with a current of 15*5 amperes flowing. The P.D. between the positive and exploring carbons was found, from five measurements, to be 33 -7 O f 46 volts. Chang- ing the length of the arc appeared to have no influence on this P.D. The exploring carbon was next placed in the arc, with its point as near as possible to the bright spot on the negative carbon, and the P.D. between exploring and negative carbons was found, from six measurements, to be 8-78+ 0*17 volts. This one-sidedness in the potential of the arc, which Luggin called E, was also measured in another way, on the supposition that the fall of potential in the arc itself was perfectly uniform. E is, of course, the difference between the fall of potential between the positive electrode and the exploring carbon and the fall of potential between the exploring carbon and the negative electrode. If, then, the exploring carbon is placed in the middle section of the arc and v, the P.D. between the positive and exploring carbons, is measured simultaneously with V, the P.D. between the two electrodes, then A SHORT HISTORY OF THE ARC. 59 If the potential of the exploring carbon differs by an amount dv from the surrounding gases, the above value of E is incor- rect by 2dv, as Luggin showed. He made measurements of V and v in the manner described, only allowing the exploring carbon to touch the outer edge of the flame surrounding the arc, however, so as to cause the least possible disturbance to the arc. This probably introduced some error, but the value of E thus obtained was the same as with the earlier experi- ments, namely, 24*9 volts. Other measurements made with a current of 16\S amperes and with increasing length of arc gave V = 49 -9 volts. E = 24-5 volts. V = 53'8 E = 25-8 V = 65-2 E = 25-6 With cored positive and solid negative carbons 12mm. in dia- meter the following values were obtained with increasing length of arc : V = 44-9 volts. E = 28-3 0-24 V = 51-4 E = 29-60-61 V = 55-2 E = 30-3 0-29 V = 58-7 E = 31-40-40 Y = 64-8 E = 34-40'54 For these last experiments the exploring carbon was placed by eye only. Luggin pointed out that the two sets of experi- ments show that while with solid carbons the P.D.s between the positive carbon and the middle cross-section of the arc and between the same cross-section and the negative carbon increase at about the same rate with increasing length of arc, with a cored positive carbon the P.D. between the positive and the middle cross-section increases more rapidly than the P D. between that cross-section and the negative carbon. From another experiment it appears that, at least with a cored positive carbon, the potential of the arc itself does not fall at a perfectly uniform rate, as was supposed in making the experiment. He fastened two carbons, one on either side of a plank 3mm. thick, so that they were held at a constant vertical distance from one another. He then placed the carbons horizon- tally, so that the point of the upper was vertically over that of the under, in an arc burning between positive cored and solid negative carbons. According as the pair of carbons was near the positive or negative electrode, the P.D. between them was 60 THE ELECTRIC ARC. 12*4 or 8-05 volts. The same experiment was not tried with two solid electrodes. Placing an exploring carbon in the outside aureole of the arc, near the positive carbon, the P.D. between the positive and exploring carbons was found to be about 1 volt greater than when the latter was placed as near as possible to the centre of the crater. Luggin considered these experiments showed that the P.D. between the positive carbon and the surrounding gases was constant as a first approximation. He gave a careful description of the different parts of the arc and carbons, and mentioned that the outer green part, or aureole, as he called it, started higher up the positive carbon than the edge of the crater, and that there was a space between it and that carbon wide enough for him to insert a thin slip of car- bon into it. He mentioned that carbon pencils glowed brightly directly they were placed within the aureole, and that the latter widened out where it touched these pencils. He also noticed that the arc proper and the aureole varied in form according to the material, cross-section and position of the electrodes. He described an upright arc between solid carbons as being like an inverted bell standing on the point of the negative carbon, and said that with long arcs the middle cross-section of the arc gave less light than the ends, and that this was particularly the case with cored carbons, or with carbons in which volatile salts were mixed. He suggested also that the appearance of dividing itself into two unequal parts, which he observed in the arc with cored carbons, was connected with the irregularity in the fall of potential near the positive and negative electrodes that he had found to exist. Some experiments with hissing arcs between solid carbons led Luggin to observe that the hissing took place when the current was so strong that the crater filled the whole of the end of the positive carbon. This is a very important point that he was the first to observe. He noticed also that the longer the arc the larger the current that could be used before the arc hissed ; but that with longer arcs the end of the carbon, and therefore the crater, was larger. With long silent arcs he found that the end of the positive carbon was convex, instead of its having a crater. In the following table he called the ratio of the current strength to the size of the surface of the end of the positive A SHORT HISTORY OF THE ARC. 61' carbon, D ; hence, when the current is measured in amperes and the surface of the carbon in millimetres, D is the current strength in amperes per millimetre of end of carbon. Table VIU.(Luggin.) I (mm.}. A (Amperes). Diameter of End- surface (sq. mm.) D (Ampere). 3-7 8-5 19-2 26-3 6-87 8-25 0-51 0-49 Luggin found that the quantity he called E, i.e. the difference between the fall of potential between the positive carbon and the arc, and the fall of potential between the arc and the negative carbon, was somewhat smaller with hissing than with silent arcs, showing that the fall of potential that took place when the arc began to hiss was chiefly between the positive carbon and the arc. He tried to find evidences of polarisation and hence a back E.M.F. in the arc immediately after the current was cut off, but was unsuccessful, and he considered that his experiments showed that there is no important back E.M.F. in the arc O005 second after the current is turned off. 80 In 1890 Prof. Ayrton, with some of his students at the Central Technical College, began the series of experiments that were described in the Paper he read at the Electrical Congress in Chicago in 1893. The Paper was unfortunately burnt before it could be published, but the experiments and their results, of which the laboratory notes were retained, will be discussed later on. In 1891, in an account that included a revision of all that was known of the physics of the arc up to date, Prof. Elihu Thomson mentioned that he had found that, while both short and long arcs could be made to burn steadily, there was an intermediate stage of flickering and unsteadiness. He considered that the hollowness of the crater was due to the evaporation of carbon from its surface, and that the temperature of the crater was that of the boiling-point of carbon, or, " more correctly, of sublimation at atmospheric pressure." He found that the carbon of the crater was in a plastic state, and proved it by pressing the carbons together . 62 THE ELECTRIC ARC. with arcs of from 150 to 200 amperes, and finding that they would fit each other perfectly afterwards. He was also able to bend sticks of carbon a quarter of an inch thick, by passing a big enough current through them almost to vaporise them, and causing them to emit a light nearly as intense as that of the arc. Hence he argued that it was probable that carbon might be liquefied if subjected to the temperature of the arc under high pressure in an inert gas. He considered that the formation and maintenance of the arc might be due to electrolytic action, the hot vapour taking the part of the bath, and acting by a molecular interchange of carbon atoms. He mentioned that constant potential arcs 65 CO .? 55 50 45 40 35 A 4. r Q 6 10 15 20 25 30 35 40 Current in Amperes. FIG. 18. were impossible, and that " for stability the resistance should not be dependent wholly on the current passing." 81 series of articles on the alternate-current arc, published ), M. Blondel showed how, with a direct-current arc, to determine graphically the conditions of dynamo and of resist- ance outside the arc, so that a steady arc of given length might be maintained between carbons of given diameter. Having drawn experimentally the curve MNP (Fig. 18), which showed the connection between the P.D. at the A SHOUT HISTORY OF THE ARC. 03 terminals of the lamp and the current flowing while the arc was maintained at the given constant length, he drew QQ, the characteristic of the circuit taken at the terminals of the lamp. He then pointed out that if this curve cut M N P at N, the necessary and sufficient condition for stable equilibrium was that Q Q should cut M P from above downwards in the direction of increase of current. If the potential of the dynamo were a constant V, represented by the horizontal straight line A C, a resistance R would have to be added to the lamps, such that the new characteristic of the feeding circuit A B (E = V - R A) should satisfy the preceding condition. Suppose, for instance, that MNP were the curve for an arc of 4mm., and that E D, the tangent to M N P at N, cut the axis of volts at the height of 55 volts. Then, as M. Blondel pointed out, it is impossible to supply an arc of 4mm. with a current of 25 amperes with a constant potential of less than 55 volts, with the given carbons. And in order that the arc should be perfectly steady, the constant potential of the dynamo would have to be 60, or even 65 volts. 82 Cravath made many experiments in 1892 to discover the causes of hissing in the arc. He considered that the principal of these were air currents, impurities in the carbons, and short- ness of the arc. As he noticed that during hissing the stream of carbon vapour appeared to issue from a part only of the crater, and that this part was constantly changing, it occurred to him that perhaps hissing was due to the heating and cooling of the carbons caused by this change of position. He, there- fore, tried the effect of moving one carbon horizontally over the other while a steady silent arc \vas burning. When the positive carbon was pointed and the negative flat the arc burned silently as before, but when the negative carbon was pointed and the positive flat, each change of position caused a hiss. Cravath measured the diameter and depth of the crater, the length of the arc and the diameter of the knob of the negative carbon under varying circumstances, and he found that " the arc burns away the carbons so as to keep all points at an equal distance from each other." 83 He considered that the sudden diminution of the P.D. between the carbons when hissing began was due to the dampening effect of the cool carbon preventing the consumption of energy. 84 04 THE ELECTRIC AEC. In 1892 Stenger sought for evidence of a back E.M.F. in the arc thus : A shunt-dynamo sent a current through an arc, 5 accumulators, and a tangent galvanometer, in series. The accumulators were joined up so as to oppose the current, and the needle of the galvanometer was pressed against a stop so that it was not deflected by the dynamo current, but could move freely in the opposite direction. On short-circuiting the shunt- dynamo the conduction of the arc lasted long enough for the accumulators to send a current and produce a deflection of over 90deg. in the galvanometer ; but, when the experiment was repeated with the accumulators removed from the circuit, a deflection of only about fdeg. occurred, produced by the spring of the stop. Hence any back E.M.F. in the arc either ceased with the main current, or was very small compared with 10 volts. 86 In a Paper read before the British Association in 1892, Prof. Silvanus Thompson gave an approximate formula connecting V, the P.D. in volts between the carbons, /, the length of the arc in millimetres, and A, the current in amperes, viz. : bl V- + T where the constant a, however, varied between 35 and 39 volts and the constant b between 8 and 18. The constant part of the P.D. which is independent of the current for an invariable length is sometimes called the apparent back E.M.F., and, although Dr. Thompson did not affirm that there was an actual back E.M.F., he considered that the arc acted as though it were the seat of a back E.M.F. He described his experiments, made with an auxiliary exploring carbon, which showed that the drop of potential in the arc itself was small, and that the main drop was at the positive carbon. The latter, he considered, was accounted for by the volatilisation of the carbon at the crater, which, he suggested, was always at the temperature of boiling carbon, und this idea was confirmed, he thought, by^Bapt.' Abney's discovery that the brilliancy of the same o.uaUy of car- bon per square centimetre was a constant. A&&- Crookes's experiments, which showed that the flaming discharges produced by very high- pressure very short period alterna- A SHOUT HISTOEY OF THE AUG. 65 ting currents were endothermic flames of nitrogen and oxygen, had led hhn to try whether the combination of nitrogen and oxygen produced by the high temperature of the arc had anything to do with the E.M.F. observed there. To test this he surrounded the arc with a glass tube, and introduced successively oxygen, nitrogen, carbon dioxide, hydrogen, &c., but with a normal arc taking 10 amperes not one volt difference in the P.D. was observed. When chlorine or carbon monoxide surrounded the arc the positive carbon was flattened over the end, and the end of the negative became a very obtuse cone, while with hydro-carbon gas the crater was very deep; and, lastly, when the arc was formed in oxygen the carbons burnt away very rapidly. The gases had to be introduced quietly, since blowing on an arc in ordinary air Dr. Thompson found raised the P.D. to 75 volts. 87 Later in the same year M. Violle published an account of some experiments he had made in order to determine the temperature of the positive carbon and the arc. He cut a deep trench all round the positive carbon a little way from the end, so that a small piece was left, only con- nected with the rest of the carbon by a narrow neck. When most of this piece was burnt away, and the remainder was all of the same brightness, it was shaken off, and fell into a little cup, after which the amount of heat given off by it was measured in the usual way. Assuming the ordinarily received value of the specific heat of carbon, M. Violle found by this method that the temperature of the crater was about 3,500C., whatever power was spent in the arc whether 10 amperes were flowing at 50 volts, or 400 amperes at 85 volts. He concluded, therefore, that the candle-power per square centimetre of the crater was the same for all arcs with the same kind of carbons. 88 In 1893 M. Violle made some further experiments on the temperature and brightness of the crater. The carbons were placed horizontally, and inclosed, in order to reduce the cooling effect of the surrounding air. The temperature was measured in the same way as in his previous experiments, and led to the same result, namely, that the temperature of the crater was about 3,500C. He considered that the arc itself was at the same temperature, and that this was the temperature of boiling 66 THE ELECTRIC AEC. carbon. He laid great stress on this, as may be seen from the following quotation : " The most important result of my researches is to establish the fact that the voltaic arc is the seat of a perfectly definite physical phenomenon, the ebullition of carbon." To determine the amount of light given out per square milli- metre of crater he employed two methods, (1) the use of the spectrophotometer, (2) photography. They both led him to the same conclusion, that the amount of light per square mm. was constant, and independent of the current used. Finally M. Violle gave reasons for believing that the arc is an electrolytic phenomenon, in which there is a continual stream of carbon vapour passing from the positive to the negative electrode. 89 In August, 1893 Messrs. Duncan, Rowland and Todd pub- lished an account of the effects they had obtained on producing an arc under pressure and in a vacuum. They began their Paper by stating that the two causes alleged for the back E.M.F. in the arc the vaporisation of the positive pole and the thermo-electric effect produced by the carbon vapour in contact with the unequally heated carbons must both be operative ; but that the first must cease to exist directly the main current ceased to flow, and could not therefore be detected even immediately after the circuit was broken, while they con- sidered it must be possible to detect evidence of the latter for a short time after the main current had been stopped. The first part of the back E.M.F. , viz., that due to the volatilisation of the carbon, they considered must be a constant a, while the second part must be a function of the current and the length of the arc. From these considerations they sug- gested that the complete equation connecting P.D., current, and length of arc should be where V was the P.D. between the carbons, I the length of the arc, and A the current. They next called attention to the fact that the P.D. between the carbons diminished as the current increased, and gave the results of experiments supporting this. The following they suggested as an explanation of the phenomenon. If V be the A SHORT HISTORY OF THE ARC. 67 P.D. between the carbons, a the constant back E.M.F. due to volatilisation of the carbon, and a the back E.M.F. due to thermo-electric action, V - a - of Now, a' diminishes with increase of current, since the tem- perature of the negative carbon increases while that of the positive remains constant. Hence V diminishes as A increases. Keeping the current constant at six amperes, and the arc of a fixed length, they found that, starting with the atmospheric pressure, V increased as the pressure was increased, but at a slower rate. When, on the other hand, the pressure of the surrounding air was reduced below that of the atmosphere, V also increased except in the case of the T \th-inch arc when V diminished on reducing the pressure. This except tional result, however, arose probably from the arc hissing. Hence, for a given current and length of silent arc, V has a minimum value for atmospheric pressure. The increase of V as the pressure was reduced below that of the atmosphere they considered was caused by an increase of a', for they said that a, the constant counter E.M.F., was probably lower in a vacuum, and the positive carbon not so hot, but the negative carbon seemed to cool proportionately faster than the positive. The counter E.M.F., they concluded, increased apparently with the pressure above one atmosphere, while the ohmic resist- ance of the arc did not greatly change. As regards the formula, their experiments showed that a varied with I for each pressure employed, and they failed to arrive at any exact law connecting V, I and A, even for one pressure, the equation that most nearly fitted their results being, they thought, but this, they remarked, was only approximately correct. 90 In some articles published in 1893 M. Blondel gave it as his experience that, although the maximum brilliancy of the crater was independent of the current flowing in the arc, yet that the average brilliancy of the incandescent portions increased both F2 68 THE ELECTEIC ARC. with the intensity and with the density of the current, until the crater was well saturated. If, he said, the value of the current be suddenly varied, the intrinsic brilliancy undergoes a temporary and very appreciable variation which may reach ten per cent., and which diminishes gradually until the dimensions of the crater are so altered as to restore the surface of emission to the value that it ought to have for the new current. He considered that the heating of the crater only took place at the surface, and that the temperature of volatilisation was only reached by a very thin superficial film. In order that the light of the crater should not vary with the carbons employed, he was of opinion that it was necessary that the carbons should contain a very small admixture of foreign substances, and. that the molecular condition of the light giving surface should be always the same. He thinks that the surface of the crater is always turned into graphite with carbon electrodes, so that they always fulfil the second condition. He found the intrinsic brilliancy of the crater to- vary between 152 and 163 "bougies decimales." With the hissing arc M. Blondel observed that the current flowed jerkily, the violet part of the arc became blue-green, and the arc lost its transparency, being transformed into an incan- descent mist that hid the crater. When hissing ceased, and the arc became violet again, he noticed that the crater appeared to- be covered with black specks which gradually disappeared, a fact which he thought pointed to a lowering of the temperature during hissing. The arc while hissing gave from 10 to 20 per cent, less light than when silent, and M. Blondel concluded therefore that while with the silent arc most if not all of the carbon that is transferred from one pole to the other is volati- lised, with the hissing arc a large part of it is transferred by disruptive discharge. 91 In 1894 M. Violle renewed his inquiries into the temperature of the arc with a still larger range of current than before, namely, 10 to 1,200 amperes. He found that in all cases the temperature and intrinsic brilliancy of the positive carbon remained constant. The arc he employed was enclosed, and he found by spectroscopic methods that the brilliancy of the arc itself increased as the current increased. While doubting that the brilliancy of luminous rays contributing to the spectra of A SHORT HISTORY OF THE ARC. 69 gases was connected with the temperature by the same relation as the brilliancy of the corresponding regions in spectra of solid bodies, he still considered that his experiments led to the con- clusion that the temperature of the arc proper increased with the current, and was in general higher than that of the positive carbon. 92 In the same year, while experimenting with a view to using a fixed portion of the supposed uniform light of the crater of an arc as a practical standard of light, Mr. Trotter made his notable discovery of the rotation of the arc. By the use of a double Rumford photometer, giving alternating fields, as in a Vernoa Harcourt photometer, his attention was called to a bright spot at or near the middle of the crater. The use of rotat- ing sectors accidentally revealed that a periodic phenomenon accompanied the appearance of this bright spot, and though it is more marked with a short humming arc, the author believes that it is always present. An image of the crater was thrown on to a screen by a photo- graphic lens ; and a disc having 60 arms and 60 openings of 3, and rotating at from 100 to 400 revolutions per minute, was placed near the screen. Curious stroboscopic images were observed, indicating a continually varying periodicity, seldom higher than 450 per second, most frequently about 100, difficult to distinguish below 50 per second, and becoming with a long arc a mere nicker. The period seemed to correspond with a musical hum of the arc, which generally broke into a hiss at a note a little beyond 450 per second. The hum was audible in a telephone in the circuit, or in shunt with it. The current was taken from the mains of the Kensington and Knightsbridge Electric Light Company, often late at night, after all the dynamos had been shut down. The carbons were not cored ; six kinds were used. A rotating disc was arranged near the lens, to allow the beam to pass for about yj^th of a second, and to be cut off for about yj^th of a second. It was then found that a bright patch, occupying about one-quarter of the crater, appeared to be rapidly revolving. Examination of the shape of this patch showed that it consisted of the bright spot already mentioned, and of a curved appendage which swept round, sometimes changing the direction of its rotation. This appen- 70 THE ELECTRIC ARC. dage seemed to be approximately equivalent to a quadrant sheared concentrically through 90. The author inclined to the theory of constant temperature of the arc, and attributed this phenomenon, not to any actual change in the luminosity of the crater, or to any wandering of the luminous area, such as is seen with a long unsteady arc, but to the refraction of the light by the heated vapour. All experiments, such as enclosing the arc in a small chamber of transparent mica, or the use of magnets, or an air blast, failed to produce any effect in altering the phenomenon. A distortion of the image of the crater while the patch revolved was looked for, but nothing distinguishable from changes of luminosity was seen. 03 FIG. 19. Prof. Fleming, in the course of experiments on the arc in 1894, was led to believe that the carbon boiled at the crater, and that the violet core of the arc consisted of a torrent of carbon vapour passing towards the negative pole. This violet core may be heated to a higher temperature than that of the crater by the passage of the current through it. He thought that at the cooler negative pole some of the carbon vapour was condensed, but that some of it was deflected back again on to the positive carbon, " causing the golden aureole or flame and creating thus a double carbon current in the arc." The negative carbon, he thought, gave evidence after use of having been worn away by a kind of sand blast action. A SHORT HISTORY OF THE ARC. 71 Joining the positive carbon, an electric bell, and a third car- bon which dipped into the arc, in series, he found that sufficient current passed in the circuit to make the bell ring, but if the negative carbon were jomed up instead of the positive, the bell gave no sound. This led him to conclude that there was no perceptible P.D. between the arc and the negative carbon. Fig. 19 shows the arrangement used by Prof. Fleming in experimenting on the conductivity of the arc. The third carbon T, upon which the arc was made to play steadily by means of the magnet, was joined up in series with the galvanometer G, the battery of 15 secondary cells B, and the negative carbon. When the negative pole of the battery was joined to the negative carbon the galvanometer needle was deflected, showing that a current was passing, but when the poles of the battery were reversed there was no deflection of the galvanometer. Hence Prof. Fleming concluded that the arc possessed a unilateral conductivity, allowing a negative current to flow through it from the negative carbon to the positive, but not allowing a positive current to flow in the same direction. After performing this experiment it was found that the third carbon T was cratered, and that its tip was converted into graphite. 94 A measurement of what was considered to be the true resistance of the arc was made in 1895 by Mr. Julius Frith with the Wheatstone's bridge seen in Fig. 20. Two of its arms, P, Q, consisted of the two halves of a stretched platinoid wire, each having a resistance of 5 -35 ohms. The third arm was composed of a battery of 26 accumulators, E, which, together with a shunt dynamo D^ sent a current through a resistance, RU an ammeter C and the arc X in series, the arc being 2mm. in length, formed with carbons llmm. in diameter. The fourth arm consisted of a shunt dynamo, D 2 , exactly similar to D 1? only at rest, together with resistances R 2 and R 3 and a coil L, whose self-induction could be varied by moving an iron core. The resistances of D x and D 2 were each 0-04 ohm ; of Rj and R 2 , each 8 ohms ; of E, 0*25 ohm ; and of R 3 0'3 ohm. Before closing the switch S, the speed of the dynamo Dj and the length of the arc were varied until the potential of the points A and B were equal, as tested by the voltmeter V, 72 THE ELECTRIC ARC. which, by means of the switch K, could be connected either across the accumulators E or across the arc X. An alternator D 3 sent an alternating current through a wire, any two points of which could be tapped to supply the alternating P.D. to the bridge, and, after closing the switch S, the resistance of R 3 and the self-induction of L were varied until the sound in the telephone T became a minimum, the condenser M, inserted in the telephone circuit, cutting off' from the telephone any direct current effect that might be caused by want of perfect equalisation of the potentials of the points A and B. The best results were obtained with R 8 having a resistance of about 0'6 ohm, and an alternating P.D. of 5 volts supplied to the bridge. This makes the resistance of the arc about 0*6 ohm, which, together with the readings of the ammeter C and the voltmeter V, give the back E.M.F. in the arc as 39 volts. Other methods of testing were employed by Mr. Frith, and results were obtained agreeing with the above. 95 Mr. Wilson has experimented on the electric arc under considerable atmospheric pressures. As the pressure was increased, and the current kept constant, he found that the apparent resistance of the arc increased. When the pressure had been raised to five atmospheres the temperature of the crater had fallen, while at 20 atmospheres the brilliancy of the crater fell to a dull red colour. Diminishing the pressure, on the contrary, increased the brightness. Mr. Wilson therefore concluded that "the temperature of the crater, like that of the filament in an incandescent lamp, depends on how much it is cooled by the surrounding atmos- phere, and not on its being the temperature at which the vapour of carbon has the same pressure as the surrounding atmosphere." 97 Mr. Freedman made some experiments on " The Counter Electromotive Force in the Electric Arc," using small currents up to two amperes, with electrodes of different substances. His conclusions were as follows : " 1st. There is a counter E.M.F. present in an electric arc depending simply upon the material and temperature of volatili- sation of the electrodes, and this counter E.M.F. has a constant definite value for that material. A SHOET HISTORY OF THE ARC. 74 THE ELECTRIC AEG. " 2nd. On account of the different temperatures there must be a thermo-electric effect. The counter E.M.F. due to this phenomenon must depend on the difference of temperature be- tween the electrodes. Consequently, it must increase with the length of the arc as the temperature of the negative electrode falls ; and it must decrease with the current as the temperature of the negative electrode rises. " 3rd. It is fair to assume that two amperes of current will tear off twice as many molecules, in the same length of time, from the positive electrode as one ampere ; in strict analogy to electro-deposition. If the quantity of matter is doubled the resistance is most likely halved ; so that c R would remain a constant quantity. This would be so, provided the temperature remained constant. But since the temperature rises with increase of current, c R must actually decrease with increase of current." From these considerations Mr. Freedman formed the follow- ing " complete formula for the difference of potential between the electrodes." in which n? = the constant counter E.M.F., depending upon the material of the electrodes and its temperature of volatilisation. y = the counter E.M.F. due to the thermo-electric effect, being a function of the material of the electrodes and the differ- ence of the temperature; the higher temperature being that of volatilisation of the electrode and the lower depend- ing upon the material and size of the electrode, the current and the length of the arc. c = the current strength. R = the ohmic resistance of the arc, depending upon the material of the electrodes, the length of the arc, the temperature and the current. For any given material of electrodes analytically expressed in terms of length and current, said the author, v = x+f (I, c) + c/' (I, c) or in terms of temperature and currents, At the meeting of the British Association at Ipswich in 1895, A SHORT HISTORY OF THE ARC. 75 Prof. Ayrton read a short Paper on "The Resistance of the Arc." He had been led, by the study of the various curves connecting the P.D. between the carbons with the current flowing for con- stant lengths of arc, to the conclusion that if there were, as most observers seemed to think, a back E.M.F. and a true resistance in the arc, then the resistance must be negative. Some experi- ments made by Mr. Mather at his suggestion strengthened the idea.* " In one of these experiments two points of equal potential were found in a circuit consisting of an arc, a battery, and a resistance. Another battery, consisting of a few cells of known E.M.F. and resistance was applied between these two equi- potential points, and the current flowing through the battery was noted. The resistances of the two parallel halves of the circuit, excluding the arc, were known, so that the current which, taking the arc resistance as zero, should flow through this battery, could be calculated. Now the value of this calcu- lated current was found to be less than the observed value, no matter in which direction the P.D. was applied, and this result was also obtained when an alternating P.D. was used. Hence the resistance of the arc was apparently less than zero." "The other experiment consisted in running the arc at a steady P.D. and current, suddenly altering the resistance in circuit by a small amount, and noting the changes in the ammeter and voltmeter-readings so produced. The new con- ditions were maintained only long enough to allow of these readings being taken. The arc was then brought back to its former condition before taking another reading. It was found that a change of P.D. in one direction was always accompanied by a change of current in the opposite direction. The results of both experiments were however only qualitative." It may be mentioned, that although the idea of a negative resistance in the arc occurred to Prof. Ayrton quite indepen- dently, before he had ever heard of Luggin's work on the subject, yet that able experimenter made the same suggestion as long ago as 1888 (see p. 54). In their Paper read before the Physical Society, in May, * Prof. Ayrlon's Paper was not published, but the account of it given here is taken from the Paper on the same subject read by Messrs. Frith and Rodgers, before the Physical Society, in May, 1896. 76 THE ELECTRIC AEC. 1896, Messrs. Frith and Rodgers gave the results of a long and very complete series of " Experiments on the Eesistance of the Arc," undertaken with a view to throwing some light on the discrepancy between the negative resistance obtained by Prof. Ayrton and the positive resistance found by all other experimenters. They tried several methods of experimenting, the most successful of which is represented diagrammatically in Fig. 21. D is the armature of an alternator, the current from which passes round two circuits in parallel, one of which contains the arc X, and the other an adjustable resistance R. By adjusting R the alternating currents in the two halves can be made equal. When this is the case the impedances of the two halves to alternating currents must be equal. The continuous current circuit shown to the left consists of a battery of accumulators B, the hand-adjusted arc lamp X, the resistance K, the ammeter A, and (with the commutator as shown) the resistance S and the alternator D. The alter- nator D carries the continuous current, but this does not prevent its acting as an alternator. The air transformer T was used to measure the small alter- nating current independently of the continuous current flowing. For this purpose its thick wire coil was placed in series with A SHORT HISTORY OF THE ARC. 77 the alternator D, and its thin wire coil was connected with an electrostatic voltmeter E. By means of the commutator C, the air-transformer T could be thrown into either circuit, the resis- tance S being thrown by the same operation into the other circuit. The resistance S was equal to that of the thick wire coil of T, so that when S replaced T the continuous current was unaffected by the change. When experimenting, the arc was run at the required current and P.D. by altering the number of cells in B, K being always kept the same. R was then adjusted till the deflection of E was the same when T was in either circuit. If the value of R when balance was obtained were R 1? then ^^k + bi + l + x (i) where k was the constant resistance at K, b l was the resistance to alternating currents of the battery B, I the resistance of the arc lamp and connections, and x the resistance of the arc. The carbons were next firmly screwed together and the number of cells in B reduced, till the continuous current was the same as before. R was again adjusted till the deflections of E were equal, then if R 2 were the new value of the resistance, and b 2 the resistance of the portion of the battery now used -R 2 = h + b 2 + l (ii). Next the cells were cut out and the mains leading to them were short circuited, so that the third value of R obtained was R 3 - + Z (Hi). From (ii) and (iii) the resistance of b 2 was obtained, and, by proportion, of any number of cells. Putting these values in (i) the value of x in ohms was found. Messrs. Frith and Rodgers defined the resistance of the arc as the ratio of a small increment of P.D. applied, to the small increment of current produced ; that is, they were measuring the value of -TT- when an alternating current was applied to the arc which they considered to be too small to produce any visible effect on it. They called this the "instan- taneous" -j-r to distinguish it from the steady^-; the tangent of the inclination of the tangent line to the curve representing the steady values of V and A with a constant length of arc. 78 THE ELECTRIC ARC. In order to show the difference between these two values, and also to show that in an analogous case, where the resistance could be measured apart from the back E.M.F., the instantaneous dV -V-T- found by superimposing a small alternating current on a CL A. continuous one did really give the value of the resistance, a glow lamp taking a current of 10 amperes at a P.D. of about 8 volts was joined in series with three accumulators. Thus, they had a resistance which they could measure separately in series with a back E.M.F. They then sent a small alternating current through the circuit against the E.M.F. of the accumu- lators, and plotting the curve obtained for the instantaneous dV and current, they found it very nearly coincided with the curve representing the observed resistance and the current, while the values found for the steady -y- were all smaller than the corresponding resistances. This experiment, the authors considered, justified them in concluding that if the arc consists of a back E.M.F. and a resistance, the actual value of the resistance was given by their method. They varied the conditions of their experiments as much as possible. They studied the effect on the resistance of the arc of variations in the amount, frequency, and wave form of the alternating current ; the effect of different kinds of carbons and different P.Ds. and currents ; the effect of using different com- binations of cored and solid carbons, of carbons cored with substances other than carbon, and the effect of the relative sizes of the carbons. The largest alternating current used had a root mean square value equal to about 10 per cent, of the continuous current. Frequencies between the limits of 250 and 7 complete alterna- tions per second had no effect on the resistance of the arc. Complete information respecting the carbons is given in the figures. It will be seen from. these that the ordinates of + solid - solid are all negative, those of + cored - cored are all positive, and that the other curves all lie between these two extremes. The curves in Fig. 22 connect resistance with cur- rent for a constant P.D. ; those in Fig. 23 connect resistance and P.D. for a constant current. The curves for solid carbons A SHORT HISTORY OF THE ARC. 79 are in each case all very close together, while those for which cored carbons were used show much greater divergence owing v e. -2 Current in Amperes. FIG. 22. to variations in the formation and diameter of the cores with different makes of carbons. 80 THE ELECTRIC ARC. From the curves the authors concluded that with both carbons solid the resistance of the arc was always negative with both cored it was always positive, and with one cored and < lyl <: 00 to t- O o 2 o v \ \ | \ \ X \ \ aN ? CO \ fi * \ \ k \ ?' uti 3 '':-. \ X i ( -.1 '^ TV \ \ \* \ ^ Li \ A 4 > \ \ ^ \ \ \ ^ \ ^ A . l t fc * \ \ 1 i li ) ? v & \ ' \ \ * >^\ \ \ :\ I ^ > \ \^ 1> . : ' ; y> u \ \ \ \ \ \ \ \ \ (ft \ : - V \\ * i , /' II ^ Ci \ o \ \ ( t n i /!' / 1 ;/ /// /// \ / '^ ^/ f ^ fj [n ^ ^ ,:^. 1 >/ y ' V A ,/ .- ( /y & n W/ X // i \ 4> v 1 \ / ' ^ d /' / *' A M- ,--" > // ,/ / i I ' \ / \ / \ ^ \\ >' j/ n ? i i i?? r r < o Q ' ^ \ , V V V o n = = z o aizz < < < O O sS I S o ?2 1 7 / / a! H \3 1 1 Q c 3 CO W C 3 tt 0-tt < < ffl O U U _ DC C -i 000 O O 05 i W 9 J j O : o' SO ? ill i < so o 3 u k Resistance of the Arc in Ohms. A SHOET HISTORY OF THE ARC. SI the other solid it was sometimes positive and sometime* negative. They pointed out that with a constant current the resistance of the arc appeared always to reach a minimum as the arc was lengthened out, and then to increase again. This minimum is more strongly marked and occurs with a smaller P.D. with cored than with solid carbons. It is reached with cored carbons with the shortest arc in which the dark central space appears (see p. 7). With inverted arcs the resistance with solid carbons was practically unchanged, but with cored carbons no dark space was seen, and the resistance was much less than for ordinary arcs. The authors considered that the degree of contact between the purple glow and the negative carbon had great effect on the resistance of the arc, which was most negative when that contact was most perfect. When both carbons were cored it was found that above a certain frequency the instantaneous was positive, and uA below that frequency it was negative. The critical frequency was about 1/8. With the positive carbon cored and the negative solid, at 35 volts the resistance was positive with all frequen- cies, at 45 volts it was negative with all frequencies, and at 55 volts it was positive with frequencies above 1/8, and negative with frequencies below that. The authors found that the current flowing through a hissing arc was oscillatory, the oscillatory current amounting in one case to 3 per cent, of the continuous current. 103 Arons made some fresh experiments in 1896 to prove the existence of a back E.M.F. in the arc, and to determine its value. He worked on the same lines as Stenger (see p. 64), using, however, the town mains, which gave 105 to 110 volts, instead of a dynamo. His arrangement was as follows. The mains (Fig. 24) were joined in series with two variable resistances, R, at least 3 ohms, and r, about 0'4 ohm, the tangent galvanometer T, the arc A and a battery of accumu- lators, B. Between the point of connection of R and r and the negative main, a Dubois key K was inserted. Hence, when K was open, the arc was fed by the mains, but when it was closed, a current flowed through the arc from the accumulators 82 THE ELECTRIC ARC. in the direction opposite to that which flowed from the mains. The carbons used were 15mm. in diameter, and both cored. The arc was from 1-5 to 2mm. in length. The points which Arons wished to determine were : (1) What was the least E.M.F. in the accumulators with which a current could be made to flow through the hot vapour of the arc immediately after it was extinguished. (This current would, of course, with his arrangement, flow in the reverse direction, thus helping the back E.M.F. if there were any which continued after the arc was extinguished.) (2) What E.M.F. was necessary in the battery to enable it to maintain an arc in the reverse direction, for even only a short time after the original arc was extinguished. It is evident, from the arrangement, that closing the key K both stopped the current from the mains (and therefore extinguished the arc) and turned on the reverse current from the accumulators. Hence no time was lost between the two operations. MAINS FIG. 24. As regards his first point, Arons concluded that with the carbons he employed the smallest E.M.F. of the accumulators that would send a reverse current through the arc immediately after it was extinguished was 18 volts. He attributed the fact of Stenger's having been able to send such a current with an E.M.F. of 10 volts to his having used different carbons. He considered, therefore, that both his and Stenger's experiments showed that the condition of the carbon electrodes and the vapour after the extinction of the arc was of such a nature that it required a definite outside E.M.F. to send a current through the gaseous space. Regarding the second point, Arons found that the accumu- A SHORT HISTORY OF THE ARC. 83 lators could produce an arc in the reverse direction, after the extinction of the original arc, with a very small P.D. at the first moment, but that the P.D. necessary to maintain this arc then rose rapidly till it reached its normal value. This, he thought, was because the E.M.F. of the accumulators was assisted at the first moment by the still active back E.M.F. of the original arc, which, however, very rapidly died away. From his experiments he calculated this back E.M.F. to be from 10 to 14 volts. 104 Some experiments made in 1896 by Mr. W. E. Wilson and Prof. G. F. Fitzgerald, "to determine, if possible, whether the temperature of the crater in the positive carbon varies when the pressure in the surrounding gas is changed," led to the conclu- sion that there was not sufficient evidence to affirm that the tem- perature of the crater was either raised or lowered by pressure. The experimenters first used compressed air, and found that with any pressure greater than that of the atmosphere, some of the radiation was cut off by the formation of red fumes of N0 2 , which became very plentiful when the pressure was as great as lOOlb. per square inch. In compressed oxygen the arc burnt very steadily, but there was sufficient nitrogen present in the oxygen for enormous quantities of N0 2 to be formed at high pressures. These results caused the experimenters to conclude that the red hot appearance of the crater and the reduction of radiation in their former experiments (see p. 72), were due to the forma- tion of large quantities of N0 2 when the arc was under pressure. In hydrogen contaminated with hydrocarbons, at atmospheric pressure, the arc burnt very far along both carbons, especially the negative. Trees of soot and a deposit of hard graphitic carbon formed all round the crater, as if there were electrolysis of the hydrocarbon, and carbon were electro-negative compared with hydrogen. The arc was very unsteady, both current and P D. varying continually, and the soot trees hid the crater, so that the attempt to get any measures of radiation under pressure with hydrogen was abandoned. Finally, carbon dioxide was tried, a cylinder of C0 2 being connected with the arc box. At pressures above 1501b. the arc could not be maintained long enough for radiation measures to be obtained, but at lower pressures some good measurements o2 84 THE ELECTRIC ARG. were made. With from 1 to 6 or 7 atmospheres very little change of radiation appeared to take place. Messrs. Wilson and Fitzgerald consider that the results of their experiments render it very improbable that it is the boiling point of carbon that determines the temperature of the crater, and this opinion is strengthened by the fact that the carbon is so slowly evaporated. "The crater of mercury" they say, " is dark, but then it volatilises with immense rapidiry, and the supply of energy by the current being more than 100 times that required merely for evaporation, there seems very little reason why even a considerable difference in latent heat should make any sensible difference in the rate of evaporation of mercury and carbon, especially as, at the same temperature, the diffusion of carbon vapour is nearly three times as fast as that of mercury vapour, and the temperature immensely higher." 105 M. Guillaume, in a Paper read before the French Physical Society, said that he believed the reduction of brilliancy found by Mr. Wilson in his experiments on the arc under pressure (see p. 72) was due to carbon being dissolved in the sur- rounding atmosphere. He considered his theory was proved by the fact of Messrs. Wilson and Fitzgerald having found in their later experiments above that, with an arc burning in C0 2 at a pressure of 1501b., a fog formed when the pressure was- suddenly reduced. 106 The much vexed question of a back E.M.F. in the arc was attacked by Herzfeld, who, like Stenger and unlike Arons, came to the conclusion that it did not exist. He used modifi- cations of Edlund's method ; extinguishing the arc, and switching into the circuit immediately after, some instrument for measuring the PJ). between the carbons. In his final experiment the time that elapsed between the two operations was only -g-i^sec., yet he could detect no P.D. between the carbons even so short a time after the arc had been extinguished. His next experiment was made to determine whether the P.D. between the carbons depended in any way on the amount of carbon transferred from one pole to the other. The arc was placed between two plates 6cm. high and 8cm. broad, the distance between them being varied from 2cm. to 10cm. The P.D. between them was 1,800 volts. The plates could be A SHOUT HISTORY OF THE ARC. 85 connected with a Leyden jar, and either both insulated, or one insulated and the other, with the part of the Leyden jar to which it was attached, earthed. As it was found that the ultra-violet rays of the arc quickly discharged the condenser, the charge was kept up by means of a Holz machine. It was found that although, when the electric field was excited, the particles sent out from the positive towards the negative carbon were continually attracted to the insulated plate, yet that neither the current nor the P.D. between the carbons was changed within the limits of sensibility of a Schuckert's ammeter and voltmeter by this withdrawal of carbon particles from the arc. The particles were always attracted to the insulated plate and arranged themselves radially on it (Fig. 25) whether it To the Ley Jen Jar. i To Earth. FIG. 25. was charged positively or negatively, even when it was 8cm. from the carbons, while the earthed plate was only O'Gcm. from them. If both plates were insulated the particles went to both equally. Herzfeld thought that perhaps the narrow double ring of particles that ranged themselves below the radial lines (Fig. 25) were those sent out from the negative to the positive carbon. The flow of particles could be plainly seen in an image of the arc projected through a lens. The author considered that his experiment showed that the supposed back E.M.F. in the arc cannot be due to a polarisa- tion of the electrodes taking place through separated solid particles, since the P.D. did not vary with the number of solid particles that really reached the one electrode from the other. 86 THE ELEGT11IC AEG. To see if a polarisation took place through the gaseous portion of the arc, and if, therefore, the vapour of the arc was affected by the electric field, an enlarged image of the arc was made through a spectroscope, the slit of which was perpen- dicular or parallel to the electric lines of force, but no change could be detected when the electric field was excited. Next, it was sought to discover the cause of the formation of a mushroom with hissing arcs, and of the growth of the negative carbon that takes place, even with silent arcs, under certain circumstances. It was shown, in the following way, that an absence of sufficient oxygen to burn the carbon will cause these growths. The carbons were enclosed in glass tubes 18mm. in diameter, to which the access of fresh air was restricted by a cork in one end of each. The carbon particles thus flew unburnt from the positive crater to the negative point and rested there. Thus the length of the arc remained unchanged for from five to ten minutes, the crater becoming deeper and the point of the negative carbon becoming longer all the time. The growth on the negative was in the shape of a corkscrew. To test whether this form was due to magnetic forces induced by the regulating magnet in the base of the lamp, the negative carbon was surrounded by an electromagnet to within 5cm. of its point, and it was found that changing the polarity of this magnet changed the direction of the corkscrew, which was from 1-2 to 2mm. in height, while the maximum number of screw turns was 2J. If the spirals were formed from positively electrified particles on their way from the posi- tive to the negative carbon, then those particles moved in the opposite direction from Ampere's molecular streams of electromagnets. To try what effect cooling each carbon and the arc itself separately had on the P.D. between the carbons, Herzfeld directed a thin jet of carbonic acid gas against each in turn, using 7mm. cored carbons placed in a Dubosq lamp from which the regulating mechanism had been removed. He found that whether the positive carbon was above and the negative below, or vice versa, or if the arc was horizontal ; whether the stream was directed against the positive or the negative carbon, in all cases the P.D. between the carbons increased when the cooling A SHORT HISTORY OF THE ARC. 87 jet was applied, and, although it diminished after the cooling was discontinued, it remained, in most cases, above its normal value. At the same time that the P.D. increased, the current in all cases diminished, under the cooling action of the carbonic acid. When the carbons were surrounded by an atmospaere of carbonic acid gas by being enclosed in a glass tube closed beneath and filled with the gas, it was found that directing a stream of the same gas against either carbon increased the P.D. between the carbons much less than when they were in air, unenclosed. A current of air from a foot-bellows directed against either of the carbons produced no effect on the P.D. between them when the arc was burning silently. Herzfeld considered that the effect of the carbonic acid was two-fold ; it both cooled the tips of the carbons, and increased the resistance of the arc itself by lowering its temperature. That the effect was not thermo-electric was, he thought, proved by the following experiment. A rod of graphite 1mm. thick was placed in the arc midway between the two carbons, and the P.D. between the graphite and each of the carbons was measured with a d'Arsonval galvanometer with 170,000 ohms in circuit. The P.D. of about 85 volts between the positive carbon and the graphite was increased by 2'1 volts when the positive carbon was cooled by the carbonic acid, and the P.D. of 6 volts between the graphite and the negative carbon was also increased by 2 '8 volts when the latter was cooled in the same way. In his concluding experiments Herzfeld made a comparison between open arcs and those enclosed in glass tubes, the E.M.F. of the accumulators being constant, and the arc being allowed to burn away unregulated till it went out. The following results were obtained : (1) The time between the P.D. between the carbons attain- ing a given value and the arc going out was much greater when the arc was enclosed. (2) The P.D. between the carbons when the arc went out was greater when it was enclosed. (3) Greater lengths of the ends of the carbons glowed after the arc went out when it was enclosed. 88 THE ELECTRIC AUG. When the enclosing tube was filled with carbonic acid gas the carbons burnt away very quickly, and after the arc was extinguished a blue light was frequently seen, both of which facts appeared to the author to show that the carbonic acid was split up, in higher temperatures, into carbonic oxide and oxygen, the latter enabling the carbons to burn away more quickly. The conclusion arrived at by the author, as the result of his experiments, was that the great heat produced at the crater is not a Peltier effect, but that a substance of great resistance is accumulated at the boundary between the positive carbon and the *a?i which is heated by the passage of the current through it, and which vaporises the positive carbon. This vapour, he thinks, condenses into fluid and solid drops in the cooler parts of the arc. 107 The same question of the existence of a back E.M.F. in the arc was attacked by M. Blondel in the following manner. The circuit of a continuous current arc was periodically interrupted FIG. 26. at very short intervals and for very short periods, and during each interruption the two carbons were connected with a galvanometer. These operations were carried out by the revolving commu- tator in Fig. 26, which also shows the circuits and general arrangements. The commutator T, driven by a continuous- current constant speed motor, consisted of an ebonite core on which there were two copper rings b and b', one of which was broader than the other. The ring b had a piece cut out of it, and in this indentation there was a tongue a forming part of the ring b' and two copper insulated plates c A SHOBT HISTORY OF THE ARC. 89 and c'. All these parts were separated by strips of mica, and the brushes themselves were also insulated from their holders by ebonite, so that the insulation resistance between any two of the brushes resting on the commutator and between each brush and earth always exceeded 5 megohms. This commutator revolved at a speed of about 40 revolutions a second. The piece cut out of the ring b was about one-fifth of the circumference. The arc lamp was fed by the battery B, giving about 70 volts. The current traversed successively the steadying resistance S, and the commutator between M and P across the ring b, then the lamp E F and the switch C. At every re volution the circuit was broken during 1/5 x 1/40 = 1/200 of a second by the passage of the indentation beneath the brush P, the spark being taken on the insulated plate c. These interruptions were very brief and followed very close on one another. The arc was perfectly stable, and could not be distinguished from an ordinary continuous-current arc. The arc having become steady, q and r were connected so that the arc was short-circuited by the galvanometer G, which was fairly sensitive, during the passage of the tongue a under the brush P (about -g^th of a second). The author considered that with this arrangement there was no reason to fear the in- fluence of cooling on the physical conditions of the arc during its extinction, nor, consequently, during the passage of the tongue a. If there existed, therefore, an E.M.F. or ordinary polarisation, it should betray itself, the author thought, by producing a permanent and easily-observed deflection of the galvanometer. A battery, p, usually a single cell, interposed in the galvano- meter circuit, first one way and then the other, enabled him to estimate the value of this E.M.F. and satisfy himself as to the sensitiveness of the method ; it was only necessary to take two readings of the deflections obtained with the battery plus the arc, and to compare them with that given by the arc alone. Finally, he substituted the resistance R, taking the same current at the same voltage, for the arc itself, and then carried out the same series of measurements as on the lamp, and was thus able to discover in what the two phenomena differed. These experiments were carried out under the most diverse conditions, with long arcs and short, silent ones and whistling, 90 THE ELECTRIC AEG. with carbons far apart and sticking together, with solid car- bons S, or cored carbons C, and the results presented no other difference than such as would arise from experimental errors. The speed of rotation of the commutator was also varied within wide limits without causing any appreciable difference. It was found, however, that a speed of the order previously mentioned or even a higher one, was necessary in order to obtain steady arcs and steady galvanometer deflections. Table IX. is a summary of a few of the series of figures obtained. Table IX. (Blondel). *j Arc. Resistance. *o S o'C Nature of Ter- Galv. Deflections Ter- Galv. Deflections. " P. X Carbons. Amp. minal Volts. Arc alone. Arc plus cell. Amp. minal Volts. Resist, alone. Resist, plus cell. Upper Lower + _ + _ 1 C S 5 35 7 70 -78 5 34-5 71-5 -75 2 S S 8 25 1 75 -72 8 27-7 -9-5 66 -83 3 S S 10 18 75 -73 10 18 -4 73 -78 4 S S 8 18 -3-5 73 -75 8 18 -8 67 -82 5 S S 11 4 1-3 80 -73 11 4 0-5 76 -73 6 C S 7 20 1 73 -73 7 20 1 76 -74 7 C S 7-5 20 2 71 -74 7-5 20 -3 71 -75 8 C S 8 18 5 70 -7 8 17-7 -6 68 -79 9 S S 8 19 -1 72-5 - 77 8-25 17-5 1-2 75-5 -73 10 C S 6 29 2-5 70 -75 6 29 2-5 77 -74 M. Blondel pointed out that the deflections produced by the arc plus the cell of 2 '25 volts E.M.F. were very large com- pared with those produced by the arc alone. He considered that the above table showed that if there were a constant counter E.M.F. in the arc it could not be greater than 1x2-25 = 0-16 volt. M. Blondel concluded from his experiments that, although the arc may not be of the exact nature of an ordinary resis- tance, yet that it behaves sensibly like a resistance, and pos- sesses no counter E.M.F., in the ordinary sense of the term, comparable with the observed P.D. It is not due, therefore, he thinks, to an electrolytic phenomenon, and if there be a residual E.M.F. due to thermo-electric causes, this cannot exceed a fraction of a volt. 109 A SHORT HISTORY OF THE ARC. 91 Granquist, in criticising Arons' latest experiments on the back E.M.F. of the arc (see p. 81), said that he thought the reason Arons could not apparently get a current to flow in the reverse direction through the carbons, immediately after the arc was extinguished, with a less P.D. than 18 to 22 volts, was that the tangent galvanometer he used was not sensitive enough to detect the current. He pointed out that since the dying out of the vapour between the carbons after the arc was extinguished was a cooling effect, it was probable that the time taken by the operation depended to some extent on the amount of vapour existing while the arc was burning, and therefore on the current flowing through the arc. The very sending of a current through the carbons would tend to increase the heat of this vapour, and hence to retard the dying-away process. He had himself found this to be the case, for he could send a current through the arc for a much longer time after it was extinguished when a large current had been flowing, than when there had been a small one. Also, he could send a large current in either direction for a longer time than a smaller one, after the arc was extinguished. Granquist himself had found that he could send a current in either direction through the carbons immediately after the arc was extinguished, with a single DanielPs cell. The experi- ments were made in 1894, but as the results were only published in Swedish, he gave a short account of them in a Paper published in German in 1897. Fig. 27 shows the apparatus used. D was a Siemens shunt dynamo, G an ammeter, A the arc, B a DanielPs cell, M a mercury contact, and B. a reversing switch by means of which the current from B could be reversed ; G' was a galvanometer constructed by Granquist himself on the principle of unipolar induction, which, as it contained no coils of wire, might be considered to be free from self-induction ; a, b and c, were three metal brushes which rubbed against the wheel W and the two wheels attached to it, each 235 -5mm. in circumference, the one of ebonite and the other of metal. All three wheels were joined firmly together, so that they rotated on the same axis. In the periphery of the metal wheel a slot 34mm. in length was cut and filled in with ebonite. Similarly, in the 92 THE ELECTRIC ARC. periphery of the ebonite wheel a slot, 21mm. in length, was cut right down to the mstal axis, and filled in with brass, so that when this part of the wheel came under the brush 6 there was electric connection between b and the wheel W. The wheels were so arranged that when the brush a was on the ebonite part of the metal wheel, the brush b was on the metal part of the ebonite wheel. Thus, when the dynamo circuit was broken, the circuit c A M R b was closed. It was necessary that the dynamo circuit should be open longer than the galvanometer circuit was closed, in order to allow time for the spark which would pass at breaking to die away, and for the arc circuit to be really completely broken before the galvanometer circuit was closed. Hence, the ebonite part of the metal wheel was 34mm. in length, while the metal FIG. 27. part of the ebonite wheel was only 21mm. Thus, the dynamo circuit was broken 1'5 times as long as the galvanometer circuit was closed, so that by moving the brush b, and changing the speed of rotation of the wheels, the time between the open- ing of the dynamo circuit and the closing of the galvanometer circuit could be altered at will. The following was the method of experimenting. After the wheels had been set in motion and the carbons brought into contact, the dynamo circuit was closed. As soon as the arc was well established, the circuit of the cell B was also closed by means of the mercury contact M. A deflection 'U 1 was thus obtained in the galvanometer G'. The current was then A SHORT HISTORY OF THE ARC. 93 reversed by means of the switch E, and the deflection U 2 observed. Then, if E were an E.M.F. in the arc, and the E.M.F. of the cell were e, In the following table U^ and U 2 were the deflections of the galvanometer, and E the supposed back E.M.F. of the arc. The time which elapsed between the complete breaking of the current and the closing of the galvanometer circuit was O'OOOO second. Table X. (Granquist.) Current in arc. U,. U 2 . E. 6-2 + 30-0 -181 0-27 6-2 24-0 141 0-26 5-0 22-0 13-5 0-26 5-2 23-8 14-5 0-24 3-2 19-7 11-5 0-26 7-5 20-2 13-5 0-20 5-6 14-4 10-0 0-20 8-9 14-5 17-7 0-11 5-0 20-5 12-7 0-23 40 17-0 10-5 0-24 mean 0'227 volt. Hence Granquist found, as Lecher, Luggin, and Stenger had already done, that there was no back E.M.F. in the arc after it ivas extinguished greater than about O227 volt. Unlike Blondel, however, he did not think this precluded the possi- bility of a far greater back E.M.F. in the arc ivhile it was burn- ing, but he considered that the larger back E.M.F. and the current ceased to exist at the same moment. 110 In commenting on M. Blondel's method, given above, of proving that the arc possesses no back E.M.F. in the ordinary acceptation of the term, Prof. Fleming suggested that there might be a back E.M.F. due to a "Thomson effect" along the hot vapour of the arc itself that is to say, a back E.M.F. due to the temperature gradient of the hot vapour. Prof. Fleming mentioned that he and Prof. Dewar had shown that in carbon between the temperatures 200 and + 200, the E.M.F. caused by the "Thomson effect" acts from cool to hot as it does in copper. If in carbon vapour the " Thomson effect " keeps the same sign as in solid carbon, he thinks there might be a back 34 THE ELECTEIG ABC. E.M.F. due to it along the column of vapour. This, he said, would account for the fact that when the negative carbon is heated the P.D. between the carbons for the same current is less than when it is unheated, and also for the smaller P.D. necessary for an alternating current arc, because the positive and negative carbons must be more nearly equal in temperature. 111 CHRONOLOGICAL LIST OF ORIGINAL COMMUNICATIONS CONCERNING THE ARC. 1 Nicholson's Journal, 4to, 1801, Vol. IV., p. 326 DAVY. 2 Gilbert's Annalen, 1801, Vol. VIL, p. 161 GILBERT. 3 Gilbert's Annalen, 1801, Vol. VII., p. 248 PFAFP. 4 Gilbert's Annalen, 1801, Vol. VII., p. 516 . ... PFAFP. 5 Gilbert's Annalen, 1801, Vol. VIII., p. 370 PFAFF. 6 Gilbert's Annalen, 1801, Vol. IX., p. 341 RITTER. 7 Nicholson's Journal, 8vo, 1801, Vol. III., p. 136 ... DAVY. 8 Journal of the Royal Institution, 1802, Vol. I., p. 166 ... DAVY. 9 Journal of the Royal Institution, 1802, Vol. L, p. 209 ... DAVY. ( FOURCROY, 10 Annales de Chimie, An. IX. (1801), Vol. XXXIX. ...J VAUQUELIN, ( THNARD. 11 Nicholson's Journal, 4to, 1802, Vol. V., p. 238 TROMSDORFF. 12 Gilbert's Annalen, 1802, Vol. XI., p. 396 , ANON. 13 The Monthly Magazine, 1803, Vol. XV., p. 259 PEPYS. 14 Nicholson's Journal, 1804, Vol. VIII., p. 97 CUTHBERTSON. is " Practical Electricity and Galvanism," 1807, p. 260 .... CDTHBERTSON. 16 MS. Note Book at the Royal Institution, 1808 DAVY. 17 Philosophical Transactions, 1809, p. 46 DAVY. 18 MS. Kote Book at the Royal Institution, 1809 DAVY. 19 The Monthly Magazine, August 1, 1810, Vol. XXX. , p. 67 DAVY. 20 "Elements of Chemical Philosophy," 1812, Vol. L, p. 152... DAVY. 21 Annales de Chimie et de Physique, 1820, Vol. XV., p. 101 ARAGO. 22 Philosophical Transactions, 1821, p. 18 DAVY. 23 Silliman's Journal, 1821, Vol. III., p. 105 HARE. 2i Silliman's Journal, 1822, Vol. V., p. 108 ... SILLIMAN. 25 Silliman's Journal, 1823, Vol. VI., p. 342 ... ... SILLIMAN. 20 Silliman's Journal, 1826, Vol. X., p. 123 SILLIMAN. 27 Philosophical Magazine, 1838, p. 436 ... GASSIOT. ( GASSIOT, 28 Iransactions of the London Electrical Society, 1837 to I WALKER, 1840, p. 71 ... 1 STURGEON, 29 Philosophical Transactions, 1839, p. 92 ... 30 Philosophical Magazine, 1840, Vol. XVI., p. 478 31 Comptes Rendus, 1840, Vol. XL, p. 702 ... MASON. DANIELL. GROVE. BECQUEREL. A SHORT HISTORY OF THE ARC. 95 32 Comptes Rendus, 1841, Vol. XII., p. 910 33 Comptes Rendus, 1841, Vol. XIII., p. 198 34 Archives de I Electricity 1841, p. 575 35 Poggendorff's Annalen, 1844, Vol. LXIII., p. 576 36 Comptes Rendus, 1844, Vol. XVIIL, p. 746 37 Poggendorff's Annalen, 1845, Vol. LXVL, p. 414 33 Comptes Rendus, 1846, Vol. XXII., p. 690 39 Comptes Rendus, 1846, Vol. XXIII., p. 462 40 Comptes Rendus, 1850, Vol. XXX., p. 201 41 Comptes Rendus, 1852, Vol. XXXIV., p. 805 42 Philosophical Transactions, 1852, p. 88 ... 43 Comptes Rendus, 1865, Vol., LX., p. 1,002 44 Poggendorff's Annalen, 1857, Vol. CXXXL, p. 586. ... 45 Poggendorffs Annalen, 1868, Vol. CXXXIIL, p. 353 ... 46 Poggendor&s Annalen, 1868, Vol. CXXXIV.,pp. 250, 337 47 Poggendorff's Annalen, 1870, Vol. CXXXIX., p. 354 ... 48 Poggendorff's Annalen, 1870, Vol. CXL., p. 552 49 The Electrician, 1879, Vol. II., p. 76 50 The Electrician, Vol. II., 1879, Jan. 18th, p. 107 ; and 25th, p. 117 51 Royal Engineering Committee Extracts for 1879, Appendix III. 02 La Lumiere Electrique, 1879, Vol. I., p. 41 53 Philosophical Transactions, 1879, p. 159 54 La Lumiere Electrique, 1879, Vol. I, p. 235 55 Journal of the Society of Telegraph Engineers, 1880, Vol. IX., p. 201 56 La Lumiere Electrique, 1881, Vol. III., p. 220 57 La Lumiere Electrique, 1881, Vol. III., p. 285 58 La Lumiere Electrique, 1881, Vol. III., p. 287 59 Proceedings Physical Society, 1882, Vol. V., p. X97 80 Proceedings of the Royal Society, 1882, Vol. XXXIII., p. 262 61 EleUrotechnitche Zeitschrift, 1883, Vol. IV., p. 150 Zeitschrift fur Elektrotechnik, 1885, Vol. III., p. Ill ... 63 Wiener Akad., 1885, Vol. XCL, 844 64 Centralblatt fur Electrotechnilc, 1885, Vol. VII., p. 443... 65 Wiedemann's Annalen, 1885, Vol. XXV., p. 31 63 Wiedemann's Annalen, 1885, Vol. XXVI., p. 518 67 Proceedings of the American Academy of Sciences, 1886, p. 227. Centralblatt fur Elektrotechnilc, 1886, Vol. VIII., pp. 517,619 69 Wiedemann's Annalen, 1887, Vol. XXX., p. 93 70 Wiedemann's Annalen, 1887, Vol. XXXI., p. 384 71 Centralblatt filr Elelctrotechnik, 1887, Vol. IX., p. 219 ... 72 Centralblatt fur EleUrotechnilc, 1887, Vol. IX., p. 633 ... DE LA RIVE. BECQUEREL. MACKRELL. CASSELMANN. f FIZEAU, \ FOUCAULT. NEEF. DE LA RIVE. VAN BREDA. MATTEUCCI. QUET. GROVE. DE LA RIVE. EDLUND. EDLUND. EDLUND. EDLUND. BEZOLD. ATRTON. SCHWENDLEB. DU MONCEL. / DE LA RUE, \ MiJLLER. ROSSETTI. ANDREWS. ROSSETTI. LE Roux. NlAUDET. / AYRTON, \ PERRY. DEWAR. FROLICH. PEUKERT. VON LANG. Vox LANG. STENGER. EDLUND. f CROSS, ( SHEPARD. NEBEL. ARONS. VON LANG. VOGEL. UPrENBORN. 96 THE ELECTRIC AUG. 73 BeiUiittcr, 1888, Vol., XII., No. 1, p. 83 74 CentralUatt fur EleJctrotechnik, 1888, Vol X., p. 3 75 CentralUatt filr Elcktrotechnik, 1888, Vol. X., p. 48 .., 76 CentralUatt fur Elcktrotechnik, 1888, Vol. X., p. 102 ... 77 CentralUatt fur Elcktrotechnik, 1888, Vol. X., p. 567 .., 78 Centralblattfilr Elektrotechnik, 1888, Vol. X., p. 591 .., 79 CentralUatt fiir Elcktrotechnik, 1888, Vol. X., p. 749 .. 80 Wien Sitzungsberichte, 1889, Vol. XCVIII., p. 1,192 .. M" Proceedings of the Royal Society, 1889, Vol. XLVIL, p. 118 81 The Electrical World, 1891, Vol. XVII., p. 166 8 - La Lumiere tilcctrique, 1891, Vol. XLIL, p. 621 83 The Electrical World, 1892, Vol. XIX., p. 195 * 4 The Electrical World, 1892, Vol. XX.. p. 227 85 The Electrician, 1892, Vol. XXVIII., p. 687, Vol. XXIX., P. 11 86 Wiedemann's Annalen, 1892, Vol. XLV., p. 33 87 The Electrician, Vol. XXIX., 1892, p. 460 88 Comptes Rendus, 1892, Vol. CXV., p. 1,273 39 Journal de Physique, 1893, Vol. II., p. 545 UPPENBORN, FEUSSNER. LECHER. UPPENBORN. LUGGIN. SCKREIHAGE. DTTBS. LUGGIN. FLEMING. f ELIHU THOM \ SON. BLONDEL. CRAVATH. CRAVATH. ' Electrical Engineer of New York, 1893, p. 90 ... TROTTER. ... STENGER. ... S.P.THOMPSON ... VIOLLE. ... VIOLLE. f DUNCAN, ...-! ROWLAND and ( TODD. 91 The Electrician, 1893, Vol. XXXIL, pp. 117, 145, 169 ... BLONDEL. 92 Comptes Rendus, 1894, Vol. CXIX., p. 949 VIOLLE. 9:j The Electrician, 1894, Vol. XXXIII., p. 297 TROTTER. 94 " Electric Lamps and Electric Lighting," p. 153 ... FLEMING. 95 Memoirs and Proc. of the Manchester Lit. and Phil. Soc., 1895, Vol. IX., Series IV., p. 139 FRITH. 9(i Wiedemann's Annalen, 1895, Vol. LV, p. 361 LEHMANN. 97 Proc. Roy. Soc., 1895, Vol. LVIIL, p. 174 WILSON. 1)8 BeiUdtter, 1895, Vol. XIX, p. 97 GRANQUIST, 99 The Electrical Review, 1895, Vol. XXXVII. , pp. 230.253,301 FREEDM AN. 100 The Electrical World, 1895, Vol. XXV., p. 277 MARKS. 101 The Electrical Engineer of New York, 1895, Vol. XIX., p. 198 MARKS. TJie Electrical World, 1896, Vol. XXVII., pp. 262, 378J 103 The Philosophical Magazine, 1896, p. 407 IM Wiedemann's Annalen, 1896, Vol. LVII., p. 185 105 Proceedings of the Royal Society, 1897, Vol. LX., p.377-1 WILSON, ( FITZGERALD. 106 The Electrician, 1897, Vol. XXXVIII., p. 642 107 Wiedemann's Annalen, 1897, Vol. LXIL, p. 435 * 08 L'Adairage tilcctrique, 1897, Vol. X., pp. 289, 496, 539 ' 9 The Electrician, 1897, Vol. XXXIX., p. 615 110 Ofversigt af Kongl. Vetenskaps-Akademiens Forhand- lingar, 1897. N : o 8, Stockholm, p. 451 111 The Electrician, 1898, Vol. XL., p. 363 f FRITH, RODGERS. ARONS. GUILLEAUME. HERZFELD. BLONDEL. BLONDEL. GRANQUIST. FLEMING. CHAPTER III. PHENOMENA CONNECTED WITH THE "STRIKING" OF THE ARC AND WITH SUDDEN VARIATIONS OF CURRENT. AT the Electrical Congress held in Chicago in August, 1893, Prof. Ayrton read a long Paper on the subject of the Electric A, which gave the results of experiments that he had been carrying out with his students during the three preceding years. Neither the Paper, nor any abstract of it, was published in the report of the Congress, for while it was in the hands of the secretary of Section B of the Congress, it was unfortunately burnt five months after it had been read. The experiments to which Prof. Ayrton specially directed his attention were briefly : 1. Obtaining the time variations, after striking the arc, of the P.D. between the carbons, with various constant currents, various constant lengths of arc, and with the ends of the carbons variously shaped. 2. Obtaining the time variation of the P.D. between the carbons when the current was suddenly changed, and the length of the arc was kept constant. 3. Obtaining curves connecting the steady final values of the P.D. between the carbons with the current, for different currents, lengths of arc, and sizes of carbons, cored and uncored. 4. The influence of varying the current and the length of the arc on the depth and width of the crater. 5. The distribution of potential throughout the arc. 6. The candle-power and efficiency of the arc. with various currents, P.Ds., and lengths of arc. 98 THE ELECTEIC ARC. The lamp used in these experiments (Fig. 28) was hand- regulated, the adjustments being effected by turning pinion P T JTL ^N^v^^W^x^^ FIG. 28." Hand-fed " Arc Lamp. to alter the height of the positive carbon, pinion P 2 to alter the height of the negative carbon, and pinion P 3 to raise P.D. AFTER "STRIKING" THE ARC. 99 both carbons together. By turning the nut Nj the positive carbon could be turned about a horizontal axis in the plane of the figure, and by turning the nut N 2 the positive carbon was moved round a horizontal axis at right angles to the plane of the figure. To measure the P.D. between the tips of the carbons, the voltmeter was attached to two thin carbon rods kk, sliding in tubes in a block of asbestos, A, and pushed against the main carbon rods C C by spiral springs S S. Had the P.D. been measured between the lamp terminals, a variable error would have been introduced, from the drop of pressure in the carbons themselves, which would have been serious with large currents and long carbons. Since the voltmeter had a resistance of about 80,000 ohms in circuit Box Light Tight. Red Glass for Examining Arc. ^Diagram , Screen.. -- FIG. 29. Plan of Arc Lamp, Lens, Mirror and Diagram Screen. with it, the resistance between the ends of these auxiliary voltmeter carbons kk and the main carbons CC introduced no practical error. The length of the arc was always taken to be the vertical distance between the point of the negative carbon and the hori- zontal plane drawn through the edge of the crater of the positive carbon. Length of arc "0 millimetres" does not, therefore, mean that the carbons were in contact, but that the point of the negative carbon was just entering the crater at the end of the positive carbon. This distance was measured on an image formed on the diagram screen, as shown in Fig. 29 by the lens L and the plane mirror M. This image of the arc was exactly ten times full size. H2 100 THE ELECTRIC AEC. When these experiments were first started, at the beginning of 1890, it was not known what were the conditions necessary for the P.D. between the carbons to remain constant when the current and length of arc were both kept constant, and con- sequently it was found, as had been found by all previous ex- perimenters, that a given current could be sent through an arc of given length by many different potential differences, and that no set of experiments made one day could be repeated the next. In the earlier experiments a reading was taken soon after the current had been brought to the desired value; hence the curves connecting P.D. with current for a constant length of arc were different for each set of experiments, and were always too steep. For example, with both positive and negative carbons cored, and both 13mm. in diameter, the early curves show that when the arc had a constant length of 5mm. the P.D. fell from 59 volts for a current of 4 amperes to 24 volts for a current of 30 amperes; that is, it was diminished by 35 volts. Whereas, in the later experiments, with a 13mm. cored positive carbon and an llmm. solid negative, the P.D. fell from GO'S to 4S'S volts, or only 11 '7 volts for the same change in current with the same length of arc. The first step in advance was made by keeping each new current flowing for a certain minimum time before taking the observations. This resulted in making the curves connecting P.D. with current for a given length of arc much flatter, and not quite so widely different with different sets of experi- ments; but it was still found that the curves for values of current ascending and those for values of current descending were different. Fig. 30 gives one of the sets of curves drawn during this series of experiments made in 1890, when it had been found that allowing a certain time to elapse before the reading was taken after the current had been altered made the readings for ascending and descending current more nearly equal, and also made the curve connecting P.D. with current for a given length of arc less steep. It was also found that, if the whole series of readings could be taken without the arc going out, better results were obtained ; therefore, during the five hours occupied by the experiments from which Fig. 30 was taken the arc was never extinguished. P.D. AFTER "STRIKING " THE ARC. 101 A large number of experiments were now carried out, each of which occupied the greater part of a day, as the current, which was made to slowly vary backwards and forwards between two limits, was never stopped, nor the arc allowed to go out, for many hours at a time. However, even with all these precautions, looped curves similar to those in Fig. 30 were obtained, and it is apparent from these curves that the P.D. needed to send a given current through the arc, which was kept at a constant length of 4mm., was never twice the same. For instance, a cur- rent of 10 amperes (Fig. 30) was sent through the arc by 40 10 15 20 Current in Amperes. FIG. 30. 18mm. cored carbons. Arc not allowed to go out during the b hours' run. Termination of experiment due to wasting of carbons. Arc at a constant length of 4mm. Current increasing, ?- Current decreasing, ^ Latter half of curve 6 is dotted owing to the length of arc being indeterminate. This was due to ine- quality in the carbons. P.Da. of 51, 49-5, 49, 48, 46-5, 46-2, and 46 volts respectively, so that for this one current the P.Ds. ranged from 46 to 51 volts. Hence, from these curves it would be impossible to find any exact relation between P.D. and current for a given length of arc. 102 THE ELECTRIC ARC. Consequently, when the work was taken up again, it was thought advisable to make a complete investigation of the variation of P.D. with the time that elapsed after the arc had been started or the current suddenly changed, the current and length of arc subsequently being kept constant during each experiment. The questions to which answers were sought were the follow- ing : (1) Does the P.D. ever become a constant for a given current and length of arc ? (2) If there is a final constant P.D. for each current and length of arc, is this P.D. the same, and is the time taken to reach it after starting the same, whether a cored or an uncored positive carbon is used ? (3) What are the causes of this variation of P.D. ? (4) How is the time before this P.D. is reached affected by the employment of (a) different lengths of arc, (b) different currents ? (5) How is this period of time affected by the current that was flowing through the arc before the change was made ? The experiments from which Figs. 31 to 35 were taken answered the first three questions. They showed that the P.D. does reach a final constant and steady value, that coring the positive carbon increases the period of time which elapses after starting the arc before the final value of the P.D. is reached, and they showed the causes to which the variation of the P.D. is due. These experiments were all made with positive carbons 18mm. and negative carbons 15mm. in diameter. The positive carbon was in some cases cored as is indicated in the figures, and in other cases solid, and the negative carbons were solid in all cases. Also the current used was 10 amperes, and the length of the arc was 3mm. for all the experiments except those which answered question (4). The first point on each of the curves was taken the moment the carbons had been separated to a distance of 3mm. after striking the arc. It is evident that question (1) is answered in the affirma- tive, for after a shorter or longer time the P.D. in all cases finally reached a constant steady value of from 44 to 46 volts,. when the positive carbon was cored, and from 47 to 50 volt& P. I). AFTER "STRIKING" THE ARC. 103 when it was solid (Figs. 31 to 35), the slight variation of P.D. finally arrived at with the same current and length of arc for the same kind of carbons being accounted for by the fact that every pair of carbons differs slightly from every other pair in hardness and structure. 65 50 45 40 35 25 20 10 20 30 Time in Minutes. 40 60 FIG. 31.- -Current suddenly started and maintained at 10 amperes. Length of arc maintained at 3mm. Carbons : Positive, 18mm. cored ; negative, 15mm. solid. The positive carbon was shaped as it came from the makers, thus, shown full size. The negative was shaped by being pre- viously used in a 3mm. arc with a current of 10 amperes. 104 THE ELECTRIC AEC. Fig. 31 shows the connection between P.D. and time after starting the arc, when the positive carbon is cored and shaped as it came from the maker, and the negative has previously been used with a current of 10 amperes and an arc of 3mm. till the P.D. has become constant. To save using this expression again and again, I shall call a carbon 'normal' when it has been burnt long enough, with a given current and an arc of given length, for the P.D. to have reached its steady value, and I shall call an arc * normal ' when it is burning with ' normal ' carbons. It will be observed in Fig. 31 that after the length of the arc had been adjusted at 3mm. the P.D. between the carbons fell to the low value of 16 volts. Hence a genuine arc 3mm. in length can be maintained silently, at any rate for a short time, with a P.D. of only 16 volts. It was thought probable that this very low P.D. might have been caused in some way by the soft core of the positive carbon, and experi- ments were, therefore, made with cored and uncored positive carbons under precisely similar conditions. The tips of the positive carbons were filed flat, and they were used with negatives that were 'normal' for 10 amperes and 3 millimetres. The results may be seen in Fig. 32, curves A A A and B B B. Curve A A A, which was obtained with a solid positive carbon, starts with a P.D. of 44 volts, while BBB, for which the positive carbon was cored, starts with one of 25 volts. The low P.D. at starting is, then, caused by the positive carbon being cored. But why should there be such a great difference, namely, 19 volts, in the P.Ds. at starting, when the difference between the steady values of the P.Ds. is only about four volts ? To settle this question an arc was started with a cored posi- tive carbon shaped as when it came from the makers, and a ' normal ' negative, and, after burning for less than one second, the current was suddenly turned off. On examining the car- bons it was found that the core had been torn out of the posi- tive carbon to the depth of one eighth of an inch, while the negative carbon was covered with the finely-powdered material. All this extra loose and easily volatilised carbon would, of course, much enlarge the cross-section of the arc, and thus lower its appa- rent resistance, and also the current probably flows with a much smaller P.D. when it is conveyed by means of small particles P.D. AFTER "STRIKING" THE ARC. 105 of carbon actually travelling across the arc than when it flows simply through volatilised carbon. For this reason, it is pro- bable that the fact that particles of unvolatilised carbon fall in showers from the positive carbon when there is hissing partly accounts for the fall of P.D. in the arc in that case. In curve C C C (Fig. 32) the crater of the positive carbon had already been formed mechanically, and therefore the P.D. started higher than in curve B B B, and remained higher for about 45 minutes; in fact, for half an hour it more nearly 30 40 50 Time in Minutes. FIG. 32. Current suddenly started and kept at 10 amperes. Length of arc kept at 3mm. Carbons : Positive, 18mm. solid or cored ; negative, 15mm. solid. Negative carbon in each case shaped by being previously used for a long time to form an arc 3mm. long, with a current of 10 amperes. A A A : Positive carbon solid, end filed flat. B B B : Positive carbon cored, end filed flat. C C C : Positive carbon cored, with a crater mechanically made at the end after it was filed flat. coincided with A A A, the curve for solid carbons, than with B B B, which is not to be wondered at, seeing that the part s>f the carbon from which the core had been mechanically 106 THE ELECTRIC ARC. extracted, was practically solid ; and thus, while it burnt away, there was very little loose soft carbon to be easily volatilised, and so lower the P.D. The time that the P.D. takes to reach its constant value when the positive carbon is flat to start with is very remark- able. From Fig. 32 we see that with a flat- tipped positive carbon of 18mm. diameter and a * normal ' negative carbon of 15mm. diameter, when a constant current of 10 amperes was flowing through an arc of 3mm., the P.D. did not acquire its constant value till 50 minutes after the arc ivas struck with a solid positive carbon, and an hour after with a cored positive carbon. How important a fact this is may be gathered from the consideration that the P.D. which would send a current of 10 amperes through an arc of 3mm. when the positive carbon was cored, might have been put down as being anything from 25 to 48 volts (curve B B B, Fig. 32), according to the time that had been allowed to elapse after striking the arc before the reading was taken. Of course such a wide range of P.D. for such a current would only be possible when the positive carbon was cored and had been flat before striking the arc, but curve A A A, Fig. 32, shows that even with a solid positive carbon the P.D. may range from about 44 to 52 volts. With small currents of 2 or 3- amperes I have found that with both carbons solid the P.D. may take as much as two and a half hours to acquire its constant value, even when the positive carbon has not been filed flat, but has been shaped beforehand by some such current as 5 or 6 amperes. It is possible that the extra low P.D. at starting in Fig. 31 may have been caused by the positive carbon with a pointed tip being easier to volatilise than the one with a flat tip. The reason that the P.D. took such a short time to reach its steady value only five minutes must have been that when the carbon from the crater had been volatilised it only came in contact with the hot tip, and was not cooled down by the mass of comparatively cold carbon surrounding the crater, as happened when the tip was flat. This mass of cold carbon is evidently the cause of the P.D.'s not retaining its constant value when it first reaches it, but rising to a higher value and then falling again, as it does in all the curves in Figs. P.D. AFTER "STRIKING" THE ARC. 107 31, 32, and 33. For, from the time of starting the arc, this mass of carbon was heated sufficiently for it to gradually burn away, therefore part of the heat of the crater was used in warming up this surrounding carbon until it was all burnt away, and the positive carbon had become normal. This took place between 50 minutes and an hour after the arc was started. The extra amount of heat needed during this time meant, of course, that a higher P.D. was required to send the same current through the arc ; for, since the rate of production of heat depends upon the current multiplied by the P.D., and the current was kept constant, the P.D. was bound to be higher. Hence the " hump," which will be found in every curve for which a flat positive carbon has been used. 26 30 40 50 Time in Minutes. FIG. 33. Current suddenly started and kept at 10 amperes. Length of arc kept at 3mm. Carbons : Positive, 18mm. solid ; negative, 15mm. solid. Negative carbon normal in each case. A A A : End of solid positive carbon filed flat. D D : Hole 2in. deep drilled in end of solid positive carbon. E E E : Hole lin. deep drilled in end of solid positive carbon and packed tightly with soft carbon, end filed flat. The curves in Fig. 33 are interesting as showing how completely and certainly the core of the positive carbon is responsible for a very low P,D. on starting the arc. 108 THE ELECTRIC ARC. With the curve E E E, in which the P.D. started at about 27 volts, the positive carbon was solid, but drilled to the depth of one inch, and packed moderately tightly with the carbon from a soft core. For the first three minutes, therefore, it behaved exactly as if it were cored in the usual way, and after that it acted like a completely solid carbon. It is a little curious that the effect of a whole inch of soft core should apparently have exhausted itself in three minutes, and that from that time onwards the curve obtained with the drilled and packed positive carbon should be almost identical with that obtained with an ordinary solid positive carbon (see curve A A A, Fig. 33). One would have expected the 'hump' to be lower with the drilled and packed positive, on account of the loose soft carbon. Probably, however, the carbon was not as tightly packed as in a manufactured core, and, therefore, most of it was shot out during the first three minutes after starting the arc, only enough of it being left to keep the posi- tive carbon from behaving as if it had merely a hole and no core at all. Curve D D, Fig. 33, shows what that behaviour would have been. The positive carbon in this case had a hole two inches deep drilled in it, and left hollow, and this kept the P.D. slightly higher throughout the whole variable period than when an ordinary solid positive carbon was used as in curve A A A, Fig. 33. In order to find what influence, if any, a flat negative carbon would have in retarding the period at which the P.D. became constant, cored and uncored normal positive carbons were used, with flat uncored negatives. In Fig. 34, A A is the curve obtained with the uncored, B B that obtained with the cored positive carbon. From these curves it is evident that the shape of the negative carbon plays a very small part in the change of P.D. that takes place on starting the arc, for in each case the P.D. reached its steady value in about 8 minutes, and in neither case did it deviate more than about 5 volts from that steady value, whereas, as has been shown, with a flat positive carbon, the P.D. took about 50 minutes to reach its steady value, and it deviated by from 7 to 33 volts from that steady value before reaching it. P.D. AFTER "STRIKING" THE ARC. 109- Fig. 35 gives a sort of bird's-eye view of the differences caused in the change of P.D. after starting the arc by using (1) A A A, both carbons solid and flat. (2) B BB, positive carbon cored and both flat. (3) B'B', positive carbon cored, both normal, arc started with cold carbons. (4) B", positive carbon cored, both normal, arc started with hot carbons. After three minutes from starting the arc the curve A A A (Fig. 35) differs very little from the curve A A A (Fig. 32), in which the negative carbon was normal instead of flat, and all the other conditions were the same. The reason there is so little appearance of 'hump ' is, I find on referring to the labora- tory note books, that certain somewhat high P.Ds. obtained P.D. betu'cen Carbons in Volt* s s s s ,-, ^W A ^ . B , B 10 20 30 40 Time in Minutes. FIG. 34. Current suddenly started and kept at 10 amperes. Length of arc kept at 3mm. A A, Carbons : Positive, 18mm. solid ; negative, 15mm. solid. B B, Carbons : Positive, 18mm. cored ; negative, 15mm. solid. Positive normal, negative filed flat, in both instances. between 10 and 35 minutes after the arc had been started have been omitted in drawing this curve, presumably because it was supposed that these observations were wrong. Had points corresponding with these somewhat higher P.Ds. been plotted, and the curve A A A (Fig. 35) drawn through the average position of all the points, it would have shown a hump such as exists in all the other curves obtained from experiments with a flat positive carbon. B B B (Fig. 35) also differs very slightly from B B B (Fig. 32) in which the negative was normal instead of flat ; in Fig. 35 the curve starts with rather a higher P.D., 27 instead of 110 THE ELECTEIC ARC. P.D. AFTER "STRIKING" THE ARC. Ill 25 volts, and rises a little more slowly. Thus in both this and the preceding case it is evident that the difference made by the shape of the negative carbon is very small. B' B' B' and B" (Fig. 35) show how small is the change that takes place in the P.Ds. when the arc is started with both carbons normal, whether they be hot or cold beforehand. Started cold the P.D. is about 1J volts higher than started hot, which is what one might have expected. The whole change of P.D., however, is very small, under both circumstances, not more than about 1 J volts altogether. Thus we may gather from Figs. 31 to 35 that the changes that take place in the P.D. of an arc just after it is started are due in order of importance : (1) To the core of the positive carbon, if it has one very low P.D. at starting. (2) To the shape of the tip of the positive carbon the ' hump.' (3) To the shape of the tip of the negative carbon. (4) Very slightly to the temperature of the carbons before starting the arc. Coming now to Question (4), to see how changing the length of the arc affected the time during which the P.D. remained variable after the arc was started, an 18mm. cored positive carbon and a 15mm. solid negative were again used, the ends of both carbons were filed flat, and the current was again kept constant at 10 amperes; but the length of the arc was kept constant at 6mm. instead of at 3mm. as before. It was found that in this case, as with the 3mm. arc, there was a very low P.D. at starting, a rise to a maximum, and then a slight fall, and finally the steady P.D. But the whole series of changes, which extended, as we have seen, over a period of 55 minutes with the 3mm. arc, took only 20 minutes with the 6mm. arc. Next, to see how varying the current affected the time during which the P.D. remained variable after the arc was started, an 18mm. cored positive carbon was again used with a 15mm. solid negative, the ends of both carbons were filed flat, the arc was kept at the constant length of 3mm. ; but a constant current of 20 amperes was maintained, instead of one of 10 amperes, as in all the previous experiments on the variation of the P.D. with the time after starting the arc. 112 THE ELECTRIC AEC. Again the curve obtained was found to be of the same character as curve BBB (Fig. 35), with which, also, both carbons were flat, and the positive cored ; only, with the cur- rent of 20 amperes the changes were more rapid than with that of 10 amperes, and the P.D. became constant 38 minutes after starting the arc, instead of 55 minutes after. We may gather from these last two experiments that the time during which the P.D. between the carbons remains variable after starting the arc with flat carbons is longer (a) The shorter the arc, (6) The smaller the current; and thus Question (4) is answered. The next question to determine was what change took place in the P.D. between the ends of the carbons when the current was suddenly changed from a lower to a higher and from a higher to a lower value, the length of arc being kept constant during each series of experiments. The experiments, the results of which are noted in the curves in Figs. 36 and 37, were made in order to answer this question. These curves, as well as all the others published in this chapter, are merely specimens of a number of sets of curves that have been obtained under similar conditions. Since, at the very first instant that a change of current is- made the arc cannot have had time to change its cross section, it would seem as if at that first moment the arc should act like a wire, and a rise of potential should accompany an increase of current, and a fall of potential a decrease. In 1893 I made som? experiments to see if I could detect this first momentary similarity of sign between the change of P.D. and change of current, and found that in some cases it could be easily detected, and in others not at all. Being pressed for time, T did not then continue the investigation; but when the dis- cussion about a negative resistance in the arc arose in 1896 (see p. 75), I repeated the experiments with Mr. Frith, for they seemed to have some bearing on the question. We then found that in all cases where the first momentary similarity of sign could be perceived, either one or both carbons were cored. The whole question of the instantaneous change of P.D. with change of current will be discussed later on, in the chapter on the resistance of the arc, &c. SUDDEN CHANGE OF CURRENT. 113 A (o < 10 d 1L CM a < en if ^^r^ 114 THE ELECTRIC ARC. The changes of P.D. in Figs. 36 and 37 are very striking. With wires one is accustomed to associate an increase of current 8 nA with a rise of potential and a diminution of current with a fall. But with the arc, except, perhaps, in the very first instant, SUDDEN CHANGE OF CURRENT. 115 exactly the reverse takes place, and no experiments that I know of are better calculated to impress upon one the immense difference between the way in which a current flows through the arc and the way in which it flows through a wire than those from which these curves were taken. With the arc (with the above exception), a sudden rise of current is in every case accompanied by a sudden fall of potential, and a sudden fall of current by a sudden rise of potential, even when, as in the case of an arc of 1mm. with a cored positive carbon (lower curves, Fig. 36), the final steady value of the P.D. is higher with the larger current than with the smaller. Indeed, in nearly every case the P.D. overshoots the mark, as it were, and goes much lower with an increase of current, and much higher with a diminution, than its own final steady value. This exaggeration of the decrease and increase of P.D., which is very marked when the currents are small, becomes less and less marked as the currents increase in value, until finally, with currents of 30 amperes and over, it ceases to exist with the carbons we have tried, and the P.D. remains practically constant, whether the current is changed suddenly or gradually. In fact, when we get on to the flat part of the curves con- necting P.D. with current for constant lengths of arc (Chap. IV., pp. 121 to 130) the P.D. is practically a constant, however quickly or slowly the current may be changed. The curves in Fig. 36, the upper of which is for a solid and the lower for a cored positive carbon, show that the excessive sudden rise and fall of P.D. with a sudden diminution and increase of current does not depend entirely upon the core, for it takes place in both sets of curves alike, although it is .more marked in the lower. The upper curves are a little deceptive, because the hissing, which took place in this particular experiment at 15 amperes, lowered the P.D. considerably, quite apart from the sudden change of current. Some experiments I have made since these, as well as the above curves, amply verify the following deductions. With a sudden change of current : (1) The sudden change of P.D. is greater with a cored than with a solid positive carbon; i2 116 TEE ELECTRIC ARC. (2) The subsequent slow rise, or fall, of P.D. is greater with a cored than with a solid positive carbon; (3) The time during which this slow change of P.D. takes place is greater with a cored than with a solid positive carbon. The curves in Fig. 37 show, although not to a very marked extent, that the time the P.D. takes to reach its steady value after a sudden change of current is less with a longer than with a shorter arc. Experiments made later prove this point quite conclusively. For instance, with an 18mm. cored positive carbon and a 15mm. solid negative, arcs of 6mm. and 1mm., respectively, were maintained. The current was, in each case, kept first at 4 amperes, and, when the P.D. had become steady for that current, it was suddenly changed to 9 amperes, and kept constant at that value till the P.D. had become steady. It was found that, after suddenly altering the current from 4 to 9 amperes, the time that elapsed before the P.D. assumed its steady value for 9 amperes was 9 minutes in the ease of the 6mm. arc, and 16 minutes in that of the 1 mm. arc. These sudden exaggerated changes of P.D. probably depend upon the difference between the shapes of the carbons and craters with small and large currents, an idea which i strengthened by the fact that with very large currents the shapes of the carbons alter very slightly with a change of current, and, as we have just seen, the P.D. also scarcely alters. It is probable that the action is as follows : It has been shown (Chap. I., p. 13) that with a large current both carbons are burnt away much farther down than with a small current, thus making the lengths of the pointed parts of the carbons shorter the smaller the current. Hence, when a small current has been flowing through the arc for some little time, the carbons are very blunt, and the larger amount of volatile carbon sent off by the larger current when it is suddenly switched on will be squeezed out laterally, thus making the cross section of the arc abnormally great, and its resistance exceptionally small; therefore, the P.D. necessary to keep the current flowing will be below the steady value. Then as the points of the carbons burn away and become tapered under the influence of the larger current, the volatile carbon can stretch out more lengthwise, and gradually take its normal SUMMARY. 117 form for the larger current, and at the same time the P.D. rises to its final steady value. Similarly, when a small current was turned on after a large current had been flowing for some time, the volatile carbon would at first be too much elongated owing to the ends of the carbons being much tapered, and as these burnt away and became blunter the volatile carbon would be squeezed out more laterally, the cross section of the arc would be increased, and the P.D. would fall to its final steady value. The exaggerated change of P.D. when the current is sud- denly altered depends in another way also on the tips of tb e carbons being blunter with small currents than with large ones. For the mean distance of the tips of the carbons from one another is less when they are blunt, i.e., normal for a small current, than when they are pointed, i.e., normal for a large one, even although the length of the arc is maintained the same in both cases (see definition of length of arc, p. 99). Hence the mean length of the arc must also be less in the first case than in the second. But if the mean length of the arc is less, the P.D. r ecessary to maintain a given current flowing through the arc will be less, all other conditions being the same. Therefore the P.D. necessary to maintain a large current flowing through an arc of given length will be less when the carbons are normal for a small current than when they are normal for a Large one, and vice versd. SUMMARY. I. After the arc has been maintained of a constant length and with a constant current flowing for a certain time, the P.D. between the carbons finally becomes constant also. II. The time that elapses before the P.D. becomes constant is less : (1) The more nearly the original shapes of the carbons approximate to the shapes they finally take when the P.D. becomes constant ; (2) The longer the given arc ; (3) The greater the value of the constant current 118 THE ELECTRIC ARC. III. The time that elapses before the P.D. assumes ite constant value is less and the P.D. is greater with solid than with cored carbons. IV. When the current is suddenly changed from a higher to a lower, or a lower to a higher value, the P.D. between the carbons increases or diminishes to a value greater or less respectively than its final constant value for the new current, and then gradually falls or rises to that constant value. V. This first excessive increase or diminution is greater the greater the difference between the original and final current. VI. For a given sudden change of current the first excessive increase or decrease of P.D. is greater the smaller the original current, while with large currents it is practically non-existent. VII. When a cored positive carbon is used the P.D. is some- times as low as 16 volts for a short time, with a perfectly silent arc. VIII. With a cored positive carbon the change of P.D. is sometimes observed to be in the same direction as the corres- ponding sudden change of current, for the first instant. This first increase of P.D. with an increase of current and decrease of P.D. with a diminution of current has never been observed with solid carbons. CHAPTER IV. CURVES CONNECTING THE P.D. BETWEEN THE CARBONS WITH THE CURRENT FLOWING FOR CONSTANT LENGTHS OF ARC, AND CURVES CONNECTING THE P.D. BETWEEN THE CARBONS WITH THE LENGTH OF THE ARC FOR CONSTANT CURRENTS. When Prof. Ayrton first directed his attention to obtaining a series of observations of the arc which would enable him to form curves connecting any two of the variables, while a third was kept constant, the three variables of which direct observa- tions were made were the P.D. between the carbons, the current flowing, and the length of the arc. From these the apparent resistance and the power consumed in the arc could also be found. Most of the experiments were made with cored positive and solid negative carbons ; but a single set of results was obtained with both carbons cored, and another with both carbons solid, in order to see what variations in the curves these changes produced. When beginning to study the arc on my own account, it appeared to me that it would be better to avoid the com- plications arising from the use of cored carbons, and to study the problems under their simplest conditions by employing none but solid carbons. Accordingly, my experiments were conducted with solid carbons for both positive and negative, the positive carbon being llmm. and the negative 9mm. in diameter in all cases. The make of carbon employed was the " Apostle," the same as had been used in all the investigations carried out under Prof. Ayrton's direction, so that the results obtained with solid carbons might be compared with those obtained when a cored positive carbon was used. As the relations existing between the variables of the arc 120 THE ELECTRIC ARC. 'stl<>A w ? CONSTANT LENGTHS OF AEC. 121 are undoubtedly simpler when both carbons are solid, it -will be best to examine the curves for solid carbons (Fig. 38) first. The values used in plotting the curves in Fig. 38 were the means of the results obtained on different days with different pairs of llmm. and 9mm. solid carbons, and, in order to indicate to what extent these means differed from the actual observations, a sample is appended, in Table XL, of the actual results that were obtained when the arc was 5mm. in length : Table XL Specimen of the Actual Daily Results obtained when the Arc ivas 5mm. long. Carbons both solid. Positive, llmm. ; negative, 9mm. Current in amps. Potential Difference between Carbons in Volts. I. II. III. IV. V. VI. VII. Mean of the 7 days' results. 1-96 2-45 2-95 3-45 3-96 4-46 4-97 5-47 5-97 6-47 6-97 7-97 9-0 10-07 11-07 12-07 14-06 16-04 18-03 '^0-0 22-0 26-0 84-4 77-1 73-1 67-7 66-3 64-8 62-8 61-3 58-9 57-9 57-4 56-0 84-9 84-65 75-1 71-65 67-7 65-9 64-45 62-64 61-4 59-77 59'4 58-5 57-4 56-4 56-0 55-0 54-8 54-0 52-5 53-5 53-0 43'0 43-0 ... ... 73-1 70-2 ... ... 65-5 64-5 63-0 62 : 8 61-7 60-7 59-9 69-2 53-0 57-0 56-4 ... 64-8 63-0 62-0 63-7 61-6 60-7 59-7 58-9 584 57-0 56-0 57 : 2 56-5 55-5 55-0 54-3 53-5 52-5 ... 55-2 54-4 ... ... ... ... 53-5 53-0 A3-0 ... ... 43-0 The numbers in italics refer to hissing arcs. The numbers in any one column in Table XL are the results of the experiments carried out in a single day with a 5mm. arc, and, although the carbons did not require to be changed each day, sometimes a new positive and sometimes a new negative carbon had to be inserted, so that, on the whole, 122 THE ELECTRIC AEC. about three different positive and three different negative carbons were used in obtaining the numbers given in the last column of this Table. Table XII. gives the means of the whole series of results from which the curves in Fig. 38 were plotted. Table XII. Means of the Experimental Results used in Plotting the Curves in Fig. 38. Carbons both solid. Positive^ llmm. ; negative, 9mm. Cur- rent in amps. 1=1. P.D. in volts. 1=2. P.D, in volts. Z=3. P.D. in volts. Z = 4. P.D. in volts. 1 = 5. P.D. in volts. 1=6. P.D. in volts. 1 = 7. P.D. in volts. 1-96 50-25 60-0 67-0 79-5 84-6 2-46 48-7 55-75 62-75 67-7 75-1 82-0 85 V 9 2.97 47-9 53-5 59-75 65-0 71-7 76-1 ,81-0 3-45 47-5 52-0 58-5 63-0 67-7 72-4 77-0 3'96 46-8 51-2 56-0 61-0 65-9 69-6 75-1 4-46 45-5 50-6 54-5 59-0 64-45 67-5 71-25 4-97 45-7 49-8 53-5 58-25 62-6 65-9 70-25 5-47 ... 52-75 57-25 61-4 64-6 68-2 5-97 45-0 49-0 52-0 56-25 59-75 63-1 67-3 6'47 ... . . c . . 59-4 62-4 66-55 6-97 44-0 48-1 51-4 55-1 58-5 61-4 65-65 7-47 61-1 64-65 7-97 43-6 47-4 50-6 54-3 57'4 60-5 64-2 8-48 .. . 63-25 9-0 43-5 50-2 53-5 56-3 59-5 626 10-07 42-8 46-b 49-8 53-0 56-0 58-8 61-5 11-07 ... 55-0 58-2 12-07 42-35 45-5 48-5 51-75 54-8 57-6 60-35 14-06 42-2 45-0 ... 50-6 54-0 56-8 59-5 16-05 ... ... 52-5 56-0 58-75 16-55 44-5 ... ... ... 16-85 si-o ... ... ... 17-54 ... S8'4 47-5 ... 17-64 ... ... ... 49-4 ... ... 18-03 ... SS'O ... 53-5 ... ... 18-53 ... 38 : 5 ... ... 19-0 ... ... SS'O ... ... ... 19-22 ... ... ... 50-0 ... t ... 19-42 ... 55-5 ... 200 S4'5 SS'O ... 53-0 20-5 ... ... ... 39-3 ... 55-5 ... 21-0 ,. ... 56-9 22-0 ... .. . 43-0 46-5 ... 23-0 48-0 25-0 ... 34 : 5 36-5 40-0 .. . 26-0 ... 43-0 47-0 29-97 ... ... 40-5 46'0 48'0 The numbers in italics refer to hissing arcs. CONSTANT LENGTHS OF ARC. 123 These curves connect the P.D. between the carbons with the current flowing for the various constant lengths of arc, with solid carbons. Each point on each curve represents the P.D. between the carbons after the current had been kept flowing at its specified value for a considerable time, and the length of the arc kept at its specified value during the whole of that time. The carbons had thus acquired their normal shape for the particular current and length of arc. The time required for this varies from about 10 minutes to over two hours under different circumstances. It was the want of appreciation of the very long time that it is necessary in certain cases to keep the current and length of arc constant before the carbons acquire their final shape, that led to so much labour being wasted in 1890, in obtaining the looped curves for ascending and descending currents, of which Fig. 30, Chap. III., is a specimen. The general character of the curves indicates an inverse connection between the P.D. and current for any given length of arc. That is to say, the P.D. diminishes as the current increases. It diminishes rapidly with small currents, and more and more slowly as the current increases, never, however, becoming constant with solid carbons. Take, for example, the 5mm. arc. With an increase of current of 4 amperes from 2 to 6 amperes the P.D. falls 23 volts from 83 to 60 volts ; with a further increase of 5 amperes from 6 to 1 1 amperes ' the P.D. falls only 5 volts, and with a still further increase of 9 amperes from 11 to 20 amperes it falls only 2'5 volts. Thus the P.D. never becomes constant, but it falls very slowly as the hissing point the point at which the current is so large that any increase would cause the arc to hiss is approached. The position of these hissing points, which evidently varies with the length of the arc, will be discussed in the chapter on hissing. The curves for the shorter arcs are much less steep than those for the longer ones ; but from their shape it is evident that this is only because the steeper parts of the curves for short arcs would belong to smaller currents than 2 amperes, the smallest used. In other words, the ratio cf change of P.D. to change of current is greatest, not only when the current is least, but also when the arc is longest. 124 THE ELECTE1C AEG. For instance, in the 5mm. arc (Fig. 38), when the current starts at 2 amperes, an increase of 4 amperes is accompanied by a fall of 23 volts in the P.D. between the carbons, but in the 1mm. arc, when the current starts at 2 amperes, a rise of 4 amperes is accompanied by a fall of only 6 volts. It would be necessary, indeed, for the current to start at 1 ampere, or even less, with an arc of 1mm., for a rise of 4 amperes to be accompanied with so great a fall of the steady P.D. as 23 volts. In their Paper read before the Physical Society in 1882 {Proc. Phys. Soc., Vol. V., p. 197) on "The Resistance of the Electric Arc," Messrs. Ayrton and Perry said, in speaking of the curve given in that Paper, which they had drawn from the results of their experiments connecting the P.D. between the carbons with the length of the arc with solid carbons for arcs up to 31mm. long: "The curve we have obtained is also strikingly like that obtained by Drs. W. De La Rue and Hugo Mliller for the connection between the electro- motive force and the distance across which it would send a spark. Those gentlemen also made experiments on the elec- tric arc with their large battery. 4 . . The result of an experiment in air between two brass points is given ; but, according to that, when the arc was half an inch in length the difference of potential between the brass points was about 700 volts. How far the very high electromotive force found by Drs. W. De La Rue and Hugo Miiller to be necessary in this case arose from a combination of the material employed for the electrodes and the smallness of the diameter of the brass elec- trodes, or whether the law that ' the electromotive force neces- sary to maintain an arc depends mainly on the length of the arc, and hardly at all on the strength of the current,' fails when the current is below a certain small limit, we are unable to say; but of course both the diameter of the brass electrodes they employed and the strength of the current that was passing (0'025 ampere) in the arc was very much less than that used in any ordinary electric light, to which the experiments of Mr. Schwendler and ourselves especially refer. It is very pro- bable that the difference in the material of the electrodes has mainly to do with the difference between their results and ours ; and we think it very probable that, with very sofb carbons, an arc of a given length could be maintained with a P.D. CURRENT AND LENGTH OF ARC. 125 much less difference of potentials than that found by us, since it would be more easy for a shower of carbon particles to be maintained between the ends of the carbons." Two results are here foreshadowed, which have both since been verified, the one that the P.D. for a given current and length of arc would be found to be smaller if the carbons were made softer, the other that the P.D. for a given length of arc would be far higher with very small currents than with those which are used practically with an arc lamp. The first result Table XIII. Means of the Experimental Results used in Plotting the Curves in Fig. 39. Positive carbon, 18mm., cored; negative carbon, 15mm., solid. Cur- rent in amps. 1=0-5 P.D. in volts. 1 = 1 P.D. in volts. 1 = 2 P.D. in volts. l=7> P.D. in volts. 1 = 4 P.D. in volts. 1 = 5 P.D. in volts. 1 = 6 P.D. in volts. 4-0 ... 37-0 ... ... 5-0 49-3 ... ... 6-0 33-0 36-0 47-0 50-5 53-0 54-75 59-5 7'8 34-5 ... ... 8-0 345 36-0 55-0 10-0 ... 43-0 46-5 47-5 49-75 11-0 361 ... ... 12-0 35 V ... ... ... 15-0 ... ... 42-0 44-5 46 V 5\ 46'OJ 48-0 49-5- 16-0 ... ... 44-0 ... ... 17-0 381 ... ... ... 18-0 38 V ... ... 20-0 38-75 42-0 44 V ... 48-0 22-0 ... ... 43 V 5 ... 23-0 39-75 ... .. . ... ... 24-0 39-0 ... ... ... ... 25-0 ... ... ... 44 V 2 46-0 48 V 0" 27-5 ... 40-0 ... 28-0 ... ... 43-0 ... 30-0 ... 40 V 41-5 43-0 44-2 45-5 48-a 33-0 40-1 ... ... ... 34-0 39-5 ... ... ... 35-0 ... IM ... 44-0 45-4 47-7 40-0 40 V 40-9 ... 43-9 45-75 47-5 41-0 ... ... 43-0 45-0 ... ... ... 46-0 47-5 47-0 ... ... 43-0 43-9 47-25 ... 43-2 ... 47-5 33-0 ... ... ... 48-0 ... 35-0 ... ... 48-75 ... 42-5 ... ... The numbers in italics refer to hissing arcs. 126 THE ELECTRIC ARC. was found to be true when cored carbons were subsequently manufactured, and the second is borne out by the strikingly rapid rise in the curves in Figs. 38, 39, 40 and 41, as the current becomes very small. In fact, for very small currents, whether one, or both, or neither of the carbons be cored, the P.D. falls rapidly with increase of current, probably on account of a small current arc presenting a large cooling surface in proportion to its cross- section. Tables XIIL, XIV. and XV. give the results of the experiments made by students of Professor Ayrton at the Central Technical College, London, with cored positive and solid negative carbons. Each number gives the mean of several observations. Table XIV. Experimental Results used in Plotting the Curves in Fig. JfO- Positive carbon, 13mm., cored ; negative carbon, llmm., solid. Cur- rent in amps. 1 = 0. P.D. in volts. 1=1. P.D. in volts. 1 = 2. P.D. in volts. 1 = 3. P.D. in volts. 2=4. P.D. in volts. 1=8. P.D. in volts. 1=8. P.D. in volts. 2-0 47-1 ... 71-2 2-5 56-0 63-0 2-8 42-0 fm 3-0 40-5 56-5 61-5 62-0 64-5 76-2 4-0 ... 39-5 ... 58-25 69-5 4-5 ... 49-0 ... 5-0 ... ... 56-5 {CC.fl \ ... 6-0 35-0 37-5 46-0 50-2 DO U \ 54-0 1 52-7 f 55-0 63-3 52-4 J 8-0 35-5 ... ... ... 9-9 ... 39-0 43-0 f47-5j \46-5/ ( 49-2^1 \ 49-7 \ [50-2 j 52-0 (607 159-2 12-0 37-0 ... ... s l=i. J=2 Z=3 l=t is, n ! Differ- fj* 1 d \ ence of \ Diam. * d Differ- ence of Diam. d* d Differ- ence of Diam. * d Differ- ence of Diam. 4 7 10 15 iiO 9-9! 3-14 1 + 0-04 15-6 3-95| -0-25 21-1 14-59 \ + 0-34 30-3 5-5 1+0-05 39-5 6-28-0-^ 11-7 17-4 22-9 32-1 41-3 3-42 4-17 4-78 5'67 6-43 -0-38 -0-03 + 0-03 + 0-07 + 0-03 12-6 18-3 23-8 33-0 42-2 3-55 4-28 4-88 5-74 6-49 + 0-08 + 0-39 + 0-09 13-2 18-9 24-4 33-6 42-8 3-63 4-35 4-94 5-80 6-54 + 0-08 - 0-05 + 0-04 - 0-06 Fourteen of the nineteen diameters taken from the curves differ from the observed diameters by less than O'lmm. Of the other five one differs by 0'12mm., one by 0'25mm. and the other three by between three and four tenths of a milli- metre. Hence there are four really bad points, two belonging to the 1mm. arc, one to the 2mm. and one to the 3mm., and all four belonging to different currents. It seems pretty certain then, that the curves in Fig. 54 do really represent the relation between the current and the square of the diameter of the crater for the different lengths of arc, and that we may safely use the values obtained from them to plot the curves con- necting the length of the are with the square of the diameter of the crater for constant currents. These curves are given in Fig. 51, and verify the first prediction made about the area of the crater in Chap. IV., namely, that it would increase as the length of the arc increased with a constant current. In order to calculate the crater ratios for each current and length of arc from Table XVII. it is necessary to know the diameter of the core of the positive carbon employed. This was 3mm., and therefore to obtain the ratio of the area of the core to the area of the crater that is, the soft crater ratio the number 9 must be divided by each of the squares of diameter given in Table XVII. The hard crater ratio, that is, the ratio of the area of hard carbon in the surface of the crater to the area of the crater, is obtained by subtracting the soft crater ratio from 1 in each case, for if s be the area of soft carbon and h the area AREA OF CEATEE. 155 of hard carbon in the surface of the crater, and if a be the area of the crater, then h a s + s = =1 - -. a a a 45 40 10AMP52. 30 Q25 & 20 15 10 12345 Length of Arc in Millimetres. FIG. 51. Square of Diameter of Crater and Length of Arc for various Constant Currents. Carbons : Positive. 13mm., cored ; negative, llmm., solid. 156 THE ELECTRIC ARC. Table XVIII. gives the soft and hard crater ratios with the corresponding currents, P.D.s, and lengths of arc. Table XVIII. Crater Ratios calculated from Table XVII., ivith corresponding Currents, P.Ds., and Lengths of Arc. Carbons: Positive, 13mm., cored; negative, llmm., solid. I to M M 1 Current in 1 ocnovpCpoa tHOLbcVjOOOD-OLO^J-rbK) COI>OvOvQLOLOLOLOLOLOLO OvOLOLOLOLOLOUOLOLOLO iHr-r-lCT>pK)l>r-pLp co a> >-H oa i> vo i> LO LO O5 LO O3 ct O KD LO K) sO iH l> * rH CO LO . 63 cb vb LO =r ^t rb rb rb CNI 63 : K5 LO * ^1 L> ^J- rH CJ o do o LO <;t =! rb K> K) 6a 6a LO3-5T 185 186 THE ELECTRIC ARC. current or of the length of the arc makes a large error in the P.D. when the current is small. There can be no doubt, then, that equation (3) accurately gives the law connecting P.D. current, and apparent length of arc for solid carbons of the size and hardness that I have used. The general form of this equation is (4) which may be written Now this is the equation to a rectangular hyperbola when I is constant, and the asymptotes are one the axis along which P.D. is measured, the other a line parallel to the axis along which current is measured. Hence the curves in Fig. 61 are a series of rectangular hyperbolas, having one asymptote in common, which is used as the axis of P.D., while their other asymptotes are lines parallel to the axis of current and at a distance from it depending upon the value of I. In fact, if d be the distance of the asymptote of any one of the curves from the axis of current, then or d = 38-88 + 2-074 Z, where I stands for the number of millimetres in the length of the arc, and the unit of length for d is the length that has been arbitrarily taken to represent a volt in drawing the curves in Fig. 61. These curves have not the appearance of rectangular hyper- bolas, but that arises from different units of length having been taken to represent a volt and an ampere. In Fig. 64 I have therefore redrawn the particular curve in Fig. 61 which corresponds with a constant length of arc of 5mm., and, since ' the same length has been taken to represent a volt and an ampere in Fig. 64, the identity of the curve in this figure with a rectangular hyperbola becomes evident. The asymptotes, the axis, and the focus of this rectangular hyperbola are also indicated. The law embodied in equation (4) connecting the P.D. between the carbons with the length of the arc and the current flowing has been proved to be true for the solid carbons I used P.D. CURRENT, AND LENGTH OF AUG. 18 Both Carbons Solid. 82 SO 78 76 74 72 70 3 ^ 68 I 6 ' 5 64 1 Cj a; 62 60 58 56 54 52 50 1 \ / / / ymptote. \ / / "< \ / / \ /F / \ / / \ / \ / / X . / / ^^ "^ ^ / / Asyrr ptote. 2 4 6 8 10 12 14 16 18 20 Current in Amperes. FIG. 64. Hyperbola showing connection between P.D. and Current for constant Length of Arc of 5mm., when Volts and Amperes are drawn to the same scale. O M, N are the two asymptotes, F the axis, and F the focus of the hyperbola. 188 THE ELECTEIG ARC. (it cannot be too carefully borne in mind that this law does not apply to cored carbons) ; but before it can be accepted as a universal law, it must be shown to apply to the results obtained by other experimenters with solid carbons. In their Paper published in the American Electrical Engineer for August 2, 1893, of which an abstract is given on p. 66, Messrs. Duncan, Rowland and Todd, after quoting not quite correctly the equations employed by various experimenters to connect the P. D. between the carbons with the current flowing and the length of the arc, said : " In fact, almost any results may be obtained by modifying the size and composition of the carbons." I shall show, however, from the results of the very experimenters whose equations they quoted that this is not the case, and that the form of the true equation connecting these variables is the same whatever the size of the carbons may be, and whatever their composition, as long as the carbons are solid. The values of the constants in the equation does, however, depend on the hardness of the carbons, and perhaps on their size. It will be found, also, that although in certain eases my equation does not support the conclusions arrived at by pre- vious experimenters, it is really more in accordance with the results of tkiir oivn experiments than were the conclusions they themselves deduced from them. If we take equation (2) W = 38-88 A+ 11-66 + (2-074 A + 10-54) I. A 10-54 . ., and put A = - _-- in it, wehave W= 38*88 x (- ~ 5 \ + 11 66, that is, we have a value for A, and a corresponding one for W, both of which are independent of the value of I, showing that all the lines connecting A and W for the various constant lengths of arc must pass through one point, the co-ordinates of which are 2-074 and W = 38-88 x f - L-| 4 ) + 11-66; or, A = - 5-08 and W=- 185-92. POWER LAWS. 189 00. 00 Similarly, by putting I = - - 9 the coefficient of A dis- appears in the same equation, and we find that all the lines connecting W and I for the various constant currents must pass through a point, the co-ordinates of which are 1= -187, W= -185-92. Hence the laws upon which equation (4) is founded, and upon which it depends absolutely, may be put in the following form : 1. When the current is constant, a straight-line law connects the power consumed in the arc with the length of the arc. 2. When the length of the arc is constant, a straight line law connects the power consumed in the arc with the current flowing. 3. The straight lines representing the connection between power and length of arc for constant currents all meet at a point. 4. The straight lines representing the connection between power and current for constant lengths of arc all meet at a point. The first of these four laws follows directly from Edlund's law, that, with a constant current, the apparent resistance of the arc is equal to a constant part plus a part that varies with the length of the arc. The other three have not hitherto been enunciated, but it will be seen that the whole four laws are true for the results of all the experiments made with solid carbons of which detailed information regarding the numbers has been published. Edlund gave only the ratios of the currents he used, so that it would not be possible to construct a complete equation, including all three variables from his results ; but the equation he discovered, r = a-t-bl for constant currents, is, as stated above, really another form of the first law I used, for if we multiply this equation throughout by the constant A 2 we obtain an equation of the form a linear equation connecting W and I for constant currents. 190 THE ELECTRIC ARC. The resistance form of my equation (3) is 38-88 + 2-074 Z , 11 6 :, . (5) A A 2 and making A constant in this, we get an equation of the form where and = 38-88 11-66 ~~ ~~ 2-074 ^10-54 T~ A 2 ' Now Edlund concluded from the results of his experiments that a and b both diminished as the current increased, and this is borne out by the above values for a and b' } but he also thought that a varied inversely as the current, which although not exactly correct, was nearly so for all but small currents, for unless A were very small in the above value for a, the term would be , ... 38-88 A ' 2 small compared with -. A Further, that the values which Edlund found for a A were not constant, as they would be if a varied inversely as A, but in every instance but one showed a decrease as the current increased, is very easily seen from the following table, which gives the results Edlund obtained from his experiments with arcs between carbon electrodes : Table XXII. Results obtained ly Edlund. Numbers proportional to A. Numbers proportional to a A. Series of experiments. 1-2387 1-0176 0-6661 0-3239 0-3416 0-3336 1 5> 1-1139 0-9435 6-69 6-877 2 0-9618 0-7738 6-34 6-48 6 5J 1-3270 0-9827 4-45 521 4 The experiments of one series must not be compared with those of another, for each was carried out under different EDLUND. 191 circumstances. But a comparison of those in each series will show that, except for one in the first series, the product a A increases as the current A diminishes, which is exactly what would follow from my value of a A, viz. : A Hence deviations which Edlund mistook for errors of observa" tion were evidently caused by the presence of the term -i -j t / / corresponding with - in the value of a A, and what A Edlund did not notice was that with one exception all his errors were in the same direction. Thus the conclusion to be drawn from my equation (4) with regard to a A, which Edlund called the back E.M.F. of the arc, is more in harmony with the results of his experiments than his own conclusion was. It is hardly necessary to enter into Edlund's theoretical reasons for supposing the term a A to be independent of the current, since his own results really proved that it was not so. To show the fallacy of his theory that, with a generator of constant E.M.F., the total power expended in the arc was proportional to the current, I need only point out that, if it were so, A V would be equal to k A, where k is a constant, or V would be a constant for all currents. In the experiments used by Frolich there was no sort of order. Only in two cases were more than two currents em- ployed with the same length of arc, and in no case was the same current used with more than two lengths of arc ; thus it is impossible to construct a complete equation from them. Fortu- nately, however, several currents were used with an arc of 2mm., and by calculating the power expended, from the numbers given for currents and P.Ds., it is possible to plot the curve connecting watts and amperes for length of arc 2mm., and this proves to be a straight line, as it should be according to the second law upon which my equation is founded. The equation to this straight line obtained from the experi- ments used by Frolich was from which we get the P.D. in volts, V. 40-25 A 192 THE ELECTRIC ARC. Table XXIII. shows the value of the P.D. for each current quoted by Frolich for the 2mm. arc, and the value calculated from the preceding equation. Table XXIII. Results used by Frolich. Current in amperes. P.D. from experiment. P.D. from equation. 27-4 42-7 42-75 11-6 46-3 46-13 8-39 50-1 48-38 7-67 47-1 4915 6-92 501 5011 The general agreement of the values for V obtained by experiment and calculation is striking, considering that different pairs of carbons were used by different people in obtaining the experimental results, and this agreement renders it quite certain that V and A are connected by an equation of the form I have given. Frolich's statement, therefore, that the P.D. between the carbons was independent of the current, and that the true equation was V = m + n I, where m and n were constant for all currents, is indeed astonishing, and still more so is the fact of his having given values for m and n viz., 39 and 1'8, and having asserted that the equation was true for all currents up to 100 amperes. For, to take only the numbers given in Table XXIIL, which are for length of arc 2mm., his formula would give V = 42 -6 volts for all the currents, whereas 42-7 volts is the smallest P.D. for the largest current, and the P.D. for the smallest current is 50 volts, or 7J volts greater than the P.D. as calculated by Frolich. Such discrepancies as these, however, he dismissed as errors of observation, and he, like Edlund, did not notice that all or nearly all these apparent errors of observation were in the same direction. Since Frolich's equation did not really express the results of the experiments upon which he founded it, it is unnecessary PEUKERT. 195 to dwell upon the other equations which he deduced from it, and which were equally at variance with the experimental results. Indeed, the only suggestion made by Frolich in his Paper that appears likely to prove true was that the cross- section of the arc was directly proportional to the current. The first systematic attempt to find the P.Ds. that would send a given constant current through many lengths of arc was made by Peukert, who first, after Edlund, saw the value of eliminating one of the three variables, P.D., current and length of arc in his experiments. Having measured the P.Ds. corresponding with various currents and lengths of arc, Peukert plotted curves connecting apparent resistance and length of arc, and found them to be straight lines. He gave the equations to these lines, and from them I have constructed the following equations connecting power and length of arc for each of the currents he used, by multiplying each equation through by the square of the current which corresponded with it : For A = 10 amperes, W = 366 + 23 I. A=15 W = 517 + 33-75J. A = 20 W = 720 + 32/. A = 25 W-812-3 + 46-87J. These, when plotted, give the four straight lines seen in Fig. 65, and thus it is evident that Peukert's results follow the first of the four laws enunciated on p. 189. It is clear that the line for 20 amperes is wrong for it does not make a large enough angle with the axis of I, hence the coefficient of J, which determines the slope of the line, must be too small in the power equation for 20 amperes. That that is the case is seen from an examination of these four power equations, for while the coefficients of I with 10, 15 and 25 amperes increase as the current increases, that with 20 amperes viz., 32 is less than 3375, the coefficient with 15 amperes. If from the four lines connecting power and length of arc for each current we take the number of watts corresponding with length of arc 10mm., and plot them as ordinates with their respective currents as abscissae, we shall obtain a curve representing the connection between the power absorbed in the arc and the current flowing when the length of the arc is kept 194 THE ELECTEIC ARC. constant at 10mm. Similar lines may be obtained in the same way for all the other lengths of arc down to Omm. These lines, From Peukert's Experiments. 1600 1500 1400 1300 1200 1100 1000 900 700 600 500 400 4 6 8 10 12 Length of Arc in Millimetres. 16 Fia. r 65. Power and Length of Arc for Different Constant Currents. PEUKEET. 195 of which those for 10mm. and Omm. are given in Fig. 66, are all straight Lines showing that Peukert's results follow the second law given on p. 189, namely that with a conatant length of arc the connection between the power absorbed in the arc and the current flowing follows a straight line law. The equations to these lines are W 10 = 46-22 A + 129-42, W = 30A + 66. Substituting these values for W 10 and W in W-W _W 10 -W / 10 which is the equation to any one of the lines in Fig. 65 con- necting power with length of arc for a constant cm-rent, we find the equation W = 30 A + 66 + (1-622 A + 6-342) I, representing the connection between power, length of arc and current, when all three may vary. Dividing throughout by A, we have A which is the general equation representing the connection be- tween the P.D. between the carbons, the current flowing and the length of the arc with the solid carbons used by Peukert. In order to test how nearly the equation given above really expresses Peukert's results, we may divide by A, and obtain the equation for the apparent resistance of the arc : 30 + 1-622? 66 + 6-3421 A ~^2 If we now give A the values respectively of 10, 15, 20 and 25 amperes in this resistance equation, we find the equations on the right-hand side of Table XXIV. : Table XXIV. From Peukert's Results. Current in amperes. Peukert's equations. From the above general equation. 10 15 20 25 r = 3-66 + 0-23 1 r = 2-3 +0-151 r=l-Q + Q-G81 r = l-3 + 0-075 1 ? = 3-66 + 0-23 1 r =2-29 + 0-14 1 r = 1-67 + 0-096 1 r = 1-31 + 0-075 1 o2 196 THE ELECTRIC ARC. \ \ Q> ' o a x UJ CO t o \\ \ PEUKEET. 197 Comparing the two sets of equations, we find a striking agreement in the case of the first, second and fourth equations, while the third, which differs from that given by Peukert, expresses the result which Peukert would have obtained if he had not, as already explained, made an error when testing with 20 amperes. Thus it is apparent that the results of Peukert's experiments lead to an equation of exactly the same form as my equation (4), differing from it only in its constants, hence his results must not only follow the two first laws upon which equation (4) was founded, but they must also follow the last two. That this is so is easily seen, for, if we put A = - in the power equation for Peukert's J. 'bLilj results, the coefficient of I disappears, and we have W-68-80xgg. Hence A= -3-91 and W=-51-3 are the co-ordinates of a point where all the lines connecting power and current for the various constant lengths of arc must meet. 30 Similarly putting I = - , the coefficient of A disappears, and we get 1= -18-5 and W=-51-3 as the co-ordinates of a point at which all the lines connecting power and length of arc for the various constant currents must meet. Thus the results of Peukert's experiments completely fulfil all the four laws upon which my equation (4) is founded and are, therefore, completely in harmony with my results. It is easy to show that where the conclusions he drew differ from mine, his own experiments prove him to have been mistaken. The resistance form of the general equation deduced above from Peukert's results may be put in the form r = a + b I, 30 66 where a = + A A 2 , 1-622 6-342 and 6=_+_. 198 THE ELECTRIC ARC. The second term in the value for a is never very big compared with the first term, with the currents Peukert used, for the numerator of the second term is only about twice as great as the numerator of the first, whereas the denominator of the second is at least ten times as great as the denominator of the first, since the smallest current Peukert used was one of 10 amperes. Hence it is not very surprising that Peukert followed Edlund in considering that the variations in the value of a caused by the presence of this term were due to errors of observation, and in asserting that a varied inversely as the current. Yet his own results show that this is not the case, for if it were, a A would be a constant, whereas multiplying the first term in each of Peukert's own equations by the corresponding current, the resulting numbers are 36-6, 34-5, 36, and 32*5, which, except in the case of the equation for 20 amperes, which I have already shown to be wrong, go in descending order as the current increases, as my equation indicates that they should. He saw, however, that b diminished more rapidly than the current, and this he was able to do because, on examining the expression I have given above for 6, we see that the coefficient of the second term is four times as great as that of the first term. Hence even with fairly large currents the second term is not negligible compared with the first, and consequently Peukert was able to find an approximate law for the value of 6, for which the last equation gives the full and exact law. From the experimental observations published by Messrs. Cross and Shepard I have plotted curves connecting the apparent resistance and length of the silent arc for each current they used, and have found an equation to each of these lines which fits their results rather more closely than those which they themselves gave. From these slightly more accurate equations I constructed the following equations con- necting power and length of arc, by multiplying each equation by the square of the corresponding current, For A = 5-04 amperes, W = 201-31 + 3-34 I A = 7-0 W = 273-01+3-6Z A = 7-92 W = 310-01+ 6-24 1 A = 10-04 W = 380-01 + 8-94 I CROSS AND SHEPAED. 199 These, when plotted, give the straight lines in Fig. 67, showing that Cross and Shepard's results follow the first law on p. 189. As with Peukert's curves, one line the line for 7 amperes has the wrong slope, as may also be seen from the power equations. For evidently the coefficient of I for 7 amperes is too near in value to the coefficient for 5 -04 amperes, and not near enough to that for 7 '9 2 amperes. From Cross & Shepard's Experiments. 500 400 200 ^ 12 14 2 4 6 8 10 Length of Are in Thirty-seconds of an Inch. FIG. 67. Power and Length of Arc for Different Constant Currents. Taking the number of watts corresponding with length of arc 10 from each of the four lines in Fig. 67, and plotting them 200 THE ELECTRIC ARC. with their respective currents, we obtain the upper line in Fig. 68, and plotting the watts for length of arc with their corresponding currents, we get the lower line. That these are straight lines is very evident, although one point of each is off the line, and it is thus evident that Cross and Shepard's results, as well as Peukert's, follow the second of the four laws on p. 189. From Cross & Shepard's Experiments. 500 400 300 200 100 89 0123466 Current in Amperes. Fia. 68. Power and Current for Arcs of 10 thirty-seconds of an inch and thirty-seconds of an inch. The equations to the two lines in Fig. 68 are W 10 = 48A + 93-6, W = 37A + 14'8. Substituting these values for W 10 and W in the equation W-W _W 10 -W 10 11 I 10 which is the equation to any one of the lines in Fig. 67, we have as the general equation connecting the power, current and length of arc, when any of the three may vary, with the carbons used by Cross and Shepard. Dividing by A we have CEOSS AND SHEPARD. 201 as the general equation connecting P.O., length of arc and current for the Cross and Shepard results. If now we divide this last equation throughout by A we get 37 14* /l-l 7j88\ A A 2 \T" 1*7 for the resistance equation, and giving A the values of the currents used in the experiments, we get the equations on the right-hand side of the following table : Table XXV. From Cross and Shepard's Results. Current in amperes. From experiments. From general equation. 5-04 7-0 7-92 10-04 r = 7-925 + 0-525 1 r = 5'57 + 0-277 1 r = 4-94 + 0-259 1 r = 3'77 + 0188 1 r =7-923 + 0-528 1 r = 5'59 + 0-317 1 r=4'91 + 0-264 1 r = 3'83 + 0-187Z The two sets of equations agree very nearly as well as those obtained from Peukert's results, although the range of current was so much smaller, and the exact course of the lines was, therefore, much more difficult to obtain. This closeness of agreement shows that my general equation gives the con- nection between the three variables in the case of Cross and Shepard's experiments, as it does with Peukert's. The co-ordinates of the point at which the lines in Fig. 67 meet may be found in the same way as similar co-ordinates have been found previously. They are and /= -33-64 W= -250-12, Similarly, the co-ordinates of the point at which the lines in Fig. 68 meet are and A= -7-16 W= -250-12. Thus, Messrs. Cross and Shepard's results follow the four laws upon which my equation is founded. Besides calculating the values of the constants a and b in the resistance equation r = a + bl, Messrs. Cross and Shepard gave 202 THE ELECTEIG AEC. the value of the product a A for each of the currents used. As already mentioned, Edlund, Frolich and Peukert had con- sidered that this product was on the whole a constant, and this constancy Edlund regarded as proving the existence of a constant back E.M.F. in the arc. Messrs. Cross and Shepard, however, showed that the product diminished as the current increased ; they did not give the actual law of variation, which, in my remarks on Peukert's equations, I have pointed out is A constant a A = constant + - ; A but to them is due the credit of first noticing that as A increased a A diminished, and also of pointing out that Peukert's equations, when correctly interpreted, led to the same conclusion. The formula given by Prof. Silvanus Thompson in 1892, V = m + n , A where m might vary from 35 to 39 volts, and n might have values from 8 to 18, was the first real attempt to find one equation connecting the P.D., current and length of the arc when all three varied. Multiplying his equation throughout by A, we have the equation for the power which gives straight lines for power and length of arc with con- stant currents, and straight lines for power and current with constant lengths of arc, following the two first laws on p. 189 ; but as he did not know the law of variation of the coefficients m and n, nor what their variation depended upon, his equation was necessarily incomplete. At the meeting of the British Association at Ipswich in 1895, Prof. Thompson stated that his equation was founded on experiments made by different students at different times, with different carbons, and with different currents produced by different generators, and that the variations of m and n in it appeared to depend upon some of these differences, but he could not quite tell which. DUNCAN, ROWLAND AND TODD. 203 The Paper by Messrs. Duncan, Rowland and Todd, from which I have already quoted, begins with a list of the equations used by other experimenters, among them attributed to Edlund, and attributed to Cross and Shepard. What Edlund, and also Cross and Shepard, really proved, however, was that for any particular value of the current the equation connecting the apparent resistance of the arc with the length was r a + bl, where a and b were constants for the particular current. But \vhen the current was increased they showed that a and b both diminished ; therefore, while it is perfectly correct to add together C&J A x and b l AJ l } , in order to find Vj, the P.D. between the carbons for a length ^ and for a current A 15 for which the values of a and b are a^ and b v it is entirely wrong to attribute to Edlund, or to Cross and Shepard, as Messrs. Duncan, Rowland and Todd have done, the general equation where a and b appear to be constant for all values of A and of I It seems to be desirable to draw attention to this correc- tion, because the versions of Edlund's and of Cross and Shepard's equations given by Messrs. Duncan, Rowland and Todd have been subsequently quoted as correct by others, who have, I presume, not referred to the original publications. Messrs. Duncan, Rowland and Todd gave the values of the P.D. and current obtained experimentally for one length of arc Jin. long obtained with cored carbons. On calculating from these the values of the power, I find that the curve connecting power and current is very nearly a straight line, and therefore very nearly fulfils my second law. I have before mentioned that for cored carbons the curve connecting power and current was only almost a straight line. 204 THE ELECTRIC ARC. The equation to the straight line obtained from Duncan Rowland and Todd's experiments is therefore for the P.D. we have In Table XXVI. is given a comparison of the values of the P.D. obtained experimentally by Messrs. Duncan, Rowland and Todd, and the values calculated from the preceding equation. Table XXVI. From Duncan, Roivland and Todd's Results. P.D. in volts. From experiment. From the equation. 3-1 65'0 67-8 4-6 58-5 58-9 615 54-8 54-3 7-7 52-5 51-5 8-0 52-0 611 9-82 49-2 49-2 11-26 47-5 48-1 12-75 46-5 47-2 It is, of course, impossible to tell from the table given whether the first law connecting power and length of arc for constant currents is borne out by Duncan, Rowland and Todd's results, for they only gave the results for one length of arc. In any case, however, it was amply proved by the experiments of Prof. Ayrton's students with cored carbons, that the curve representing the connection between power and length of arc for constant current is not a straight line for cored carbons. Messrs. Duncan, Rowland and Todd gave as the equation connecting V, I and A, but, as the form of the functions was not stated, it is, of course, impossible to make a comparison between that equation and the one at which I have arrived. To sum up, then, it appears that wherever experimenters using solid carbons have given the actual results of their SUMMARY. 205 experiments in numbers, the law of those numbers can be expressed with remarkable accuracy by an equation of the same form as mine A and differing from it only in the values of the constants a, b, c and d. Hence, so far from the different experimenters on the arc having all obtained different laws, as has hitherto been supposed, their results present a striking unanimity when viewed by the light of the wider generalisations in which they have now been presented. SUMMARY. I. With solid carbons, when the current is constant, a straight line law connects the power consumed in the arc with its length, and the several lines showing this connection for ' given carbons, all meet at a point. II. With solid carbons, when the length of the arc is constant, a straight line law connects the power consumed in the arc with the current, and the lines showing this connection for given carbons also meet at a point. III. The equation representing the connection between the P.D. between the carbons, the current, and the length of the arc, with solid carbons, is where a, b, c, and d are constants depending only upon the carbons employed. IV. This is the equation to a series of rectangular hyper- bolas having the axis of P.D. for one asymptote, and a line parallel to the axis of current at a distance from it depending on the length of the arc only, for the other. V. The results of experiments made by Edlund, Frolich, Peukert, and Cross and Shepard all give equations of the same form as the above. CHAPTER VII. THE P.D. BETWEEN THE POSITIVE CARBON AND THE ARC. THE FALL OF POTENTIAL THROUGH THE ARC VAPOUR. THE P.D. BETWEEN THE ARC AND THE NEGATIVE CARBON. THE DISTURB- ANCE CAUSED IN THE ARC BY THE INSERTION IN IT OF A THIRD IDLE CARBON. It has long been known that the principal fall of potential in the arc takes place between the positive carbon and the arc. CV years ago, Lecher found that if he placed a third carbon of l'5mm. in an arc 2'5mm. in length, midway between the carbons, the P.D. between the positive carbon and this rod was about 35 volts, while the P.D. between the rod and the negative carbon was about 10 volts. At about the same time Uppenborn found only about 5 volts P.D. between the arc and the negative carbon. He tried rods of copper or platinum wire, embedded in clay, in steatite, and in glass tubes, for exploring, but had finally to abandon them all, in favour of bare carbon rods. With these he found that the fall of potential at the positive carbon varied between 32'5 and 38 volts in arcs of from 6mm. to 16mm. For some experiments made for Prof. Ayrton's Chicago Paper in 1893, by Mr. Mather, Mr, Brousson and myself, a bare carbon rod was placed close to each main carbon in succession, and thus the P.Ds,, between the positive carbon and the arc and between the arc and the negative carbon, were found, for several currents and lengths of arc. The results may be summed up as follows : (1) The curve connecting the fall of potential at the positive carbon with the current for constant lengths of arc was very much of the same shape as the similar curve for the total P.D. across the carbons. (2) The fall of potential at the negative carbon diminished as the current increased, with a constant length of arc. 208 THE ELECTRIC ARC. (3) It could not be determined whether the fall of potential at either of the carbons depended on the length of the arc or not. These results were the first ever obtained showing any definite connection between the current and the falls of poten- tial at each of the carbons, with a constant length of arc and a varying current. With the object of obtaining still more definite information as to the laws connecting the value of the current and the length of the arc with the falls of potential at the two carbons, I have made a series of experiments on arcs varying between 1mm. and 7mm, in length, and using currents varying princi- pally between 4 and 14 amperes, though a few experiments were made with larger currents with silent arcs, and some with hissing arcs. The carbons used for the whole series were, as usual, Apostle carbons, llmm. in diameter for the positive and 9mm. for the negative. With the greater part of the experiments both carbons were solid, but in order to see what was the effect of the core on the P.Ds. in question, two series of experiments were made with the positive carbon cored and negative solid, and two with both cored, For the first series in each case the current was kept constant at 10 amperes, and the length of the arc varied from 1mm to 7mm., and for the second, the length of the arc was kept constant at 5mm., and the current was varied between the limits of 4 and 24 amperes. The exploring carbons used were mostly about 1mm. in dia- meter, a few were thinner, and a few were as thick as 2mm. It was found that with the 1mm. arc the most constant results were obtained with the thinnest exploring carbons, while with the longer arcs it was better to use carbons of from 1mm. to l'5mm. in diameter; otherwise, on account of the larger amount of oxygen with which their hot parts came into contact, they burnt away so fast as to make it difficult to obtain any results. The arrangement was as follows : The exploring carbon was fixed in a metal holder, in which it could be tilted either up or down but could not be moved sideways. The holder itself was moved by means of two racks and pinions, one of which raised and lowered it, and the other moved it horizon- tally in the direction of the length of the carbon. The base of ARRANGEMENT OF EXPLORING CARBON. 209 the holder was firmly screwed to the table to which the lamp was fixed, in such a position that the vertical plane which bisected the exploring carbon longitudinally also bisected the arc carbons longitudinally, and was parallel to the magnifying lens. Thus the image of this carbon was thrown on to the same screen as that of the arc, in such a way that its dimen- sions and its distances from the arc carbons and from the arc itself were all magnified, like the arc, ten times. Hence the distance between the point of the exploring carbon and any point in the arc or on either of the other carbons could be 'deter- mined by simply measuring the distance between the two corres- ponding points on the image, and dividing by ten. The object of tilting the carbon was to enable it to be pushed right up into the crater or to touch the extreme tip of the negative carbon. FIG. 69. Diagrammatic Representation of Arrangement of Main Carbons Exploring Carbon and Voltmeter. Fig. 69 shows diagrammatically the arrangement of the three carbons and the voltmeter. V was the voltmeter, a high resistance d'Arsonval galvanometer with 1,500,000 ohms in circuit, a, 6, c, d and e were mercury cups, E was the exploring carbon and P and N the positive and negative carbons of the arc respectively, e was permanently connected with E, a and b with the positive and negative carbons, and c and d with the positive and negative poles of the voltmeter, respectively. Now when a and c were connected by means of one wire bridge and e and d by means of another, the voltmeter 210 THE ELECTRIC ARC. measured the P.D. between P and E, that is, when E was very close to P, the fall of potential at the positive carbon. When, on the other hand, 6 and d were connected, and also c and e, the voltmeter then measured the P.D. between N and E, or, when E was very close to N, it measured the fall of potential at the negative carbon. The following was the method of experimenting : When the arc was normal with a given current and length (see definition of a normal arc, p. 104), the idle carbon, properly tilted, was brought into it with its point in the centre, midway between the two carbons. In a few seconds this third carbon grew beautifully pointed and its tip became white hot. It was then raised or lowered till the tip touched the crater of the positive, or the white hot spot on the negative the " white spot," as I shall call it according to the P.D. it was desired to measure. The slow motion of the voltmeter needle, as the idle carbon was moved through the arc, was very different from the rush it made when the two carbons touched ; hence, the last reading before they touched was very easy to observe, after a little experience, and this was obviously the reading that gave most nearly the true fall of potential at the main carbon. The employment of a bare carbon for such measurements has its disadvantages, but these are much less when used as described above than when the rod is merely held in a stationary position in the arc, as has always hitherto been done. Indeed, the results of two complete series of experiments, conducted on the old stationary method, had to be abandoned, because they were so vague that no conclusions could possibly be drawn from them. But by making the rod actually touch the hottest part of the main carbon, the fall of potential at a perfectly definite point was always measured, and this led to very accurate and constant readings. One great difficulty in this mode of measurement is caused by the third carbon repelling the arc when it approaches it. This repulsion is greater the longer the arc and the smaller the current, so that with long arcs and small currents it is difficult to get the idle carbon into the arc at all. The arc slips away from the carbon exactly as if the one were an air ball suspended by its two ends and the other were trying to penetrate it. Under EFFECTS DUE TO TRIED CARBON. 211 certain circumstances, not yet very well defined, the carbon appears to attract the arc when once it has been made to dip well into it. This subject of the repulsion and attraction of the arc by the third carbon would well repay further investigation. The third carbon disturbs the arc in other ways as well as by repelling it. If left in long enough near either carbon, it grows by receiving carbon from it, especially when left close to the positive pole. It also cools the arc at first, and it alwavs disturbs the distribution of potential in it. The first difficulty is overcome by allowing the third carbon to remain for only a short time close to either carbon ; the second by keeping it for a little while in the centre of the arc before bringing it up to the main carbon to take a reading. The third has to be allowed for in our interpretation of the results of the experiments. It has been mentioned that the third carbon always becomes beautifully pointed when placed in the arc. This is the case when its diameter is small compared with those of the main carbons, but I found that when a flat rod was inserted so as to screen the hot parts of the two carbons from one another, two arcs formed one between the positive carbon and the rod, and one between the rod and the negative carbon ; and in that case the rod became cratered on the side opposite to the nega- tive carbon and a small rough excresence formed on the side opposite to the positive carbon. It was not possible to detect the presence of the two arcs from the image, which showed, apparently, only one big arc, but the voltmeter indicated it at once, for, as soon as the second arc was formed, the voltmeter deflection became nearly doubled. In order to eliminate any error that deficiences in the hardness and texture of the carbons might introduce, even though they were all of the same make, none were employed except those of which the total P.D. across the carbons with the normal arc used was within a half a volt of that given by equation (3) (p. 184), for the same length of arc and current. Lecher, using a bare carbon rod as I have done, but keeping it stationary in the arc instead of making it touch the main carbon, found the positive carbon P.D. to be about 35 volts. Uppenborn, by the same means, found that it varied between 32 -5 and 38 volts for arcs of from 6mm. to 16mm., while Luggin r2 212 THE ELECTRIC ABC. obtained 3370'46 volts for the value with a current of 15-5 amperes, and could observe no change when he changed the length of the arc. All these results agree very well with one another, as far as they go ; but, in order to find out what effect changes in the current and the length of the arc had on the P.Ds., it was necessary to make a complete series of experiments, using many different currents and lengths of arc, and finding the value of the P. D. between each carbon and the arc separately with each current and length of arc. Such a series of experiments I have made, and, as a check upon the results, I also observed the P.D. between each carbon and the arc plus the P.D., through the arc vapour itself, so that, subtracting these P.Ds. from the total P.D. across the main carbons, I might get indirect measurements of the P.D. between each carbon and the arc, as well as the direct measurements. Thus four sets of cases were observed : (1) The P.D, between the positive carbon and the third carbon, just before the point of the latter touched the crater. (2) The P.D. between the third carbon and the negative carbon, just before the point of the former touched the white spot. (3) The P.D. between the positive carbon and the third carbon, just before the point of the latter touched the white spot. (4) The P.D. between the third carbon and the negative carbon, just before the point of the former touched the crater. The first and second P.Ds. we may call, for convenience sake, the positive and negative carbon P.Ds., respectively ; the third and fourth are those same P.Ds. with the P.D. through the arc vapour itself added. This last P.D. we may call the vapour P.D. The whole four cases are represented diagrammatically in Fig. 70 (1) shows how the positive carbon P.D. was measured, (2) the negative carbon P.D., (3) the positive carbon P.D. plus the vapour P.D., (4) the vapour P.D. plus the negative carbon P.D. In the first two cases the P.D. rushed down to zero when the carbons touched one another, in the last two it rushed up till it reached the value of the total P.D. across the main carbona. In each case the motion of the voltmeter needle, CAEBON AND VAPOUR P.Ds. 213 when the exploring carbon touched the main carbon, was very much quicker than it had been before they touched, so that the last deflection, before they touched could be read with a fair amount of ease. Each experiment was repeated at least six times, and if the readings of any particular P.D. differed much from one another, twelve or even more measurements of it were made. Tables XXVIL, XXVIIL, XXIX. and XXX. contain the means of the results of the four series of experi- ments with solid carbons and silent arcs. (2) FIG. 70. Diagrammatic Representation of Arrangement of Main Carbons and Exploring Carbon. (1) Positive Carbon P.D., (2) Negative Carbon P.D., (3) Positive Carbon P.D. + Vapour P.D., (4) Vapour P.D. + Nega- tive Carbon P.D. Table XXVIL gives the positive carbon P.D., as nearly as it can be measured, by means of a bare carbon placed in the arc. All such measurements are subject to the possibility that the idle carbon may not take up the potential of the part of the arc in which it is placed, that is, there may be a contact P.D. between this solid carbon and the vaporous stuff of which the arc consists. But, even if it exists, this P.D. is probably very small compared with those under consideration, and need not, therefore, be taken into account. 214 THE ELECTRIC ARC. Table XXVII. P.D. between Positive Carbon and Third Carbon with Point of Latter close to Crater of Former. All carbons solid. Positive, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. Current iii P.D. in Volts. Amperes. 1 = 1. 1=2. J=3. J=4. 1=5. 1 = 6. 1 = 1. 4 34-3 370 38-6 38-5 36-7 39-7 39-0 5 33-6 330 342 34-5 355 36-9 37-7 6 34-95 35-2 31-0 33-9 35-55 36-6 36-1 7 33-25 33-8 33-3 331 350 361 36-9 8 32-7 32-75 32-6 33-3 349 33-8 35-2 9 33-3 33-9 34-85 35-1 35-4 36-1 34-5 10 32-6 32-4 31-5 33-75 33-5 32-7 34-7 12 31-9 32-8 32-2 32-7 33-8 33-4 34-4 14 31-4 31-8 32-5 31-8 34-8 36-2 16 ... ... 32-5 32-7 33-1 33-0 20 - ... ... ... 34-2 33-6 Table XXVIL shows that the positive carbon P.D. is not a constant, but that, like the total P.D. between the main carbons of the arc, it diminishes as the current increases, and increases as the length of the arc -increases. But the degree of diminu- tion and of increase is very different in the two cases, for while the total P.D. between the carbons ranges from 42 '3 volts for a 1mm. 12 ampere arc to 74'4 volts for a 7mm. 4 ampere arc (Fig. 38, p. 120), the positive carbon P.D. given in Table XXVIL varies only from 31-9 volts to 39 volts for the same range of current and length of arc. That is, the total P.D. between the carbons has a range of about 32 volts, while the positive carbon P.D. has a range of only about 7 volts for the same variation of length and current. Hence, at any rate, when measured with a bare carbon rod (and no better means of measurement has yet been devised), the fall of potential at the positive carbon is not a constant, but varies both with the length of the arc and the current, in the same way, but to afar less extent than the total P.D. between the carbons. This will be seen even more clearly from the curves in Figs. 71 and 72, which were plotted from the numbers in Table XXVII. In Fig. 71 the curves show the connection between the positive carbon P.D. and the current, for constant lengths of arc, and in Fig. 72 the connection between the same P.D. and the length of the arc, for various POSITIVE CARBON P.D. 215 constant currents. Had these lines all been drawn from the same zero of P.D., they would have been so close together that it would have been difficult to distinguish one line from another. The zero of P.D. has, therefore, been raised 5 volts for each line, as the numbers on either side of the figures show. Thus the lines are all drawn to the same scale, but each has a different point for its zero of P.D. 4 8 10 1* 14 Current in Amperes. FIG. 71. Positive Carbon P.D. and Current for Various Constant Lengths of Arc. Solid Carbons : Positive, llmm. ; negative, 9mm. ; third carbon, O'Snitn. to 2mm. The curves in Fig. 71 are evidently not unlike those in Fig. 38 (p. 120), for the total P.D. across the main carbons with constant lengths of arc, but they are flatter. That is, as was seen from the Table, for a given range of current the range of the P.D. across the main carbons is much greater than the range of the P.D. between the positive carbon and 216 THE ELECTRIC ARC. the arc. Similarly, comparing the continuous lines in Fig. 72 with those in Fig. 44 (p. 136), we find that both are straight lines converging towards one another on the left hand side, but 012345 Length of Arc in Millimetres. FIG. 72. Positive Carbon P.D. and Length of Arc for Various Constant Currents. Solid carbons : Positive, llmm. ; negative, 9mm. ; third carbon, 5mm. to 2mm. that the lines in Fig. 44 are much the steeper, showing that the range of P.D. for any given range of length of arc is considerably greater, with the same constant current, for the NEGATIVE CARBON P.D. 217 total P.D. across the carbons than for the positive carbon P.D. Had the lines in Fig. 72 all been drawn to the same zero, it would be found that they, as well as those in Fig. 44, all met at a point to the left of the axis of P.D., showing that there is no real length of arc for which the positive carbon P.D. is the same for all currents. The meaning of the dotted lines in Fig, 72 is explained later, p. 223. Turning now to the negative carbon P.D., this has been stated by some observers to change its direction when the arc hissed, i.e., instead of the arc near the negative carbon being at a higher potential than the negative carbon itself, these observers thought that with hissing arcs the negative carbon was at a higher potential than the parts of the arc nearest to it. I have never found this to be the case, either with silent or hissing arcs ; whether cored or solid carbons were used. The fall of potential at the positive pole is always from carbon to arc, and at the negative pole from arc to carbon, so that the potential falls continuously from the positive carbon through the arc to the negative carbon. Other observers have denied the existence of a fall of potential between the arc and the negative carbon, but these experiments conclusively prove that they are wrong, and shows that with the carbons I used this fall of potential cannot be less than 7'6 volts. Table XXVIII. P.D. between Third Carbon and Negative Car- bon with Point of Former close to White Hot Spot on Latter. All carbons solid. Positive, llmm. ; negative, 9mm.; third carbon, 0'5mm. to 2mm. Current P.D. in Volts. Amperes. 1 = 1. \ 1=2. 1=3. Z=4. 1 = 5. 1 = 6. Z=7. 4 12-9 11-5 12-9 12-2 10-4 10-6 10-3 5 iO-1 10-1 11-2 104 I 10-8 10-7 9-9 6 8'6 10-3 9-6 9-4 9-7 9-2 9-3 7 8-8 9-8 9-6 9-4 9-4 9-5 9-6 8 8-2 8-8 10-9 9-3 10-0 9-3 8-9 9 7-8 8-8 8-9 91 9-6 9-0 9-0 10 8-5 8-5 9-0 8-9 i 9-2 9-2 9-2 12 8-5 8-4 9'2 9-3 ! 9-6 8-8 8-7 14 9-7 9-2 9-3 9-2 9-0 8-9 16 ... 9-3 9-2 91 9-1 20 ... ... ... ... ... 9-6 9-2 218 THE ELECTRIC AEG. Table XXVIII. gives the values of the negative carbon P.D. for the same currents and lengths of arc as those for which the P.Ds. between the positive carbon and the arc were given in Table XXVII. It is quite plain, from these numbers, that the negative carbon P.D. diminishes as the current increases, following, in this respect, the same law as the total P.D. across the carbons, 024 6 8 10 12 Current in Amperes. FIG. 73. Negative Carbon P.D. and Current for Various Constant Lengths of Arc. Solid Carbons : Positive, llmm. ; negative, 9mm, ; third carbon, O'Smm. to 2mm. and the positive carbon P.D. But how it is affected by a change in the length of the arc it is impossible to see without reference to the curves plotted from the numbers. These are given in Figs. 73 and 74, in which, like those in Figs. 71 and 72, each curve is drawn from a separate zero of P.D. in order to prevent overcrowding. NEGATIVE CARBON P.D. 219> In Fig. 73 the curves connect negative carbon P.D. with current for constant lengths of arc. They are like the similar curves in Figs. 71 and 38, but are much flatter than either, showing that, for a given length of arc, the negative carbon P.D. varies considerably less than The total P.D. across the carbons, or even than the positive carbon P.D., for the same variation of current. 01 23456 Length of Arc in Millimetres. FIG. 74. Negative Carbon P.D. and Length of Arc for Various Constant Currents. Solid Carbons : Positive, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. The lines in Fig. 74, which connect the negative carbon P.D. with the length of the arc for constant currents, show 220 THE ELECTEIC ARC. that that P.D. is not affected at all by a change in the length of the arc, for, except the line for 4 amperes, they are all practically horizontal straight lines. Thus, when measured by means of a bare carbon rod, the P.D. between the arc and the negative carbon varies with the current, but not with the length of the arc. With the help of Figs. 75, 76, and 77, it will be easy to construct equations similar to equation (3) (p. 184), for connecting each of the carbon P.Ds. with the current and the length of the arc. The lines in these figures are all power lines, and the power is measured in each case by multiplying 500 1 2 3 4 5 6 7 Length of Arc in Millimetres. FIG. 75. Positive Carbon Power and Length of Arc for Various Constant Currents. Solid Carbons : Positive, llmm. ; negative, 9mm. ; third carbon, O'Srnin. to 2mm. the carbon P.D. by the current. For convenience sake we shall call the positive carbon P.D., multiplied by the current, the positive carbon power, and the negative carbon P.D., multiplied by the current, the negative carbon power. Fig, 75 shows the connection between the positive carbon power and the length of the arc for constant currents. The lines are all straight, as are the similar ones for the total power consumed in the arc (Fig. 62, p. 180), but whereas the POSITIVE CARBON POWER. 221 total power lines converge towards one another, the positive carbon power lines are all parallel. Similarly, the lines in Fig. 76, which show the connection between the positive carbon power and the current for constant lengths of arc, are also parallel straight lines, while 02 4 6 8 10 Current in Amperes > 76. Positive Carbon Power and Current for Various Constant Lengths of Arc. Solid Carbons : Positive, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. 222 THE ELECTEIG AEC. the similar lines for the total power consumed in the arc, although straight, are not parallel, but all meet at a point (Fig. 63, p. 182). To find the equation connecting the positive carbon P.D. with the current and the length of the arc, we have the equation to any one of the lines in Fig. 75 W-W 1 _W y -W 1 l-l ~~ 7-1 ' where W is the positive carbon power in watts for length of arc I mm., Wi is the positive carbon power in watts for length of arc 1mm., \V 7 is the positive carbon power in watts for length of arc 7mm. From the lines in Fig. 76, which show the connection between the positive carbon power and the current for constant lengths of arc, we can find Wj and W*, W l - 137-2 _ 3874 -137-2 12-4 ' 7 = 31-28A+30-7. Hence, in the equation connecting W and I, we have W-31-28A-12-1 = 31 -28A + 30-7 -(31-28A+ 12-1) l-l 6 18-6 '~ir = 3-1 .'. W = 31-2SA + 12-l+31/-3-l, or W = 31 28A + 9 + 3-1Z. Dividing all through by A, we have > (6) for the equation connecting the positive carbon P.D. with the current and the length of the arc. This equation, like the similar one for the total P.D. across the carbons (p. 184), is the equation to a series of rectangular POSITIVE CARBON P.Ds. 223 hyperbolas, but, whereas with the total P.D. the hyperbolas have only one asymptote in common, with the positive carbon P.D. they have both asymptotes in common; one, the axis of P.D., and the other, a line parallel to the axis of current, at a distance from it equal to 31-28 times the distance taken to represent one volt. Table XXIX. gives the positive carbon P.Ds. calculated from equation (6) for all the currents and lengths of arc for which values were obtained by experiment. Table XXIX. Positive Carbon P.Ds. calculated from Equa- tion (6). Solid carbons. Positive, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. Current in P.D. in Volts. Amperes. 1 = 1. 1 = 2. Z=3. Z=4. 1=5. 1 = 6. 1 = 1. 4 34-3 35-1 35-9 36-6 37-4 38-2 39-0 5 33-7 Z4-3 34-9 35-6 36-2 36-8 37-4 6 33-3 33-8 34-3 34-85 35-4 35-9 36-4 7 33-0 33-45 33-9 34-3 34-8 35-2 35-7 8 32-8 33-2 33-6 34-0 34-3 34-7 35-1 9 32-6 33-0 33-3 33-7 34-0 34-35 34-7 10 32-5 32-8 33-1 33-4 33-7 34-0 34-35 12 32-3 32-55 32-8 33-1 33-3 336 33-8 14 32-4 32-6 32-8 33-0 33-25 33-5 16 32-6 32-8 33-0 33-2 20 ... ... 32-7 32-8 A comparison of the two Tables XXVII. and XXIX. shows that of the 68 calculated P.Ds., 47 differ from the observed P.Ds. by one volt or less, 18 more by less than two volts, and only three differ by more than two volts. Considering the many possibilities of error in the observation of these P.Ds., the equation must be allowed to fit the experi- mental results with great accuracy. To show exactly what is the degree of accuracy, the dotted lines in Fig. 72 have been drawn. These lines are the ones obtained from equation (6), while the complete lines are drawn as nearly as possible through the average positions of the observed points. To obtain the equation connecting the negative carbon P.D. with the current and the length of the arc, the equation to the 224 THE ELECTRIC AEC. line in Fig. 77 only is required. The points for this line were found by taking the average negative carbon P.D. for each current from Table XXVIIL, and multiplying it by the current. 2CO 0. 1 S JL 1 g ^ >*--' , o \ > " 5 12 14 k > 2 4 6 8 10 Current in Amperes. FIG. 77. Negative Carbon Power and Current for All Lengths of Arc. Solid Carbons : Positive llmm. ; negative 9mm. ; third carbon, 0'5mm. to 2mm. This was done because it was found from the curves (p. 219) that with a given current the negative carbon P.D. was the same for all lengths of arc. The equation to the line in Fig. 77 is W-44_12Q-44 A-4 = 10 = 7-6. Hence W = 7'6A + 13-6. And, dividing all through by A, we have T -* <> for the equation connecting the negative carbon P.D. with the current and the length of the arc. This is the equation to a single rectangular hyperbola of which the asymptotes are the axis of P.D., and a line parallel to the axis of current, at a distance from it 7*6 times the distance which represents one volt. Table XXX. gives the negative carbon P.Ds. calculated from equation (7) for all the currents for which such P.Ds. were obtained by experiment. Comparing these values with those in Table XXVIII., it will be found that, of the 68 observed values, 42 differ from the calculated values by half a volt and under, 16 more by less than one volt, and 9 by between one and two volts. Thus equation (7) may fairly be taken to represent the connection between the negative carbon P.D., the current, and the length of the arc. NEGATIVE CARBON P.Ds. 225 Table XXX. Negative Carbon P.Ds. calculated from Equa- tion (7). Solid carbons. Positive, llmm. ; negative, 9mm. ; third carbon, O'Smm. to 2mm. Current in Amperes. P.D. in Volts. Current in Amperes. P.D. in Volts. 4 5 6 7 8 9 11-0 10-3 9-9 9'5 9-3 91 10 12 14 16 20 9-0 87 8-6 8-45 8-3 From equations (6) and (7) we can find the equation for the positive carbon P.D. plus the negative carbon P.D. ; i.e., the whole fall of potential from carbon to carbon minus the fall of potential through the arc itself. It is V- 38-88 + (8) Now equation (3) for the total P.D. between the main carbons, which includes, of course, the drop of P.D. in the arc itself, is V- 38-88 + 2-07 (3) The coincidence between the first terms of equations (8) and (3) shows that this constant quantity belongs, not to the positive carbon alone, as has hitherto been supposed, but to both the positive and negative carbons in the proportion of about four-fifths to the former and one-fifth to the latter. Hence, if, as many investigators imagine, this constant term involves the existence of a constant back E.M.F. in the arc, this back E.M.F. must be considered to reside, not at the positive carbon alone, as has hitherto been taken for granted, but at both carbons ; and this fact will necessitate a considerable modification in any theory of the arc yet enunciated that involves the existence of a constant back E.M.F. Table XXXI. gives the sum of the observed values of the two carbon P.Ds., taken from Tables XXVII. and XXVIII. Table XXXII. shows the corresponding values calculated from 226 THE ELECTRIC ARC. equation (8). From a comparison of these two tables it will be seen that, of the 62 calculated values, 39 differ from the observed values by one volt and under, 18 by two volts and under, and 5 by more than two volts. Although the calculated values for the sum of the two carbon P.Ds. appear to agree less perfectly with the observed values than those for each carbon separately, yet it will be found that the curves in Fig. 78, which have been taken from equation (8), go almost exactly 8 10 12 14 Current in Atnperes. FIG. 78. Positive Carbon P.D. plus Negative Carbon P.D., and Current. for Various Constant Lengths of Arc. Solid Carbons : Positive, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. through the average position of the observed points, which are the ones given in the figure ; showing, of course, that equation (8) does really represent very accurately the connection between the sum of the two carbon P.Ds., the current, and the length of the arc. SUM OF CABBON P.Ds. 227 Table XXXI. Sum of the observed Values of the Two Carbon P.Ds. taken from Tables XXVII. and XXVIII. Solid carbons. Positive, llmm. ; negative, 9mm. ; third car- bon, 0'5nim. to 2mm. P.D. in Volts. Current in Amperes. 1=1. 4 47-2 5 i 43-7 6 43-55 7 42-05 8 40-9 9 41-1 10 41-1 12 40-4 14 ... 16 20 ... 1=2. Z=3. Z=4. 1 = 5. 1 = 6. 1-7. 48-5 51-5 50-7 47-1 50-3 49-3 43-1 45-4 44-9 46-3 47-6 47-6 45-5 40-6 43-3 45-25 45-8 45-4 43-6 42-9 42-5 44-4 45-6 46-5 41-55 43-5 42-6 44-9 43-1 ! 44-1 42-7 43-75 44-2 45-0 45-1 ! 43-5 40-9 40-5 42-65 i 42-7 41-9 | 43-9 41-2 41-4 42-0 43-4 42-2 ' 43-1 41-1 41-0 41-8 41-0 43-8 45-1 ... 41-8 41-9 42-2 42-1 ... 43-8 42-8 Table XXXII. Values of the Sum of the Tivo Carbon P.Ds. cal- culated from Equation (8). Solid carbons. Positive, llmm. ; negative, 9mm,. ; third car- bon, 0'5mm. to 2mm. Current in Amperes. P.D. in Volts. 4 5 6 7 8 9 10 12 14 16 20 1=1. 1=2. J=3. Z=4. 1=5. 1 = 6. 1 = 7. 45-3 46-1 46-85 47-6 48-4 49-2 49-95 44-0 44-6 45-3 45-9 46-5 47-1 47-7 43-2 43-7 44-2 44-7 45-2 45-75 46-3 42-55 43-0 43-4 43-9 44-3 44.8 45-2 42-1 42-5 42-9 43-3 43-6 44-0 44-4 41-7 42-1 42-4 42-8 43-1 43-5 43-8 41-45 41-8 42-1 42-4 42-7 43-0 43-3 41-0 41-3 41-5 41-8 42-05 42-3 42-6 ... 40-9 41-15 41-4 41-6 41-8 42-0 ... 411 41-3 41-5 41-7 ... ... ... ... 40-9 411 So far it has been taken for granted that the P.D. measured by the voltmeter, between the main carbon and the bare idle carbon dipping into the arc, was the actual fall of potential between the main carbon and the arc. That this is not absolutely the case is quite certain, for the bare carbon must bring all the parts of the arc that it touches to practi- cally the same potential. And this potential will be greater Q2 228 THE ELECTE1G AEG. than the least and less than the greatest of the potentials that existed in the arc before the insertion of the exploring carbon. Thus it is quite possible that the variable part of the fall of potential at each of the carbons, given by equations (7) and (8), may be mainly produced by the exploring carbon being in communication with the arc, not only at its tip, but also along a part of its length. For, whether the fall of potential at the carbon itself be a constant or not, it is quite certain that the potentials of the other points at which the arc touches the exploring carbon vary both with the current that was flowing and with the length of the arc, before that carbon was inserted. Hence, at least a portion of the variation in the values given by equations (6) and (7) must have been created by the use of a bare carbon in the arc. It is possible to show, however, at least indirectly, that the part of the variation of P.D. that depends upon the current alone, while it is increased by the use of a bare carbon rod dip- ping into the arc, is still a genuine variation of the carbon P.Ds. In other words, the term in equation (7) and ~- in equation A. A (7) show genuine changes with change of current in the posi- tive carbon P.D. and the negative carbon P.D. respectively. In order to prove this, it will be necessary to find the equation connecting the current and the length of the arc with the total P.D. across the carbons when the third carbon is in the arc. It has been mentioned that the insertion in the arc of a third carbon caused the P.D. between the main carbons to be increased by from 0'5 to 3 volts. This increase is usually rather greater with the third carbon near the positive pole than near the negative. Tables XXXIII. and XXXIV. give the actual values of this P.D., the first with the exploring carbon near the positive, and the second with it near the negative pole. Equation (8), which gives the sum of the two carbon P.Ds., was formed from equations (6) and (7), for one of which the third carbon was near the positive pole, and for the other near the negative. In order, therefore, to be able to compare equation (8) with the new equation for the total P.D. across P. I). WITH THIRD CAliBON IN AEG. 229 Table XXXIII. P.D. between Main Carious with point of Third Carbon in Arc dose to Crater of Positive Carbon. Solid carbons. Positive, llmm. ; negative, 9mm. ; third car- bon, 0-5mm. to 2mm. Current in Amperes. P.D. in Volts. l-l. 1 = 2. 2=3. Z=4. 1=5. 2 = 6. 1 = 1. 4 48-3 51-5 571 62-6 66-4 70-3 5 45-8 51-3 55-5 60-7 63-8 67-3 70-7 6 45-5 50-6 55-9 58-5 61-5 64-5 69-2 7 45-0 50-5 53-5 57-4 60-7 63-9 67-4 8 44-0 492 52-4 55-7 59-6 61-6 64-9 9 43-4 47-9 52-0 54-4 57-4 60-6 , 64-2 10 43-1 47-5 511 54-4 58-8 60-7 63-2 12 42-6 46-7 50-5 53'0 57-5 58-9 63-5 14 ... 46-0 50-6 51-8 55-3 58-7 61-9 16 .... ... ... 51-3 551 57-2 60-6 20 ... 57-2 59-2 Table XXXIV. P.D. between Main Carbons with point of Third Carbon in Arc dose to White Not Spot on Negative Carbon. Solid carbons. Positive, llmm. ; negative, 9mm. ; third carbon, O'Smm. to 2mm. Current P.D. in Volts. Amperes. 1=1, 1=2. 2=3. 2 = 4. | 2 = 5. 2 = 6. 1=1. ._ l I 4 49-5 52-2 57-2 63-9 68-3 70-5 5 46-0 51-5 55-3 60-5 64-5 68-3 70-5 6 45-5 50-7 55-0 588 61-8 65-5 701 7 45-0 50-5 53-9 57-3 61-2 655 690 8 44-0 48-7 52-2 55-7 60-0 61-6 64-9 9 434 49-2 51-3 54-5 57-6 61-2 65-2 10 43-5 47'3 51-2 54-7 58-8 607 63'8 12 42-6 46-7 50-7 53-5 581 59-3 631 14 46-0 51-5 53-5 56-6 591 60-6 16 511 55-4 57-3 60-0 20 ... ... ... 58-0 59-3 the carbons with the third carbon in the arc, it will be necessary that this new equation shall connect the current and the length of the arc with the mean of the total P.Ds. observed when the third carbon is placed near the positive and negative carbons respectively. That is, the mean of each P.D. in Table XXXIII. 230 THE ELECTEIC AEG. and the corresponding P.D. in Table XXXIV. must be taken to- obtain the new equation. These mean P.Ds. with their respective currents and lengths of arc are given in Table XXXV. Table XXXV. Mean Total P.D. between Main Carbons with Third Carbon in Arc near Positive and Negative Carbons- respectively. Solid carbons. Positive, llmm. ; negative, 9mm. ; third car- bon, 0'5mm. to 2mm. P.D. in Volts. Current in Amperes. 1 = 1. 1 = 2. = 3. Z=4. 1=5. 1=6. 1=1. 4 48-9 51-85 57-15 63-25 67-35 70-4 5 45-9 51-4 55-4 60-6 64-15 67-8 70-6 6 45-5 50-65 55-45 58-65 61-65 65-0 69-65 7 45-0 50-5 53-7 57-35 60-95 64-7 68-2 8 44-0 48-95 52-3 55-7 59-8 61-6 64-9 9 43-4 48-55 51-65 54-45 57-5 60-9 64-7 10 43-3 47-4 51-15 54-55 58-8 60-7 63-5 12 42-6 46-7 50-6 53-25 57-8 59-1 63-3 14 46-0 51-05 52-65 55-95 58-9 61-25 16 51-2 55-25 57-25 60-3 20 ... ... ... ... 57-6 59-25 By multiplying each of the P.Ds. in Table XXXV. by the corresponding current, we obtain the total power in watts expended between the carbons when the third carbon is in the arc. The laws connecting this power with the current for constant length of arc and with the length of the arc for constant current are both straight line laws, just as they are when there is no third carbon in the arc (p. 189). By com- bining these two laws in the same way as when there was no third carbon we get = 38-56 (9) as the equation representing the connection between P.D., current, and length of arc, with a third carbon in the arc. Of the 67 P.Ds. calculated from this equation, 59 differ from the observed values by one volt and under, and the remaining 8 by less than 1-7 volts. These calculated P.Ds. are given in Table XXXVI. P D. WITH TRIED CARBON IN AEG. 231 Table XXXVI. Mean P.Ds. between the Main Carbons with Third Carbon in the Arc, calculated from Equation (9). Solid carbons. Positive, llmm. ; negative, 9mm. ; third cnrbon, 0'5mm. to 2mm. Current in P.D.. in Volts. Amperes. 1 = 1. 1=2. 1 = 3. Z = 4. 1 = 5. 1=6. 1 = 7. 4 48-8 53-3 57-8 62-3 66-8 71-3 5 4V3 51-4 55-5 59-6 63-7 67-8 71-9 6 46-2 59-1 53-9 57-7 61-5 65-4 69-2 7 45-5 49-1 52-8 56-4 60-1 63-7 67-4 8 44-9 48-4 51-9 55-4 58-9 62-4 65-9 9 44-5 47-9 51-3 54-7 58-0 61-4 64-7 10 44-2 47-5 50-8 54-1 67-3 60-7 64-0 12 43-6 46-8 50-0 531 56-3 59-5 62-6 14 4635 49-4 52-5 55-6 58-6 61-7 16 ... 52-0 55-0 58-0 61-0 20 ... ... ... ... 57'1 60-0 To see how the disturbance of the P.D. caused by the presence of the third carbon is distributed, we must compare equation (9) with equation (3) for which there was no third carbon in the arc. We have V = 38-56 + '2- 38-88 + 2-072 + 11-66 + 10-542 (9) (3) The constant terms in the two equations may be considered to be identical, since there is only 0*32 volt difference between them. Thus the third carbon does not interfere with this constant term. It appears to increase the part of the P.D. that varies with the length alone, and to diminish that which varies with both length and current, while it practically doubles the part that varies with the current alone. Let us now compare equation (9) with equation (8) for the sum of the carbon P.Ds : V- 38-88 + 2 and we find that, not only the constant terms, but also those which vary with the current alone are practically identical. Hence, leaving out the small variations in those two terms- 232 THE ELECTRIC ARC. (which probably arise from experimental errors), we find that if we subtract the sum of the two carbon P.Ds. from the total P.D. between the carbons, we have, for the fall of potential through the carbon vapour itself, two terms, of which one varies with the length of the arc alone, and the other with both the current and the length of the arc, but no term varying with the current alone. It seems, therefore, probable that that part of the variation in the positive and negative carbon P.Ds., which depends on the current alone, is not caused solely by the use of a bare idle carbon in the arc, but is a true variation which takes place when there is no such cause of disturbance, and is only increased by the insertion of the rod. In other words, the term ~~ ^ in equation (3) seems really to belong to the carbon P.Ds., which are not, therefore, constant for all currents. We can now, with tolerable certainty, locate three out of the four terms in the equation which connects the P.D. across the main carbons of the arc with the current and the length of the arc (equation 3). Apparently the first and third terms I I .Cf} 38-88 + - belong entirely to the carbon P.Ds., and the A. second term belongs entirely to the vapour P.D. The fourth term- is more difficult to locate; part of it certainly belongs to the vapour P.D., but whether any of it really belongs to the positive carbon P.D., as equation (6) appears to show, or whether this term depends entirely on the use of the bare third carbon, cannot be determined without fresh experiments. So far, only cases (1) and (2) of Fig. 70 (p. 213) have been discussed. Tables XXXVII. and XXXVIIL give the P.Ds. found when the experiments represented by cases (3) and (4) were made. Table XXXVtI. shows the P.D. between the posi- tive carbon and the third carbon just before it touched the negative carbon, for each length of arc and current. That is, the positive carbon P.D. plus the vapour P.D. Similarly, Table XXXVIII. gives the vapour P.D. plus the negative carbon P.D. for each length of arc and current. These Tables may be used in various ways to confirm the deductions made from the other Tables in this Chapter. For instance, if the corresponding P.Ds. in each of Tables XXXVII. CARBON P.D. PLUS VAPOUR P.D. 233 and XXVIII. be added together, we shall get the total P.D. across the main carbons, for we shall have added the negative carbon P.D. of Table XXVIII. to the positive carbon P.D. plus the vapour P.D. of Table XXXVII. As both these sets of P.Ds. were obtained with the third carbon close to the negative pole (cases (2) and (3), Fig. 70, p. 213), their sum ought to correspond with the total P.Ds. across the main carbons, with the third carbon in the same position, given in Table XXXIV., except that the increase of the P.D. caused by having a third carbon in the arc is counte4 twice over in Tables XXVIII. and XXXVII. and only once in Table XXX IV. It will be found that agreement between the two sets of P.Ds. is so close 1 that 43 of the pairs of values differ from one another by less than one volt, and the remaining 18 by less than two volts. Again, Table XXXVIII. may be used in the same way, in conjunction with Tables XXVII. and XXXIII., to find indirectly the total P.D. across the carbons with the third carbon close to the crater, and the positive carbon P.D. A comparison of these with the corresponding P.Ds. obtained by direct observation will also show that all the values agree extremely well with one another, though not quite so well as the experiments made with the third carbon near the negative pole, because the arc is always more disturbed when the third carbon is near the positive pole. Table XXXVII. P.D. between Positive Carbon and Third Carbon with Point of latter close to White Spot. Solid carbons. Positive, llmm. ; negative^ 9mm. in diameter ; third carbon, 0'5mm. to 2mm. in diameter. P.D. in Volts. Current in Amperes. 1=1. j Z = 2. Z=3, Z=4. 1 = 5. 1 = 6. 1 = 7. 4 35-6 39'8 44-5 52-3 56-0 60-8 63-8 5 35-7 41-4 45-1 50-1 533 57-8 59-4 6 37-1 401 45-8 49-6 51-1 55-0 59-1 7 37-3 40-9 44-5 4S-0 51-0 54-6 57-6 8 36-2 38-6 41-5 45-8 ! 49-1 50-8 54-8 9 35-4 40-3 42-8 43-9 48-3 50-9 54-8 10 34-8 38-7 41-8 45-4 49-3 51-4 54-8 12 34-0 38-0 41-5 44-6 48-1 49-5 52-9 14 ... 36-1 40-7 44-7 47-5 49-7 51-7 16 43-1 47-0 48-6 51-3 20 ... 48-8 50-4 I 234 THE ELECTEIC ARC. Table XXXVIII. P.D. between Third Carbon and Negative Carbon, with Point of latter close to Crater. Solid carbons. Positive, llmm. ; negative, 9mm. in diameter ; third carbon, 0'5mm. to 2mm. in diameter. Current in Amperes. JT.JU/. Ill VUll/O. Z=l. 1=2. 1=3. Z=4. 1=5. 1=6. 1=1. 4 14-8 14-1 19-4 24-9 30-7 30-5 34-2 5 11-2 193 19-1 24-4 24-5 28-9 34-4 6 11-9 159 22-8 21-9 26-0 29-8 31-0 7 9-9 17-7 20-9 25-8 27-1 27-5 31-7 8 10-5 15-5 19-2 20-7 23-0 28-4 28-2 9 9-4 15-6 16-6 19-7 22-8 24-1 28-7 10 11-0 15-3 201 20-4 24-7 27-5 27-8 12 10-4 14-2 17-7 20-8 23-0 25-2 27-1 14 141 17-8 20-0 21-9 23-1 26-8 16 ... ... ... 18-6 20-6 24-0 28-0 20 ... ... ... 22-4 26-3 It has been mentioned that four series of experiments were made with cored carbons, two with cored positive and solid negative carbons, and two with both carbons cored. The results of these experiments, together with the similar results obtained when both carbons were solid, are given in Tables XXXIX. and XLI. The limited number of the experiments with cored carbons renders it difficult to judge of the effect on the various P.Ds* of changing the current and the length of the arc, as was done in the case of solid carbons. But the general result of substituting cored for solid carbons is easily seen, especially if, instead of comparing each set of P.Ds, separately with one another, we examine the average P.Ds. given at the end of each series. Thus the upper part of Table XXXIX. shows that with both carbons solid the average total P.D. across the carbons is 59 '9 volts, while with the positive carbon cored it is 5 6 '8, or 3*1 volts less, and with both cored it is 54 % 1 volts, or 5'S volts less than with both carbons solid. Hence, coring either carbon diminishes the total P.D., but the diminution of P.D. is almost twice as great with both carbons cored as it is with the positive carbon alone cored, with an arc of 5mm. With a current of 10 amperes and various lengths of arc the diminution in the CORED CARBONS. 235 average total P.D. is exactly twice as great when both carbons are cored as when the positive alone is cored, as is seen from the lower part of Table XXXIX. Table XXXIX. Comparison, with Gored and Solid Carbons, of P.D. between the Carbons with a Third Carbon in the Arc. Positive carbon, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. Length of Arc, 5mm. Current P.D. between Carbons in Volts. Amperes. Both solid. + Cored, -Solid. Both Cored. 4 67-35 65-6 62-5 5 64-15 59-9 57-8 6 61-65 57-3 54-8 7 60-95 57-6 54-0 8 59-8 55-9 53-7 9 57-5 55-6 53-6 10 58-8 54-2 53-2 12 57-8 53-9 50-9 14 55-95 54-2 50-3 16 5525 53-7 50-0 Average. 59-9 56-8 54-1 Current, 10 Amperes. Length of Arc P.D. between Carbons in Volts. Millimetres. Both Solid. + Cored, -Solid. Both Cored. 1 43-3 43-4 39-9 2 47-4 45-3 43-8 3 51-15 50-0 486 4 54-55 53-4 51-0 5 58-8 54-2 53-2 6 60-7 57-5 65-3 7 63-5 59-7 55-7 Average 54-2 51-9 49-6 The important thing to find out about this diminution of P.D. is whether it takes place in either of the carbon P.Ds. or both, or in the vapour P.D. Table XL. shows that a certain amount of it takes place in the positive carbon P.D., but not all, even when the positive carbon alone is cored, for although the 236 THE ELECTRIC AEC. average positive carbon P.D. is reduced by 3'3 volts, by the use of a cored positive carbon, which is about the same as the reduction in the total P.D., with an arc of 5mm., yet with a current of 10 amperes the average positive carbon P.D. is reduced by 1*3 volts by coring the positive carbon, whereas the average total P.D. is reduced by 2 -3 volts. Hence it is probable that part of the reduction in the total P.D. is caused by the carbon vapour itself being rendered more conducting by the presence of the vapour from the core. Table XL. Comparison, with Cored and Solid Carbons, of Positive Carbon P.Ds. Positive carbon, llmm. ; negative, 9mm. ; third carbon, 0'5mm. to 2mm. Length of Arc, 5mm. Current P.D. in Volts. in. Amperes. Both Solid. + Cored, - Solid. Both Cored. 4 36-7 31-2 36-9 5 35-5 3L-0 32-5 6 3555 31-1 311 7 35-0 29-7 31-3 8 34-9 34-4 31-6 9 35-4 29-2 31 -8 10 33-5 31-8 32-5 12 338 30-8 30-7 14 31-8 310 339 16 32-7 32-0 31-2 Average 34-5 31-2 32-3 Current, 10 Amperes. Length of Arc in Millimetres. P.D. in Volts. Both Solid. + Cored, -Solid. Both Cored. 1 2 3 4 5 6 7 32-6 32-4 31-5 33-75 335 32-7 34-7 34-0 31-2 31-6 32-4 31-8 31-0 30-2 31-2 33-4 33-7 34-3 32-5 31-9 321 Average 33-0 31-7 32-7 CORED CARBONS. 237 With both carbons cored the loss in the positive carbon P.D. appears to be less than when the positive alone is cored, but this is probably only an apparent difference caused by the core being harder in the one case than in the other. We may, I Table XLI. Comparison, with Cored and Solid Carbons, of Negative Carbon P.Ds. Positive carbon, llmm. ; negative, 9mm. ; third carbon, 0-5mm. to 2mm. Length of Arc, 5mm. Current P.D. in Volts. in Amperes. Both Solid. + Cored, -Solid. Both Cored. 4 104 101 10-6 5 10-8 8-9 9-2 6 9'7 8-5 9-3 7 9-4 8-6 8-6 8 10-0 8-5 7-6 9 9-6 8-6 9-0 10 9-2 8-5 9-0 12 9-6 8-5 9-1 14 9-2 8-7 7-9 16 9-2 8-8 81 Average 9-6 8-8 8-8 Current, 10 Amperes. Length of Arc P.D. in Volts. Millimetres. Both Solid. + Cored, -Solid. Both Cored. 1 8-5 8-0 7-8 2 8-5 8-8 8'9 3 9-0 8-8 8-5 4 8-9 8-6 8-7 5 9-2 8-5 9-0 6 9-2 8-7 9-0 7 9-2 8-7 8-6 Average 8'9 86 8-6 think, take it for granted that, other things being the same, the reduction of the positive carbon P.D. caused by coring is about the same, whether the negative carbon is cored or solid. Hence the increased reduction of the total P.D. caused by 238 THE ELECTRIC AEG. coring the negative carbon must be the result of a reduction either of the vapour P.D. or of the negative carbon P.D., or of both. That it is not in the negative carbon P.D. that the reduction takes place may be seen from Table XLL, for, with the positive carbon cored, the average negative carbon P.D. appears to be the same, whether the negative carbon be cored or not. Hence it appears that while coring the positive carbon reduces both the positive carbon P.D. and the vapour P.D., coring the negative carbon only further reduces the vapour P.D. The reduction of the positive carbon P.D. is probably due to the ease with which the core vapourises compared with the solid carbon. The reduction of the vapour P.D. mubt be caused by the vapour of the core having greater conductivity than that of the solid carbon. The conductivity must indeed be very much greater, for, as was mentioned in Chapter I. (p. 16), the visible cross section of the arc is always less for the same current and length of arc, with a cored than with a solid positive carbon, and hence, all other things being equal, the P.D. required to send a given current would be greater and not less with the cored carbon. It may be mentioned that a cored negative carbon always develops a deep crater just as if it were a positive carbon. SUMMARY. SOLID CARBONS. I. The positive carbon P.D. increases as the length of the arc increases, and diminishes as the current increases. TI. The negative carbon P.D. does not vary with the length of the arc, but diminishes as the current increases. The fall of potential at the junction of this carbon with the arc is always from arc to carbon, and nevar in the opposite direction. III. In the equations connecting each of the carbon P.Ds. with the current and the length of the arc, there is a constant term. The sum of these two constant terms has the same value as the constant term (commonly called the back E.M.F. of the arc) in the equation connecting the total P.D. across the carbons with the current and the length of the arc. SUMMARY. 239 IV. Hence, a part of this so-called back E.M.F. belongs to the negative carbon P.D., and only about four fifths of it to the positive carbon P.D. instead of the whole, as has hitherto been supposed. V. The term involving the current alone in the total P.D. equation belongs to the two carbon P.Ds., and the term involving the length of the arc alone belongs to the vapour P.D. CORED CARBONS. VI. The reduction of the total P.D., caused by using cored instead of solid carbons, is made partly in the positive carbon P.D., and partly in the vapour P.D. Very little of it is made in the negative carbon P.D., even when the negative carbon is cored. CHAPTER VIII. THE KELATIONS EXISTING BETWEEN THE E.M.F. OP THE GENERATOR, THE RESISTANCE IN THE CIRCUIT OUTSIDE THE ARC, THE LENGTH OP THE ARC, THE CURRENT AND THE P.D. BETWEEN THE CARBONS WITH SOLID CARBONS. Hitherto the arc alone has been considered, without any reference to the E.M.F. of the generator, or the resistance placed in circuit outside the arc. The influence on the arc of any change in either of these may be studied in two ways, graphically, by means of Fig. 79, the curves in which are a reproduction of those in Fig. 38, with certain additions ; and analytically, by examining equation (4) (p. 186), in conjunction with an equation expressing the relation between the E.M.F. of the generator, the P.D. between the ends of the carbons, the outside resistance in circuit, and the current flowing. The graphical method is, perhaps, the easier to follow, and may, therefore, be taken first. Let P (Fig. 79) be a point on the axis of P.D. such that its distance from the axis of current represents the E.M.F. in volts of the generator supplying the current, and let P Q be a line parallel to the axis of current, so that the distance of any point on P Q from the axis of current will represent this same E.M.F. Then, if R x be a point on one of the curves, the distance between Rj and the axis of current will represent the P.D. in volts used in sending the current through the arc, and R x S, the distance between Rj and P Q, will represent the P.D. employed in sending the current through the whole of the resistance outside the arc. Also, since PS represents the current flowing when that outside resistance is in circuit, the ratio of S R x to S P, which is tan. R! P Q, represents this outside resistance. If, then, with the given generator supplying the current, any line be drawn from P making an angle Q P R with P Q, and cutting the curves at various points, the positions of those points 242 THE ELECTEIC AEC. Both Carbons Solid. ALTERING CONDITIONS OF ARC. 243 will represent the relation between P.D. and current in arcs all supplied by a generator with the same E.M.F., and all having the same outside resistance in circuit namely, that represented by the tangent of the angle R P Q. We may then, for convenience sake, call such lines as P RjY resistance lines. There are three possible ways of altering the conditions of the arc when the E.M.F. of the generator is kept constant, viz. : (1) The external resistance may be kept constant, and the length of the arc varied. (2) The length of the arc may be kept constant, and the external resistance varied. (3) Both the external resistance and the length of the arc may be varied together. In the first case, since everything is constant except the length of the arc, lengthening the arc must mean increasing the resistance in the whole circuit, and consequently a diminu- tion of current must follow on it. Similarly, shortening the arc must mean a diminution of the total resistance in circuit, and therefore an increase of current must follow on it. In the second case, since everything is constant except the external resistance, increasing this must increase the total resistance in circuit, and therefore must diminish the current ; while diminishing the external resistance must cause a diminu- tion in the total resistance in circuit, and therefore must cause an increase in the current. In the third case, the current may be made to vary in any manner that is desired, or to remain constant, by suitable variations of the external resistance and the length of the arc. But the sum of the effects of the variation of each of these must be the same as if each had been varied separately while the other was kept constant, so long as one of the variations does not cause the arc to be extinguished, thus making it impossible for the other to take effect after it. While the external resistance can really be kept absolutely constant, the length of the arc cannot, for it is quite impossible, either automatically or by hand, to keep the carbons moving towards each other at exactly the same rate at which they burn away. Consequently what is called keeping the length 244 THE ELECTRIC ARC. of arc constant is really allowing it to become slightly longer than the desired length, and then bringing the carbons together till it is slightly shorter, so that the curve connecting time and length of arc when the length of arc was supposed to be con- stant, would be a zig-zag, not a straight line. Similarly, what is called a constant current is not really con- stant, for it is impossible to lengthen or shorten the arc, and at the same time alter the resistance by exactly the right amount to keep the current constant. Hence there is a con- tinual increase and decrease of current above and below the supposed constant value. Nevertheless it is possible to keep both length of arc and current constant within certain limits, which may be made very narrow by careful experimenting. If we follow one of the resistance lines, P RjY, for instance, we shall see what happens when the external resistance is kept constant, and the length of the arc varied. The first thing that strikes one about this line is that the curves for silent arcs above a certain length viz., 6mm. are not cut by it at all ; that the curve for this length is touched by the line, while those for shorter lengths of arc are cut by it in two points, or would be cut in two points, if hissing did not intervene and terminate the curve. The two points at which the line P R X Y cuts each of the curves for lengths of arc less than 6mm. are closer together the nearer the length of the arc is to 6mm., and we may consider that it really cuts the 6mm. curve at two points which are coincident. The fact of its not cutting the curves for longer arcs at all shows that no arc of greater length than 6mm. can be maintained by a generator with the given constant E.M.F. when a resistance represented by tan R t P Q is in the circuit outside the arc ; in other words, 6mm. is the maximum length of arc that can be maintained under the given conditions of generator and external resistance. From the resistance lines cutting each of the curves that they meet at two points it would appear as if, with a generator of constant E.M.F., and a constant resistance in circuit external to the arc, two widely different currents might be sent through two arcs of the same length. That is, apparently, under two precisely similar sets of conditions, two entirely different things may happen. This is, of course, absurd. Either the conditions cannot be precisely similar, RESISTANCE LINES. 245 or, if they are, the two different currents cannot permanently flow. By tracing the course of events from the moment the arc is struck it is possible to find out which of these two hypotheses is justified by facts. We know from experience that, immediately after striking the arc, in the ordinary way, the current flowing is compara- tively large, since the length of the arc is very small, and that if we lengthen the arc without altering the resistance in circuit, we diminish the current. Hence it is evident that if we want to follow the course of events after striking the arc, we must start from the right hand point of intersection with the shortest length of arc, and follow the line P RjY from right to left, because we then arrive successively at points of inter- section which show that the current diminishes as the length of the arc increases. For instance, following P RjY (which corresponds with an E.M.F. of 68'88 volts and an external resistance of 1'05 ohms) from right to left, we see that when the arc is 4mm. in length the current is about 18 amperes, when it is 5mm. the current is about 14 amperes, and when it is 6mm. the current is a little over 8 amperes. But if we start from the left hand point of intersection with the shortest length of arc, and follow the line PR X Y from left to right, we arrive successively at points of intersection which show that the current increases as the length of the arc increases. The right-hand points of intersection of the resistance lines with the curves are, then, those we are accustomed to find after striking an arc, and we know, therefore, that they are possible. Can the left- hand points also be obtained when the E.M.F. of the generator and the outside resistance are the same as for the right-hand points? is the question now to be answered. In going from right to left along the line P I^Y, everything is perfectly easy till the arc is 6mm. in length, that is, till the resistance line is a tangent to the curve connecting P.D. and current. When this point is reached, however, trouble arises, for, since 6mm. has been shown to be the maximum length of arc that it is possible to maintain with the given resistance in circuit, and since the tendency of the arc is to lengthen, unless the carbons are brought nearer together at the very moment they have become 6mm. apart, the arc will be ex- tinguished. 246 THE ELECTRIC ARC. It would, of course, be very difficult, if not impossible, to bring the carbons nearer together at the precise moment when their distance apart was 6mm., but supposing that done, the question arises, which course would the point of intersection of the resistance line and the curve for the shorter arc take ; would it move to the right or to the left, should we get a right- hand or a left-hand point of intersection between the resistance line and the curve ; or, in other words, would the current increase or diminish 1 There is not much difficulty in answer- ing that question. It has already been pointed out that, if everything else remains unchanged, shortening the arc can have only one result: it must lessen the total resistance in circuit, and therefore lead to an increase of current. Hence the point R x will move to the right when the arc is shortened, and it is thus evident that it is not possible to obtain a left-hand point of intersection between the resis- tance line and the curve by keeping the external resistance con- stant and varying the length of the arc. It still might be possible, however, to get to a left-hand point of intersection by varying the external resistance and keeping the arc at a constant length. Let us see. We may suppose that the arc has been struck, that its length has been increased from zero to 6mm., and that a silent arc is being maintained with a current of about 20 amperes flowing. If the length of the arc be now kept constant the external resistance will have to be increased, in order that we may pass along the curve for a silent arc of 6mm. As the resistance is increased the current will diminish, and the points of intersection between the resistance lines and the curve will be right-hand points, such as R 4 and R 5 , till the resistance is represented by tan RjP Q, and the resistance line is a tangent to the curve. When that moment is reached the resistance has of course gained its maximum value for a 6mm. arc, for if the angle R^Q were still further increased, the line R x P would not meet the 6mm. curve at all. Hence, at this point, the resis- tance must be diminished the moment the arc is 6mm. long, and the question again arises, Which way would the point E, go to the right or the left 1 Would the current increase or diminish when the external resistance was diminished? This question is readily answered. We know that diminishing UNSTABLE CONDITIONS. 247 the resistance, and leaving all else unchanged, can only cause a diminution in the total resistance in circuit, and hence an increase of current, which will give us over again points on the curve to the right of R^ It is, therefore, impossible to obtain the left-hand points of intersection between the resis- tance lines and the curves by varying the external resistance and keeping the length of the arc constant. It remains only now to see if these points can be obtained by varying both the external resistance and the length of the arc at the same moment, and this seems the most plausible method of all. It seems so possible, when the resistance line is just about to become a tangent to the curve, to suddenly diminish the resistance and lengthen the arc at the same moment, so as to pass quickly through the critical point, and arrive safely at a left-hand point of intersection on the other side of it. That this idea is fallacious is, however, easily proved by referring to three conclusions that have already been shown to be true. With a generator of constant E.M.F. to supply the current (1) Changing both the length of the arc and the resistance together can only have the same effect as changing each separately in quick succession, if the order of change be such that one does not extinguish the arc before the other can take effect. (2) Changing the length of the arc alone can give only right- hand points of intersection between the resistance lines and the curves. (3) Changing the resistance alone can give only right-hand points of intersection between the resistance lines and the curves. From these three facts it follows that it is impossible to obtain left-hand points of intersection between the resistance lines and the curves by altering the external resistance and the length of the arc simultaneously, and it follows that there is no possible way of varying the conditions of the arc in such a manner as to obtain left-hand points of intersection between the resistance lines and the curves connecting P.D. and current. Hence no points can be obtained on the curves connecting P.D. and current farther to the left than those which form the points of contact between the curves and the tangents drawn to the curves from that point on the axis of P.D. which indicates the E.M.F. of the generator. 248 THE ELEGTEIG AEG. It follows, therefore, that if P be a point on the axis of P.D. such that its distance from the axis of current represents the E.M.F. of the generator, and if PR be the tangent through P to the P.D. and current curve for an arc of given length at the point indicating the given current, then the given E.M.F. is the smallest that can be used to supply that length of arc and current. This was first pointed out by M. Blondel in 1891 (see p. 62). The question arises, How can the left-hand points be obtained at all ; how were they obtained ? They were obtained as right-hand points, by using a generator with a much larger E.M.F. than that indicated by the position of P. It is, of course, obvious that all the points on the curves that are higher up than the line P Q must have been obtained with a generator of larger E.M.F. than that indicated by P; but what this investigation shows is that some of the points that are much lower down in the figure than the line P Q must also have had a generator of higher E.M.F. to produce them. The point for 2 amperes, for instance, on the 2mm. curve, although corres- ponding with a P.D. of only 58'5 volts, must have been found with a larger E.M.F. than 69 volts, which is indicated by the position of P, for the tangent from Pto the 2mm. curve touches the curve at a point indicating a current of between 2 and 3 amperes. On referring to Fig. 79, it is seen that a left-hand point of intersection of a resistance line and a curve for example, the left-hand point T', where the resistance line R x P meets the 5mm. curve has the following property : If the E.M.F. of the generator be kept constant, and also the length of the arc, an increase of the resistance of the circuit corresponds with an increase of the current. Now, this is exactly the condition of the unstable solution that is obtained when a series dynamo, running at fixed speed, is in series with a set of accumulators of fixed E.M.F., the total resistance in circuit being also fixed. For in such a case, as the late Dr. J\ Hopkinson showed some years ago, there are three distinct values of the current possible, two of these corresponding with the dynamo charging the cells, while the third, which is very large and is negative, is produced when the magnetisation of the dynamo has been reversed, and the dynamo is helping the cells to discharge. Now, the smaller of LARGE E.M.F. FOR SMALL CURRENTS. 249 the two positive charging currents is unstable, for it increases in value with an increase of the resistance in circuit, so that on the slightest change in the speed of the dynamo, or in the resistance in circuit, this unstable current is suddenly changed into the larger charging current, or into the very much larger discharging current. Further, just as I have shown that a left-hand point in Fig. 79 may, for the same current and length of arc, be changed into a right-hand one by increasing the E.M.F. of the generator and the resistance in circuit, so it may be shown that Dr. Hop- kinson's unstable point may, for the same current and the same set of accumulators, be changed into a stable solution by raising the speed of the series dynamo and increasing the resistance in circuit. The impossibility of obtaining small currents without having a comparatively large E.M.F. in the generator and a large external resistance, explains a very puzzling circumstance that occurred in carrying out the experiments of which the curves in Fig. 79 are the result one which many other experi- menters must also have noticed, There were two dynamos at the Central Technical College, either of which it was convenient for me to use ; one of these produced about 120 volts, and the other about 150 volts on open circuit. The first ran much more steadily than the second, which was driven by a single-cylinder engine ; the former was, therefore, much better to employ in a general way; when, however, it was used for small currents and long arcs, the arc behaved in the most tricky manner, going out again and again for no apparent cause. The reason of this is now obvious. The curves for long arcs are so nearly vertical in the parts for small currents, that the tangents to those curves at any of the points indicating small currents are very nearly parallel to the axis of P.D., and there- fore intersect it very high up. It is this point of intersection, however, that determines the smallest E.M.F. that it is possible to have in the generator, and the smallest resistance that it is possible to have in the circuit, in order that a given current shall flow through a given length of arc. Thus, although, for the smallest current and longest arc I used, a P.D. of only about 86 volts was required for the arc itself, yet an E.M.F. of 250 THE ELECTRIC ARC. considerably over 120 volts was needed in the generator to enable the arc to be maintained at all with the given small current flowing. The remainder of this large E.M.F. had to be wasted in sending the current through the large resistance that it was absolutely necessary to have in circuit. Thus the resistance added to an arc lamp on a constant- pressure circuit fulfils three distinct functions. It prevents an enormous current flowing when the arc is first struck ; it renders it possible for a solenoid placed in series with the arc to regulate its length ; and we now see that with solid carbons this resistance fulfils a third and entirely different function, for without some resistance being placed in the circuit external to the arc it is impossible to maintain a silent arc at all. Hence the resistance placed in series with an arc lamp " to steady the arc," as is commonly said, fulfils the all-important function of making a silent arc possible. In fact, an arc possesses this very curious property, viz. : that, although a certain current of, say, A amperes flowing steadily through an arc of, say, I mm. corresponds with a P.D. of, say, V volts between the carbons, the mere mainten- ance of this P.D. of V volts between the carbons with the arc of I mm., is not a sufficient condition to ensure that the current of A amperes shall continue to flow. There must also be a resistance in the circuit outside the arc, which can not have less than a certain minimum value. As an example of this peculiarity, I may refer to the difficulty, alluded to on page 170, which I met with when experimenting on arcs with constant P.Ds. An examination of Fig. 79 shows that when, for example, a current of 11 amperes is steadily flowing through an arc 5mm. long, formed with solid carbons, llmm. and 9mm. in diameter, the P.D. between them is 55 volts. It might, therefore, be imagined that this current could be sent through such an arc with a dynamo compounded and run at such a speed as to maintain exactly 55 volts between the carbons with no resistance inserted between the dynamo and the carbons. Or it might be thought that this steady current of 11 amperes could be sent through this arc by means of, say, 29 accumulators, when such a small resistance was inserted in the circuit that, with a current of 11 amperes, the accumulators maintained a P.D. of 55 volts between the carbons. MINIMUM EXTERNAL RESISTANCE. 251 But when I tried this, and similar experiments of keeping the P.D. between the carbons constant, the arc always either went out, or the magnetic cut-out, set to open at 30 amperes, broke the circuit. The explanation of this is now clear, for what I was really endeavouring to obtain was a silent arc with a fairly small current, and a small resistance in circuit external to the arc ; in other words, I was trying to obtain the left-hand point of intersection between the 5mm. curve and the resistance line, and this, as was proved above, is impossible. Indeed, with a set of accumulators having an E.M.F. of about 58 volts and a small resistance in circuit, the only current that could flow steadily through a 5mm. arc between the carbons in question was a very large one far greater than 30 amperes. The value of this current would be known if we could find the intersection of the resistance line with the hissing part of the 5mrn. curve, at a point far off the figure, to the right. What we find, then, is that, in order that a given current may be maintained jloiving through a given length of arc, there must be a minimum external resistance in the circuit which determines, also the least E.M.F. in the generator that would maintain such a current flowing through such a length of arc, For example, whatever be the nature of the generator, the least resistance that can be placed in the circuit to send a steady current of 11 amperes through a 5mm. arc is that given by the tangent to the 5mm. curve at the point corresponding with 11 amperes. And on drawing this tangent to the 5mm. curve in Fig. 79, we find that it corresponds with a resistance of 0-64 ohm. This minimum resistance determines the minimum E.M.F. in the generator for each current and length of arc; for example, on continuing the resistance line just referred to for the 11-ampere 5mm. arc we find that it cuts the axis of P.D. at 62 volts. Hence a resistance exceeding 0'64 ohm must neces- sarily be placed in the circuit, and the E.M.F. employed must exceed 62 volts, although the arc requires a P.D. of only 55 volts. Similarly, although we see from Fig. 79 that a 12-ampere 3mm. arc requires a P.D. of only a little less than 49 volts, the preceding reasoning tells us that, with the solid carbons used, two such arcs could not be run in series off the ordinary 252 THE ELECTRIC AEC. constant-pressure 100-volt electric lighting mains, even if the supply pressure were kept absolutely constant at 100 volts. Or again, with the solid carbons I used, two 10-ampere 4mm. arcs could not be run in series off 110 volts constant-pressure mains, although each arc requires less than 53 volts. Further, the minimum resistance was so great for an arc of 7mm. and current of 2 '5 amperes, with the solid carbons I used, that it made the minimum E.M.F. required more than half as large again as the P.D. used in sending the current through the arc itself, for I have calculated that the minimum E.M.F. was about 139 volts, while the P.D. needed by the arc was only 86 volts, as has been mentioned. It may be seen from Fig. 79 that the compulsory minimum resistance outside the arc is greater (1) the greater the length of the arc, (2) the smaller the current. But the apparent resistance of the arc also increases with the length of the arc, and is greater the smaller the current, so that we arrive at this very curious fact : When a silent arc is being maintained the smallest resistance that it is possible to have in the circuit external to the arc is greater the greater the apparent resistance of the arc, or, in other words, the more resistance you have in the arc, the more you need outside it. Many more facts concerning the relations between the E.M.F. of the generator, the external resistance, the length of the arc, and the current can be ascertained by treating Fig. 79 analytically, which we will now proceed to do. Let E be the E.M.F. of a generator in volts, let r be the total resistance in ohms in the circuit outside of the arc itself, let there be a P.D. of V volts between the carbons, and let a current of A amperes be flowing through an arc of I millimetres. Then, referring to Fig. 79 (p. 242), E is represented by the distance between P and the axis of current, r by the ratio of the distance from P Q of any point on one of the resistance lines to its distance from the axis of P.D. This is the same thing, of course, as r being represented by the tangent of the angle between a resistance line and PQ. A is represented by the distance between any point at which a resistance line cuts a curve and CURVES TAKEN ANALYTICALLY. 253 the axis of P.D. and V by the distance between that point and the axis of current. Then E = V + A r. But from equation (4) (p. 186), therefore E = a + 6/ + + Ar, .... (10) A or A 2 r - (E - a - b 1) A + c + d I = ; hence A = -- - a- 6Q'- 4r ( (u) 2* T Thus we find, as before, that with a generator of given E.M.F. two different currents, or one, or none may be sent through the arc. The conditions for the three cases in the equation are that (E-a-6/) 2 shall be greater than, equal to, or less than 4 r (c + d /), and these correspond with the conditions in the figure that the resistance line shall meet the curve at two points, at one, or not at all. Since the value for A obtained by using the positive root in equation (11) is greater for any given length of arc than that obtained by using the corresponding negative root, it follows that the positive root will give values which correspond with right-hand points of intersection between the resistance line and the curve, while the negative root will give values that correspond with the left-hand points of intersection. As it has already been shown that these left-hand points can never be obtained in practice, it will not be necessary here to discuss the negative root of the equation, and therefore henceforward when equation (11) is mentioned it will be understood that the positive root only is alluded to. As before, we shall take a given E.M.F. in the generator, and we shall consider what happens, first, when r is constant and I is varied ; next, when I is constant and r is varied ; and finally, when r and I are both varied in such a way that A is constant. In equation (11), if A is to have a real value at all, (E-a-5 I) 2 must be not less than 4 r (c + d 1) whatever A, E, r, and I may be. Taking the first case r constant, i.e. t following one of the resistance lines in Fig. 79 with the positive sign before the 254 THE ELECTRIC ARC. root, A is evidently greatest when I is least, diminishes as increases, and is least when I is greatest that is, A is a maximum when I is a minimum, and a minimum when I is a maximum if the resistance external to the arc is kept constant But, since the expression under the root cannot be negative if A is to be real, I is a maximum when (E-a-&/) 2 -4r(c + d/) = 0, . . . (12) for, since E is constant, E - a - bl is smallest when I is greatest, and since r is constant, r (c + d I) is greatest when I is greatest. Hence when r is constant the condition that A shall have only one value, which is the condition that the resistance line shall be a tangent to the curve, is also the condition that the length of the arc shall be a maximum, as was shown when the subject was dealt with graphically. Since A has been shown to be a minimum when I is a maximum, it follows that the smallest current that can flow with a constant resistance in circuit when the E.M.F. of the generator is also constant is given by the equation These maximum and minimum values for I and A may be found in terms of E, r, a, 6, c, and d, all of which are known. For from equation (12) we have hence 7 = 5 ( E ~ a ) + 2c * r N/{fr(E - a) + 2 dr}*- 6 2 {(E - a) 2 - or / _ b b 2 But from equation (11) it may be seen that I cannot be TG^ greater than I when the quantity under the root is zero, otherwise A would be negative. Therefore, in the last equa- tion the negative sign must be used before the root. The quantity under the root is & 2 (E - a) 2 + 4 bdr (E - a) + 4 d 2 r 2 - 6 2 (E - a) 2 + 4 6 2 c r, which equals CONSTANT E.M.F. & EXTERNAL RESISTANCE. 255 Therefore And, substituting this value for I in equation (13) we get A= Jr{bd(&-a) + the arc hisses. Hence, it must be at the hissing point when the smallest increase in the area of the crater will make it begin to cover the side of the positive carbon, and this can only be when the tip of that carbon has very nearly the same cross-section for some little distance from its end in other words, when its sides are nearly vertical. It is thus impossible to doubt that there is some connection between the extension of the crater up the side of the positive carbon and hissing, although, so far, it has not been possible to detect which was cause and which was effect. We shall presently see that the extension of the crater is the cause and 298 THE ELECTRIC ARC. hissing the effect ; that, in fact, hissing is produced by the crater becoming too large to occupy the end only of the positive carbon, and by its, therefore, extending up its side. Before proceeding to prove this, however, it will be interest- ing to see how the laws for the largest silent currents with normal arcs, which have been already obtained from the electrical measurements on pages 279-284, may be deduced on the above hypothesis from Figs. 84 and 85. In Fig. 84 we have a series of four normal arcs of the same length, burning between solid carboas of the same diameter, but in (a) the current is 6 amperes, in (b) 12, in (c) 20, and in (d) 30 amperes. The roundness of the tip of the positive carbon may be measured by the obtuseness of the angle ABC between its side and end. In (a) the tip is very nearly round, and the area of the crater is certainly less than any but its smallest cross-section ; therefore the arc is certainly silent. In (b) the tip is less rounded, but the arc is still evidently silent; in (c) the angle ABC is much more nearly a right angle, and it is plain that a very small increase in the area of the crater would cause it to burn up the side of the tip, there- fore the arc is near the hissing point. In (d) the angle ABC is practically a right angle, the tip of the positive carbon is cylindrical, and the crater has evidently burnt partly up its side, so that the arc is hissing. Thus, keeping the length of the arc constant and gradually increasing, the current must gradually bring us to a hissing point. Next, I have shown (pp. 13-17), that with, a constant current, the end of the positive carbon becomes rounder, and occupies a larger portion of the entire cross-section of the carbon rod, the more the carbons are separated. Hence, the longer the arc, the greater must be the area of the crater, and consequently the greater must be the current before the crater extends up the side of the positive carbon. Consequently, the longer the arc, the greater is the largest silent current. Thirdly, it follows that when the current and the length of the arc have been increased to such an extent that the round, tip of the positive carbon occupies the whole cross section of the carbon rod itself, no further increase in the size of the crater is possible, without a part of it extending up the side of the positive carbon. Hence the largest silent current for a CA USE OF HISSING. 299' positive carbon of a particular diameter cannot exceed a particular value, however long the arc may be made. Lastly, similar reasoning used in conjunction with Fig. 85 tells us that the thicker the positive carbon the greater must be the largest silent current for a particular length of arc. Consequently, the fact that hissing occurs when the crater covers more than the end surface of the positive carbon and extends up its side, combined with our knowledge of the way in which the positive carbon shapes itself in practice, is sufficient to enable us to deduce all the laws given on page 279, which govern the largest current that will flow silently with the normal arc under given conditions. It is also now obvious why, when the arc is not normal, it may be made to hiss with small currents and will be silent with quite large ones. For suppose, for instance, the end of the positive carbon were filed to a long fine point, then a very small current would make a crater large enough to extend up the side of the point, and produce a hissing arc. But if, on the contrary, the end were filed flat, so as to have as large a cross section, as possible, quite a considerable current could flow silently, for in that case it would require the current to be very great for the crater to be large enough to till up the whole of the end of the positive carbon. We come now to the question, why should the arc hiss when the crater burns up the side of the positive carbon what is it that happens then that has not happened previously ? In pondering over this question, the possibility occurred to me that as long as the crater occupied only the end surface of the positive carbon it might be protected from direct contact with the air by the carbon vapour surrounding it, but that, when the crater overlapped the side, the air could penetrate to it immediately, thus causing a part at least of its surface to burn instead of volatilising. The crater would probably burn more quickly than it would volatilise, and hence, though the burning parts would be at a lower temperature than the remainder, and so look duller, they would consume more rapidly, so that little pits would form, which would deepen while the air continued to get to them. Thus, the darker, spherical parts of the crater shown in Fig. 81 (which you can see deepen by watching the image after the arc has begun to- 300 THE ELECTRIC AEC. hiss) would be the burning parts, while the brighter ridges would be volatilising. Many circumstances at once seemed to combine to show that this was the true explanation. The whirling figures, and Mr. Trotter's still faster rotations, how were they caused but 'by draughts getting into the arc ? Then the humming noise, which is so like the wind blowing through a crack, was not this probably caused by the air rushing through a slight 'breach in the crater already getting near to the critical size ? 'This air, pouring in faster and faster as the breach widened, would cause the arc to rotate faster and faster, sometimes in one direction, sometimes in another, according as the draught was blown from one side or the other. Then finally the air would actually reach the crater, burn in contact with it, and 'the P,D. would fall and the arc would hiss. The following is Mr. Trotter's own explanation of the rotation discovered by him. It is taken from a letter on the subject written by him to Prof. Silvanus Thompson, about the end of June, 1894. "The crater is pouring out a stream of carbon vapour. With a strong stream of vapour and a short arc, the stream may touch the negative ; when it does so in sufficient volume, and to exclusion of oxygen, mushrooming occurs. But as a rule most of it, if not practically all of it, ceases to be carbon vapour before it reaches the negative. This, I want to settle by spectroscope. " There is a combustion of the vapour, and that means an inrush of air. . . . The inrush of air is radial. It is partly due to the oxygen-carbon combustion, partly also, perhaps, to the oxygen-nitrogen combustion. If any accidental cause, such as a spurt of vapour from an impurity in the carbon, cause the inrush to be otherwise than radial, a rotatory motion is started, and persists, as when water running from a wash-basin moves in a vortex. In a washbasin the water can get away, in a tornado also, the air can get upwards and outwards ; but in the arc condensation due to chemical com- bination and lowering of pressure must be looked for as a sink for the vapour stream." In the open arc, whether silent or hissing, the outer envelope of the vaporous portion is always bright green. With the AIR THEORY OF HISSING. 301 hissing arc the light issuing from the crater is also bright green, or greenish blue. What so likely as that the two green lights should have a common origin, viz., the combination of carbon with air ? For the outer green light is seen just at the junction of the carbons and carbon vapour with the air, and the inner one only appears when air can get direct to the crater. Again, why does the arc always hiss when it is first struck ? Is it not because a certain amount of air must always cling to both carbons when they are cold, so that when the crater is first made its surface must combine with this air ? The cloud that draws in round the crater when hissing begins would be a dulness caused by the burning part of the crater being cooler than the parts which were still volatilising. In fact, everything seemed to point to the direct contact of crater and air as being the cause of the diminution in the P.D. between the two carbons which is the important part of the hissing phenomenon. One easy and obvious method of testing this theory imme- diately presented itself. If air were the cause of the hissing phenomena, exclude the air and there would be no sudden diminution of the P.D. between the carbons, however great a current might be used. Accordingly I tried maintaining arcs of different lengths in an enclosed vessel, and increasing the current up to some 40 amperes. No sudden diminution of the P.D. could be observed with any of the currents or lengths of arc employed, although when the same carbons were used to produce open arcs, the sudden diminution of about 10 volts in the P.D. between the carbons occurred with a current as low as 14 amperes for a 1mm. arc. Indeed, so far from there being any sudden diminution in the P.D. when the current through an enclosed arc is raised to higher and higher values, the P.D. appears to increase slightly for large currents. It was, of course, impossible, in these experiments, to avail myself of an ordinary enclosed arc lamp, since a current of some 5 or 8 amperes only is all that is used with such a lamp, whereas to test my theory it was necessary to employ currents up to 40 amperes, although my carbons were of smaller diameter than those fitted in ordinary commercial enclosed arc lamps. Accordingly, I constructed little electric furnaces, some made out of fire-clay crucibles with lids of graphite sealed .302 THE ELECTRIC AEG. on, as in Fig. 86, some moulded out of fire-clay with mica win- dows inserted, so that the image of the arc could be projected on to a screen and its length kept constant ; some constructed of iron lined with asbestos ; some with tubes inserted in them through which the air could be admitted when required, &c. It was found that when the vessel was entirely enclosed, the pressure in it was so great when the arc was first started, that -occasionally the lid was blown off. Consequently, the space between the positive carbon and the lid was left open till the L'ppor Carbon Ring of Sheet Aibartos Aobectos Fibre Graphite Lid Joint of Sodium Si!icat3 and Plaster of Paris Fireclay Pot -Fireclay Cement "Sodium Silicate and Plaster of Paris Cement "Lower Carbon FIG. 86. a-rc was well started, and then was tightly closed. This sudden increase of pressure probably took place when the carbons were first brought into contact, for Mr. Seaton, while conduct- ing some experiments for Messrs. De la Rue and Miiller in 1879 {p. 38) observed that, when the arc was completely enclosed, the increase of pressure when the carbons were first brought into contact was far greater than could be accounted for by the rise of temperature of the gas in the vessel, and that the pressure fell the moment the carbons were separated, almost ARC ENCLOSED IN CRUCIBLE. 303 to what it had been before contact was made. This fact was confirmed by some experiments made by Stenger (p. 44), in 1885. This first great rise of pressure may, of course, be partly caused by the gases occluded in the carbons being expelled on the current being started, but a complete investigation of this phenomenon has- not, as far as I am aware, yet been made. Some curves connecting the P.D. between the carbons with the current, when the arc was completely enclosed in the crucible (Fig. 86) are given in Fig. 87. The carbons were solid, the positive being llmm. and the negative 9mm. in diameter, similar to those I have used for all my experiments. As this crucible the first one made had no window, the length of the arc could not be kept quite constant, but the distance by which the carbons were separated was noted at the beginning of the experiment, and they were then allowed to burn away without being moved till the end, when the distance the positive carbon had to be moved in order to bring it tightly against the negative was noted. Measured in this way, the length of the arc was l'5mm. at the beginning and 2mm. at the end of the experiment. The current was started at 6 amperes, and gradually increased to 39 amperes ; then as gradually diminished to 6 amperes again, increased to 36 amperes, and diminished to 5 amperes, when the arc was extinguished. The P.D. between the carbons for a given current seems to have increased, as the length of time during which the arc had been burning increased ; this was undoubtedly partly due to the lengthening of the arc, but was probably also partly due to the whole of the air in the pot having been gradually burnt up, or driven out through the slag wool and the asbestos ring, by the pressure of the carbon vapour. Many other sets of curves were obtained, but all with the same result, viz., that when once the crucible had been freed from air, no sudden diminution in the P.D. could be observed on increasing the current far beyond the value at which this diminution took place on lifting up the lid and allowing the air to have access to the arc. The next thing to do was to try if an open arc could be made to hiss, and the P.D. to diminish suddenly, by blowing air at the 304 THE ELECTEIC ABC. HISSING DUE TO OXYGEN. 305 crater when the current was so small that the crater remained well at the end of the positive carbon in fact, to bring the air in contact with the crater artificially, when a much smaller current was flowing than would usually produce hissing. I first tried inserting a carbon tube in the arc and blowing through it, but this almost invariably blew the arc out. Then a tubular positive carbon was used and the air was blown down it. This plan answered admirably, for when a current of 10 amperes was flowing with an arc of about 3mm., so that the arc was quite silent, each puff of air blown down through the positive carbon was followed by a hiss and the characteristic diminution of the P.D. between the carbons. With a current of 6 amperes, however, I could get no hiss, but simply blew the arc out with each puff, probably because, with such a small current, the arc was cooled sufficiently to be extinguished before the action could take place. Oxygen was next tried, still with the open arc, and again each puff produced a hiss and diminution of the P.D., the latter being exactly the same in amount as when air was used, namely, about 10 volts. As my idea was that the diminution of P.D. was due to the chemical combination of air with carbon at the temperature of the crater, the fact of oxygen causing the same diminution of the P.D. as air seemed to show that nitrogen would produce no effect, and that all the effect produced by air was due to the oxygen in it. Accordingly nitrogen was blown down the positive carbon of an open arc, and no change in the P.D. followed, if the nitrogen was blown through gently ; but beyond a certain pressure, the arc was blown to one side, and thus lengthened, so that the P.D. rose, and, if the pressure continued, the arc went out. This experiment proved two things firstly, that it is the oxygen in the air that causes the diminution in the P.D. with hissing ; secondly, that this diminution in the P.D. is not due to cooling, for nitrogen would cool the arc as effectually as oxygen or air. To make assurance doubly sure on this point, carbon dioxide was blown down the tubular positive carbon, with the same result as when nitrogen was used, viz., no change was pro- duced in the P.D. between the carbons unless the pressure of the gaseous stream were large enough to blow the arc on HOC THE ELECTRIC ARC. one side, and then an increase and not a diminution in the P.D. was observed. If, however, the current was very near the value that made an open arc of the particular length used start hissing, blowing either nitrogen or carbon dioxide through the positive carbon sometimes started hissing ; but this was due, not to any direct action of the stream of gas on the carbon, but to the arc being deflected by the gaseous stream and burning obliquely up the side of the carbon, and thus allowing the air to come into con- tact with the crater. The proof of this was that this diminution in the P.D. had the same value as if air had been employed, and that the hissing did not cease on stopping the stream of nitrogen or carbon dioxide. This was not the case with hydrogen, however. When that gas was blown down the positive carbon in the open air, the arc would start hissing if the current were large enough, and stop hissing the moment the hydrogen ivas shut of. Not only this, but the diminution in the P.D. had a different value from that produced by air, being only about 6'5 volts instead of 10 volts. Table XLIX. gives the current and the P.D. between the carbons just before the hydrogen was turned on, just after it was turned on, just before it was turned off, and just after it was turned off. Table XLIX. Effect of Blowing Hydrogen doivn a Tubular Positive Carbon of an Open Arc. Carbons: Positive, llmm., tubed', negative, 9mm., solid. Length of arc about 3mm. P.D. between carbons in volts. Current in amperes. Before H was turned on. After H was turned on. Before H was turned off. After H was turned off. 52 52 52 52-5 52 46 45 45 46 45 46 47 45 46 46 53 52 52-2 53 52 14 12 12 12 9 Thus, the mean diminution of P.D. accompanying the hissing caused by hydrogen being sent down the positive carbon of an arc burning in the air was about 6-6 volts, or about 3J volts lower than when the hissing was caused by air alone, HISSING WITH HYDROGEN. 30 In order to exclude all possibility of doubt as to the effect of the various gases, the experiments were repeated with the arc entirely enclosed, so that the only gases that could reach it were those blown down the tubular positive carbon. The current was distinctly below the hissing point, being only 10 or 11 amperes, with an arc of from 2mm. to 3mm. long. When air was blown down the positive carbon, each puff lowered the P.D. by about 10 volts, and the moment the puff ceased the P.D. rose again. Next, oxygen was tried, with the same result. Thirdly, nitrogen with no result, or with the result that the arc was blown out if the pressure was too great. Carbon dioxide had the same effect as nitrogen, and lastly hydrogen was tried. This gas gave a totally different result with the enclosed arc from that already obtained with the open arc. For whereas, as has been previously stated, hydrogen produced a distinct hissing of its own when blown down the positive carbon in the open air, it produced none when used in the same way with the enclosed arc. To prove that, in order to produce the sudden diminution of P.D. under discussion it was necessary for the active gas to actually touch the crater, a tubular negative carbon was usedj and each gas was blown up through it in turn, gently enough not to force the gas directly against the crater. In no case was there any sudden diminution of the P.D., whatever was the gas blown through the negative carbon, and whether the arc was open or enclosed. On the contrary, there was generally a small increase, probably due to the lengthening of the arc by its being blown on one side. If oxygen or air were blown very hard up the negative carbon, they would either produce hissing, or blow the arc out, or both ; for in that case some of the gas got to the crater uncombined with the carbon vapour, and acted exactly as if it had been blown down the tubular positive carbon. An interesting proof that the air must be in contact with the crater to produce hissing is afforded by an experiment carried out by Cravatb, mentioned on page 63. He tried the effect of moving one carbon horizontally over the other, while a steady silent arc was burning. When the positive carbon was pointed and the negative flat, the arc burned silently as before, but when the negative carbon was pointed and the positive flat, each 308 THE ELECTRIC ARC. change of position caused a hiss. The reason is obvious. Each change of position caused a new crater to form of carbon that had previously been in contact with the air, and, consequently, still had some air clinging to it. The case, then, stands thus : (1) When the arc begins to hiss in the ordinary way, the P.D. between the carbons diminishes by about 10 volts. (2) If the air is excluded from the arc, this diminution of the P.D. does not take place, even when the current is nearly three times as great as would cause hissing in the air. (3) If, however, while the air is excluded, puffs of air are sent against the crater, the diminution of the P.D. does occur, even with currents much smaller than would cause hissing in the air. (4) If, instead of air, oxygen is sent against the crater, the P.D. is diminished to exactly the same extent as when air is used. (5) If, on the other hand, nitrogen is sent against the crater, no diminution of the P.D. is observable. (6) If air or oxygen is gently blown through the negative carbon, so that it cannot get direct to the crater, no diminution of the P.D. follows. Thus there can be no shadow of doubt that the sudden diminution of P.D. that accompanies the hissing of the open arc is due to the oxygen in the air getting directly at the crater and com- bining with the carbon at its surface. It only remains to show how the actual hissing sound may be produced by the burning of parts of the surface of the crater. The moment after this burning has begun, a cloud of gas, formed of the products of combustion, must spread over the burning part, protecting it momentarily from the action of the air as effectually as the carbon vapour had hitherto done. When this gas is dispersed the air will again come into contact with that part of the crater, a fresh cloud will form, and the whole action will start de novo. Thus a series of rushes and stoppages of the air will take place, setting up an irregular vibration of the very kind to cause a hissing noise. Not only this, however, but, since the crater must cease to burn each time that it is protected by the gas, the diminution of P.D. must also cease to exist at that part, since its cause is removed, and the P.D. will, therefore, rise momentarily. Thus an CAUSE OF HISSING SOUND. 309 oscillation of the P.D. between the carbons, and, consequently, of the electric current must be created, corresponding with the oscillation of the air current. That the air current does oscillate when the arc hisses was proved beyond a doubt by the following experiment. One end of a very fine single fibre of asbestos was fastened to the hole of the crucible shown in Fig. 86 through which the positive carbon was moved. Sufficient space was left between the hole and the carbon for the free end of the fibre to stretch out horizontally without touching the latter. While the arc was silent the fibre remained fairly motionless, but as soon as hissing began, instead of being sucked into the crucible, as it wonld have been with a steady inward current of air, it vibrated rapidly up and down, thus showing the oscillatory character of the current. The oscillation of the electric current was also proved beyond a doubt, by Messrs. Frith and Rodgers,* in 1893 ; and it has recently been shown, graphically, in the most convincing manner by the curves published by Messrs. Duddell and Marchant.t Mr. Duddell has since made much more detailed curves of the same kind which will shortly also be published. Thus we have seen that not only the sudden diminution of the P.D. between the carbons, but every other phenomenon that attaches to the hissing arc may easily be caused by the oxygen of the air getting directly at the crater, and combining with the carbon at its surface. SUMMARY. I. When the length of the arc is constant and the arc is silent, it may be made to hiss by increasing the current sufficiently. II. The largest current that will maintain a silent arc is greater the longer the arc. III. The hissing point always occurs on the flat part of the curve, at a point where the P.D. changes very slightly with change of current. * Phil. Mag., 1896, p. 407. f Journal lust. Elec. Eng., Vol. XXVIIL, pp. 78, 79. 310 THE ELECTRIC AtiC. IV. When the current is constant and the arc is silent, shortening it will make it hiss. V. A straight line law connects the P.D. at the hissing point with the length of the arc. VI. With a given pair of carbons the current cannot have more than a certain maximum value without causing the arc to hiss, however long it may be. VII. When the arc begins to hiss, the P.D. suddenly falls about 10 volts and the current suddenly rises. VIII. For the hissing arc the P.D. is constant for a given length of arc, whatever the current, and whether the carbons are cored or solid. IX. A straight line law connects this constant P.D. between the carbons with the length of the arc, when both carbons are solid, but not when the positive is cored. X. A straight line law connects the diminution of P.D. that accompanies hissing with the length of the arc. XI. The longer the arc, the less is the P.D. between the carbons diminished when hissing begins. XII. About two thirds of the diminution of P.D., when hissing begins, takes place at the junction of the positive carbon and the arc. The remainder is apparently due to a diminution of the resistance of the arc vapour, and none to any change in the P.D. between this vapour and the negative carbon . XIII. When the largest silent current changes to the smallest hissing current for the same length of arc, the value of that smallest hissing current depends only on the E.M.F. of the generator or the resistance in the circuit outside the arc, whichever is fixed first. XIV. When the arc is silent and the current small, the crater presents a uniformly bright appearance, but when the current is increased sufficiently, patches of bright and dark bands appear on it, whirling and oscillating faster and faster as the current is increased. XV. When the current is so great that the arc is near humming, the speed of revolution is too great to be detected by the eye, and it continues to increase to about 450 revolu- tions a second, when the arc begins to hiss. SUMMARY. 311 XVI. With humming and hissing, a green light appears in the crater, and with hissing, clouds partially cover the crater ; and the carbon vapour becomes flattened out between the carbons. XVII. With a short hissing arc a mushroom forms on the end of the negative carbon. XVIII. With a silent arc the end of the positive carbon is rounded, and the crater occupies the smallest cross-section of it. With a hissing arc the end is nearly or quite cylindrical, except where the crater has cut it away obliquely. XIX. Hissing is produced by the crater becoming too large to occti]>y t/te end only of the positive carbon, and by its therefore e,rtendi)ig up the side. XX. When the arc is enclosed in such a way that very little or no air can get to it, there is no sudden diminution in the P.D. between the carbons, even with currents three times as great as would produce that diminution with the open arc. XXI. If, however, whether the air is excluded or not, puffs of air are sent against the crater, the diminution of the P.D. does occur, even with currents much smaller than would ordinarily cause hissing. XXII. If, instead of air, oxygen is sent against the crater, the P.D. is diminished to exactly the same extent as when the air is used. XXIII. If, on the other hand, nitrogen or carbon dioxide is sent against the crater, no diminution of the P.D. is observable. XXIV. If air or any of the other gases are gently blown through the negative carbon, so that they cannot get direct to the crater, 710 diminution of the P.D. follows. XXV. Thus there can be no doubt that the sudden diminution of P.D. that accompanies the hissing of the open arc is due to the oxygen in the air getting directly at the crater and combining with the carbon at its surface. XXVI. Hydrogen, blown against the crater of a silent arc, causes hissing and a diminution of about 6'6 volts in the P.D. between the carbons, when the arc is open to the air. When, however, the arc is enclosed, so that air is excluded, no such effect can be observed. CHAPTER XL THE LIGHT EMITTED BY THE ARC. DIFFERENT CANDLE POWER IN DIFFERENT DIRECTIONS. MEAN SPHERICAL CANDLE POWER UNDER DIFFERENT CONDITIONS. LUMINOUS EFFI- CIENCY UNDER VARYING CONDITIONS. How TO OBTAIN THE MAXIMUM LUMINOUS EFFICIENCY UNDER ANY GIVEN CONDITIONS. The value of a source of light depends upon two conditions (1) the total amount of light that it emits, (2) the distribution of that light. It is absolutely essential to know both these factors in order to judge of the utility of the source, for a large total flux of light is of little use if emitted in the wrong direction, and a light may be all in the right direction, but so dim as to be practically valueless. Suppose, for instance, that the arc would only burn with the positive carbon underneath ; then, however brilliant it might be, it would be useless for street lighting ; for, although the tops of our houses would be well illuminated, the streets would be left in darkness. Again, imagine a farthing dip in a ball-room : though every ray were utilised, it would only suffice to make darkness visible. What we want to know about a source of light, then, is the quantity of light it emits and the direction of the light. Some sources are so constituted that it is physically im- possible to utilise all the light they emit. The very conditions under which they exist cause the obstruction of some of their light. Thus, while the light of a candle or a gas jet is practi- cally unobstructed, in paraffin and glow-lamps part of the light evolved is necessarily absorbed by the glass covering needed in the one case to create a sufficient draught of air to com- pletely consume the oil, and in the other to maintain a vacuum round the filament. In the arc there is a still greater difference between the quantity of light evolved and the 314 THE ELECTRIC ARC. amount that can be usefully employed, for the negative carbon usually obstructs far more of the light from the principal source the crater than would be absorbed by a clear glass covering. Moreover, with every change in the current or the length of the arc, in the diameter or construction of either carbon, the form of the negative carbon changes, and, conse- quently, the amount of the light that is obstructed changes also. Hence arise many complications in the laws governing the light of the arc, which vanish more or less completely when the amount of light evolved and the quantity that escapes and becomes perceptible to the eye are studied separately. The sources of light in the arc are (1) the crater, (2) the remainder of the hot end of the positive carbon, (3) the white- hot spot on the negative carbon, " the white spot," as I have called it, (4) the remainder of the hot end of the negative carbon, (5) the arc vapour. I shall call the light of the whole five sources together the light of the arc, and shall speak of the light emitted by the arc proper as the vapour light, or the light of the vapour. Not only the quantity but the proportion of the whole light emitted by each of the sources probably varies with each current and length of arc, as well as with the construction and thickness of either carbon. But in all cases by far the larger part of the light is due to the crater, the next greatest source being the white spot ; and, last of all, the hot sides of the carbons and the vapour, which, even when the arc is long enough to " flame," give comparatively little 'of the light. What the exact proportions are under any given set of -con- ditions, and how they change when the conditions change, has never yet been accurately determined ; nor, indeed, has much attention been paid, as far as separate photometric measurements of intensity are concerned, to the light of any other part of the arc but the crater. Sir William Abney discovered, for instance, as long ago as 1881,* that the quantity of light emitted per square millimetre of crater was practically a constant for a given quality of carbon, however the current and the length of the arc might be varied ; but whether the intrinsic brilliancy of the white spot, or of the vapour, is also a * Phil. Trans., 1881, Vol. CLXXIL, p. 890. . CANDLE POWER AND AREA OF CRATER. 315 constant, has never been determined. Similarly, it is known that with a given length of arc the area of the crater increases as the current increases, and I have shown (p. 154) that the area of the crater increases also, as the length of the arc is increased, with a given current ; but no attention whatever has been paid to the variations in the area of the white spot, which I have, nevertheless, found to depend as definitely on the current, though not on the length of the arc, as the area of the crater itself. The reason of this neglect is obvious. In the ordinary vertical arc with the positive carbon on top (which alone we are now considering) the light from the white spot must principally escape upwards, and can thus be of little use in the region far below the arc for which the light is needed. Thus, though this white spot is nearly, if not quite, as brilliant as the crater (though far inferior to it in extent), the light from it is, in a sense, unimportant. The light emitted by the arc vapour is also small compared with that of the crater, so that it also has received very little attention. In determining the light emitted by the arc then, the important points to consider are (1) the quantity of light given out by the crater, and (2) the extent to which this light is obstructed by the negative carbon. It must always have been noticed from the first that the negative carbon cuts off more or less of the brilliant light emitted by the crater ; but how much, under any given con- ditions, was never made clear till Mr. Trotter* put the whole matter in a nutshell by enunciating and proving experi- mentally the delightfully simple theorem that the great difference observable in the candle power of the arc in different directions is due solely to the different amounts of crater visible in those directions. He showed that in directions in which the view of the crater was entirely unobstructed, the candle power varied directly as the apparent area of the mouth of the crater, and that where it was obstructed by the negative carbon the candle power diminished in proportion to the increase of the obstruction. He found also that the light emitted by all parts of the arc and carbons except the crater was practically the same in all directions, with given carbons, current, and length of arc, as, of course, it would have to be for his theorem to be correct. * The Meet rk- ton, 1892, Vol. XXVIII., p. 687, and VoL XXIX-Tp. 11. 316 THE ELECTRIC ARC. The Light received from the Crater in Different Directions. Let us consider the light and the obstruction the crater and the negative carbon separately. Mr. Trotter began by correcting the erroneous impression frequently held, that the hollowing of the crater caused the light to be concentrated and cast downwards. He pointed out that the same amount of light was received from the crater in any direction as would be received in that direction from a disc of equal brightness fitting into the mouth of the crater. This is only absolutely true when none of the light is absorbed in its passage from the surface of the crater to its mouth. It will be seen later that it is more than probable that this condition is not entirely fulfilled ; but the error thus introduced is in most cases so small that we may neglect it, and consider the crater as a luminous disc of area equal to its mouth. Mr. Trotter's theorem is, then, that with the exception of a comparatively small quantity of light, which is constant for all directions, the candle power of the arc in any direction is directly proportional to the apparent area of the crater as seen from that direction. We may talk about the apparent area of the crater as looked at in a direction instead of from a point, because the diameter of the crater is always so small compared with the distance of the eye or the photometer screen from it that its apparent area is the same from all points in any one direction. Let AB, for instance (Fig. 88), be the diameter of the crater, and EC a direction in which it is viewed, then if the eye is at C, the apparent area of the crater will depend upon the angle B C A, and if it is at D it will depend upon the angle B D A. If D and C are both very far from A B, these two angles will be practically equal, and so the apparent areas of the crater, as seen from these two points, will be equal also. For the same reason the smallness of the crater compared with its distance from the eye the line joining the point from which it is viewed to any point on the crater may be called the direction in which it is viewed, for clearly when C is far away, CA, C B and C E are all parallel. Mr. Trotter pointed out that, when there is no obstruction the apparent area of the crater varies directly as the cosine of the inclination, that is, as the cosine of the angle between the APPARENT AREA OF CRATER. 317 plane through the mouth of the crater and a plane per- pendicular to the line joining the eye to the crater. In other words, the apparent area of the crater is proportional to the cosine of the angle between the direction from which it is viewed FIG. 88. Disc Viewed from a Great Distance. and the perpendicular to the mouth of the crater. This also is, of course, only strictly true when the diameter of the crater is small compared with its distance from the eye. A complete mathematical proof of it is given in the Appendix (page 441). 318 Til E ELECTRIC ARC. Mr. Trotter's experiments were very simple, but they were quite conclusive for the cases he tried. The apparent area of the crater, seen from different directions, was measured, and the candle-power of the arc in the same directions taken, and it was found that the two sets of values both varied as the (Trotter). 60. / \ 30. 50. 20. FIG. 89. Tracings of normal arc If full size. cosine of the inclination, for all directions in which the view of the crater was unobstructed. Mr. Trotter pointed out that when the radius vector of a polar curve is proportional to the cosine of the angle between APPARENT AREA OF CRATER, 319 it and the fixed line, the curve is a circle, of which the pole is one point. Thus, he argued, a polar curve with a line pro- portional to the apparent area of the crater as radius vector, and the inclination of the crater as the angle between the radius vector and the fixed line, must form a part of a circle. Hence, the candle-power of the crater, plotted as a polar curve, must also form a part of a circle for those directions in which (Trotter). 30. 15. FIG. 90. Tracings of Short Arc 1|- full size. the view of the crater is unobstructed, if this candle-power varies directly as the amount of crater visible. The tracings of the crater and the negative carbon that Mr. Trotter used to test his theory are given in Figs. 89 and 90. These show that with an inclination of 90, that is, when the eye was in a horizontal line with the plane of the crater, the crater could not be seen at all, as one would expect. With 320 THE ELECTRIC ARC. inclinations of from 90 to between 50 and 40, the crater was entirely unobstructed by the negative carbon, and with smaller inclinations the obstruction was greater the less the inclination. The apparent areas of the crater, and the candle-power of the arc, taken from the same points, are both plotted in Figs. 91 and 92, the angle between the radius vector and the fixed line being made equal to the inclination of the crater in each case. Triangles represent areas of crater, and crosses candle-power. It will be seen that the observations of areas and of candle- (Trotter.) 40 FIG. 91. Curve of Areas of Crater and Candle-Power of Normal Arc. A = area and x = candle-power. The scale of radii is arbitrary. powers coincide in a very remarkable manner with one another, and with a part of the circle which is the polar curve connect- ing the cosine of the inclination with the inclination. Fig. 93 shows the connection between candle-power and apparent area of crater, from different directions, with rectan- gular co-ordinates, ordinates representing candle-power and abscissae apparent areas of crater. The points lie very fairly well in a straight line which cuts the axis of candle-power at about 100. This, therefore, must have been the candle-power CANDLE POWER AND AREA OF CRATER. 321 of the white spot, the glowing ends of the carbons and the vapour, and the curve shows that the part of the candle- power of the arc that is due to these is practically the same in all directions, with a given current and length of arc and a given pair of carbons. Mr. Trotter's results were qualitative rather than quantita- tive ; his candle-powers were, in most cases, relative, and not absolute, but there can be no doubt, nevertheless, that he proved his point, and that the variable part of the candle- ( Trotter.) so' 10 20 80 FIG. 92. Curve of Areas of Crater and Candle-Power of Short Arc. A = area and x = candle-power. The scale of radii is arbitrary. power of the arc was very fairly proportional to the apparent area of the crater in the cases he tried. This carries with it, as he stated, the necessity for the light being uniformly dis- tributed over the crater also ; that is, his experiments show that, roughly, the quantity of light emitted per unit surface of the crater is constant over the whole surface, for otherwise the variable part of the candle-power would depend upon which part of the crater was visible from any point as well as upon how much. 322 THE ELECTRIC ARC. Although Mr. Trotter's experiments show that the light received from the crater is fairly uniform, his own later experiments and mine prove that it cannot be entirely so. For when a part of the crater is covered with the swiftly whirling figures that he discovered in 1894, and the more slowly moving ones that I showed at the Institution of Electrical Engineers in 1899, it is quite evident that more light per (Trotter.) muu 900 / / 800 700 600 / / / / 800 200 100 / / / | Light j ^ rom flai \ orange ie of arc parts.. i 20 40 60 80 100 120 140 160 180 200 Relative Areas. FIG. 93. Areas of Crater, and Light of Normal Arc. square millimetre must be received from the entirely bright parts of the crater than from the parts where there are dark bands. Quantity of Light Obstructed by Negative Carbon. We have next to consider how far the light emitted by the crater is obstructed by the negative carbon. If this carbon were of constant shape for all currents and lengths of arc, cleaily the amount of light obstructed by it would depend OBSTRUCTION OF LIGHT BY NEGATIVE CARBON. 323 simply on the length of the arc, for the farther the negative car- bon was from the crater the less crater light it would obstruct. This is by no means the case, however. As has already been mentioned, the shape of the negative carbon alters with every change in the current and the length of the arc, and alters more, for a given change, the shorter the arc and the smaller the current. With short arcs and large currents it is very sharply pointed, and the point becomes blunter the longer the arc and the smaller the current. Take, for instance, the diagrams for arcs of 3mm. in Fig. 8 (p. 10). There is con- siderably more difference in form in the negative carbons for currents of 6 and of 10 amperes than in those for currents of 16 and 21 amperes. Or, take the 6mm. arc: the difference between the negative carbons for 6 and 16 amperes is decidedly greater than between those for 16 and 30 amperes. Again, in the diagrams for 10 amperes in the same figure, the change in the negative carbon caused by lengthening the arc from 1mm. to 2mm., is greater than that caused by lengthening it from 2mm. to 3mm., and with a current of 6 amperes the difference between the negative carbons for 1mm. and 2mm. is greater than that caused by lengthening the arc from 2mm. to as much as 6mm. A comparison of the diagrams in Figs. 7, 8 and 9 (pp. 9, 10 and 12) shows that the shape of the negative carbon depends on the diameters of the carbons as well as on the current and the length of the arc. In order to study with greater ease the changes in the shape of the negative carbon, some of the diagrams in Figs. 7, 8 and 9 have been enlarged. In Fig. 94 the carbons and the current are constant, or nearly so, but the length of the arc is 1mm., 2mm. and 6mm,, going from left to right. There is a certain similarity in the forms of all three negative carbons : each has two shoulders a small one, of which the diameter is about the same as that of the crater, and a larger one, where the burning away of the sides of the carbon ceases. This larger shoulder is usually of rather greater diameter than the unburnt part of the carbon, because of the ragged fringe of frayed carbon that sticks out from its sides. The differences in the forms of the various negative carbons depend chiefly upon the relative diameters of the two shoulders and the distance between them, and on the shape T2 324 THE ELECTRIC ARC. and height of the point that rises above the smaller. Let us examine more closely the way in which the negative carbon interferes with the light of the crater. As the arc is practically an axially symmetrical source of light, we may, for theoretical purposes, examine the light in one plane passing through the axis of the two carbons, and whatever is true of the light in that one plane will be true of the light in all other planes passing through the axis, except in so far as any error is introduced by the carbons not being strictly in line, or the arc burning on one side. Let A B and A C represent, the one a diameter of the crater, and the other a line in the same plane, drawn from the end FIG. 94. Shape of Negative Carbon, with same Current but Different Lengths of Arc. of that diameter to touch the negative carbon, The angle between these two lines includes all the directions on the right-hand side of the arc from which an eye moving in the same plane as the two lines could see the crater unobstructed by the negative carbon. Hence, the angle B A C, or the mean of the two corresponding angles on either side of the arc, in the same plane, roughly measures that part of the crater light that is unobstructed by the negative carbon. Next, if B D be drawn to meet the lower shoulder of the negative carbon in D, B D is the nearest direction to the OBSTRUCTION OF LIGHT BY NEGATIVE CARBON. 325 vertical in which any of the crater can be seen at all. That is to say, the angle E B D is the largest angle that the line joining the eye to the crater can make with the horizontal for any portion of the crater to be visible. We now have in the angle B A C a rough measure of the total quantity of light received from the crater in one plane in directions in which it is unobstructed by the negative carbon, and a similar rough measure of the quantity received in directions in which it is partially obstructed in the angle B F A, which is equal to the angle E B D minus the angle BAG. It will be observed that the second is only a very rough measure indeed, for the amount of light obstructed depends on the shape of the negative carbon between the points C and D, even more than on the angle BFA. Take, for instance, the 1mm. and 2mm. arcs in Fig. 94, and compare the angle F A G in the one with the same angle in the other. This angle, which lies between the line touching the point of the negative carbon and the line touching the smaller shoulder, includes all the directions from which only a very little of the crater is hidden. Now, in the 1mm. arc this angle is more than four times as great as in the 2mm. arc, and in the 6mm. arc it does not exist at all, for the lines A C and A G coincide. Hence, although the unob- structed crater light is much less in the 1mm. arc than in the 2mm. arc, that which is only slightly obstructed is much greater in the 1mm. arc, and it is thus possible that the total amount of light received from the crater of the 1mm. arc may be as great as, or even greater than, that received from the crater of the 2mm. arc. The Light emitted by a very short Arc is greater than when the Arc is longer, with a large Constant Current. It is, of course, only the proportion of the crater light that gets out, compared with the whole light emitted by the crater that can be estimated in this way ; but when the areas of two craters are equal, or nearly so, a very good rough comparison of the relative mean spherical candle-powers of the two arcs can be made by comparing the sizes of the angles B A C, C A G, and E BD in each. JSow the 1mm. and 2mm. arcs in Fig. 94 have craters of very much the same area; for although (see 326 THE ELECTRIC ARC. p. 154) this area does increase as the arc is lengthened, even when the current is constant, yet the increase in this case is so small that I have calculated it to be only about a half per cent. Thus the relative candle-powers of the two arcs may well be estimated by the above method, which seems to show that, in this one instance at any rate, the mean spherical candle power of the 1mm. arc was at least equal to that of the 2mm. arc. This conclusion, so contrary to the generally accepted ideas, and arrived at by a mere examination of the shape of the negative carbon, could not, however, be accepted without reference to actual candle-power experiments. Let us see what these say. Screen. SCALE OF FEET I .i. Arc. FIG. 95. Side View of Three Mirrors, A, B and C, throwing the Light of the Arc through a Slit on to the Screen. Table L. shows the results of the experiments on the mean spherical candle-power of the arc made for the Paper read by Prof. Ayrton at the Electrical Congress at Chicago in 1893. They were obtained by taking what I may call a sample of the light with each current and length of arc. The arc was enclosed in a light-tight box (of which one side is seen in elevation in Fig. 95), and a wedge of light was allowed to escape, through a slit of constant width, long enough to allow the light in all directions in one vertical plane to pass. This wedge of light was received on a screen of white blotting paper (Fig. 96), and in order that the whole of the light in the one vertical plane in which it was being measured MEASUREMENT OF THE LIGHT. 327 g should be collected on the screen, the .$ lower part of the light was reflected from the three plane mirrors A, B and C (Fig. 95) on to the screen. From the -fib blotting paper the light was reflected on to the fixed photometer screen, and was compared with that of a 2 c.p. Methven Standard, which was movable along a | 2 bar graduated directly in mean spherical candles. Corrections were made for the light absorbed by the mirrors and the 2 to blotting paper, and thus the mean spheri- g -^ cal candle-power for each arc was obtained fl ^|j *ls at one reading, or rather in one series pq -^ of readings, for the mean of from 6 to "^ jB 12 readings was taken in each case. The o % carbons employed were 13mm. cored posi- J 7, tive and llmm. solid negative. For currents of 4, 7 and 10 amperes, g o the candle-power of the 2mm. arc is J'g greater than that of the 1mm. arc, but for currents of 15 and 20 amperes it is considerably less, and with a current of J a 32 amperes the 1mm. arc gives more light j & than the 2mm. arc does with a current w of 32'5 amperes. Thus with currents | that are fairly small for the sizes of the ^ .B carbons, the longer arc gives the larger 3 amount of light, but for currents great .3 ^ enough for the negative carbon to be ,2 HH~ sharply pointed, as it was in Fig. 94, the shorter arc does actually give the larger amount of light. These experiments, therefore, confirm the conclusions gathered from a comparison of the shapes of the negative carbons, and show that with short arcs and large currents the candle- power of the arc may first diminish and then increase again as the arc is lengthened. 328 THE ELECTRIC ARC. Table L. Mean Spherical Candle-power of Arcs of Different Lengths with various Constant Currents. Carbons: Positive, I3mm., cored; neijati-ce % llwiw., solid. Current in Amperes. Mean Spherical Candle-power. 1mm. 2mm. 3mm. 4mm. 6mm. 4 70 103 78 105 6 238 247 7 270 280 353 326 10 560 700 736 900 11 730 15 1,220 904 1,087 1,480 1,180 20 1,754 1,586 1,714 2,300 1,914 23-5 ., 1,874 23-75 3,204 24 ., 2,486 25 ,. 3,332 32 2,880 3,600 32-5 2,600 34 . , 3,870 35 ... 4,732 ... It seems probable that the length of arc with which the candle-power is a minimum diminishes as the current diminishes, with carbons of any given size. For the smaller the current the shorter must be the arc in order that the negative carbon should have a sharp point Thus it is most likely that if Prof. Ayrton's experiments had been carried on with arcs of less than 1mm., a minimum value for the candle- power with a current of 10 amperes would have been found for some length of arc between Omm. and 1mm. When the current is very small for the sizes of the carbons, however, the negative carbon never becomes sharply pointed, however short the arc may be, and in that case the light obstructed by the negative carbon must steadily increase, as the arc is shortened, till the carbons touch. The curves in Fig. 97, which are plotted from Table L., show very clearly how the mean spherical candle-power decreases and then increases again with the short arcs and large currents. Among the very complete and beautiful series of experiments on the total flux of light emitted by the direct current arc, CANDLE POWER AND LENGTH OF ARC. 329 made by M. Blondel,* and published in 1897, were several in which the current was kept constant and the arc was lengthened from to many millimetres. M. Blondel plotted curves connecting the flux of light with the P.D. between the carbons instead of with the length of the arc, and hence the phenomenon under discussion escaped his observation. Never- theless, indications of it are not wanting in his experiments, (Ayrton.) 4,500 4,000 3.500 3.0CO 2,500 2,000 1,500 1,000 10 Arrips Length of Arc In Millimetres. Flu. 97. Curves connecting Mean Spherical Candle Power with Length of Arc. Carbons : Positive, 3mm., cored ; Negative, 13mm., solid. notably in the two curves in Fig. 98, which are plotted from the numbers given by M. Blondel for Curves I. and III. in Table III., p. 296, of his articles. M. Blondel's method of measurement was the same in principle as Prof. Ayrton's. He placed the arc in the centre of an opaque sphere, on opposite sides of which were two * L'Edairge Elcctriquc, 1897, Vol. X., pp. 289, 496, 539. 330 THE ELECTRIC ARC. vertical openings of 18 each (Fig. 99). The whole of the light that escaped from these two slits was caught by an elliptic mirror M (Fig. 100), and reflected on to a screen of white blotting paper, and the illumination of this screen was measured by means of the " Universal Photometer," invented by M. Blondel himself. (Blonde). ) 12,000 11,000 10,000 8,000 7,000 6,000 14/IJ 1 2 3 Length of Arc in Millimetres. FIG. 98. Curves connecting Total Light emitted with Length of Arc. Positive Carbon cored ; negative solid. M. Blondel preferred to measure the total flux of light emitted by the arc rather than the mean spherical candle power, and the unit he employed was the " lumen," or the total flux produced by a source having a uniform intensity of one decimal candle in a solid angle, cutting off one square millimetre of surface from a sphere of radius 1mm. As the total flux of light emitted by a source is numerically equal to BLONDEUS APPARATUS FOR MEASURING ARC LIGHT. 331 4?r times the mean spherical candle power, M, Blondel's numbers have only to be divided by 4?r to give the mean spherical candle power of the arc in decimal candles, a unit FIG. 99. Apparatus employed by M. Blondel in Measuring the Total Light emitted by the Arc. ,.<'-\r FIG. 100. Arrangement of Apparatus used by M. Blondel. = Arc, M = Lunienonieter, G Diffusing Screen of White Blotting Paper, P = Photometer Screen . 332 THE ELECTRIC ARC. which is one-twentieth part of the Violle unit. As this unit is not universally adopted, however, it will be better to leave M. Blondel's results in lumens. For the upper curve in Fig. 98, the carbons employed were "Nanterre," 8mm. cored positive and 6mm. solid negative. For the lower curve they were both 10mm., the positive cored and the negative solid. The constant current was 10 amperes in both cases. Both curves show a tendency on the part of the light emitted to diminish or at most to remain constant as the length of the arc is increased from 1mm. to 2mm. in the one case, and from 0-5mm. to 1mm. in the other.* Thus M. Blondel's experiments also confirm the conclusion reached by a simple examination of the diagrams of arcs and carbons, in Fig. 94, viz. : that with certain currents the lighting power of the arc, after increasing at first as the carbons are sepa- rated, diminishes or remains stationary as the arc is further lengthened, and then increases again. With a Constant Current the Illuminating Power of the, Arc, Increases to a Maximum as the Arc is Lengthened, and then Diminishes again. To return to Fig. 94. When once the arc is long enough for the point of the negative carbon to have become quite blunt and round, it is plain that lengthening the arc can only enlarge both the angles, BAG and EBD, on which the amount of crater light that escapes depends. We should, there- fore, gather from this figure that the amount of light received from the crater must increase continually as the arc is lengthened beyond about 2mm. and if Mr. Trotter's theorem is correct in all cases, it follows that the candle power of the arc must also increase continuously as the arc is lengthened. To see whether this is so, we must turn again to Fig. 97, taken from Prof. Ayrton's experiments. These curves do not seem to bear out the deduction made from the shape of the negative carbon, for they prove that, far from increasing con- tinually as the arc is lengthened, the illuminating power of * The lengths of arc corresponding with P.Ds. of 43 '5 volts in the upper curve and 48'7 volts in the lower were not given by M. Blondel, and were therefore found by plotting the curves connecting the other P.Ds. with the corresponding lengths of arc in each case. TOTAL LIGHT AND LENGTH OF ARC. 333 the arc increases only till it is of a certain length, and then diminishes again as it is further lengthened. This most inte- resting and important point was first noticed by Prof. Ayrton, who announced it in the Paper he read before the Electrical 334 THE ELECTRIC ARC. Congress at Chicago in 1893. At the same time Prof. Carhart mentioned that he had found the luminous intensity of the arc to be a maximum with a certain definite P.D. between the carbons , the P.D. depending on the nature and size of the carbons. As the P.D. between the carbons, for any particular current, is determined by the length of the arc, it is plain that the two TOTAL LIGHT AND LENGTH OF ARC. 335 discoveries were identical, though I shall show later that Prof. Ayrton's was the more correct way of putting it, and that the maximum illuminating power depends directly on the length of the arc, and therefore only indirectly on the P.D. between the carbons. M. Blonde], as I have mentioned before, drew no curves connecting the length of the arc with any of the other variables, but, from the tables he gave of the results of his experiments, I have drawn the curves in Figs. 101 and 102, connecting the total light emitted by the arc with its length. For Fig. 101 both carbons were solid, and their sizes varied from 8mm. and 6mm. to 16mm. and 14mm., while for Fig. 102 the positive carbon was cored and the negative solid, and their sizes varied from 8/6 to 18/14. (This is a very convenient way, adopted by M. Blondel, of denoting the sizes of carbons. The left-hand figure always gives the diameter of the positive carbon in mm., and the right-hand that of the negative.) The current was 10 amperes in all cases. In both sets of curves, in every case where the arc was made sufficiently long, the light flux increased to a maximum and either remained stationary or diminished as the arc was further lengthened. Thus both Prof. Ayrton's and M. BlondePs experiments contradict the evidence of the diagrams of the arc and carbons, and, in order to find out where the error arises, it will be well to inquire a little more in detail into the manner in which the most important part of the light the crater light varies when the current is kept constant and the arc is lengthened. For this purpose the diagrams in Fig. 103 will be found useful. They were taken from arcs of Jmm., 1*1 mm., 2mm., 3 '2mm. and 6*6mm., burning between 18mm. cored and 15mra. solid carbons, with a constant current of 20 amperes flowing. On the assumption that Mr. Trotter's theorem was true for the arcs from which these diagrams were taken, it will be possible, with the help of Rousseau's method of finding the total light received from an axially symmetrical source, to construct figures of which the areas will be proportional to the total quantity of light received from the craters of the arcs. Then, taking the number of square millimetres in each area as abscissa, and the corresponding length of arc as ordinate, we shall be able to draw the curve connecting the total quantity of light THE ELECTRIC ARC. 1 s a Q a s ! I a a S s I 1 UNOBSTRUCTED CRATER LIGHT. 337 received from the crater with the length of the arc, for the constant current of 20 amperes. If, then, to each ordinate we add a length equivalent to the quantity of light received from the remaining four sources in the arc of corresponding length, we should, if our premises and measurements have been correct, get a curve of the same general form as those in Figs. 97 and 102. Rousseau's figures* can only be drawn for axially symmetrical sources of light, and although the arc is this theoretically, yet it is so in theory only, for the carbons are rarely perfectly in line, and consequently the arc is seldom quite central. To minimise this source of error, we shall use only measurements which are the mean of the measurements made on either side of the diagram in each case. For instance, instead of taking the angle BAG (Fig. 103) as the angle containing all the directions from which the whole crater can be seen, we shall take the mean of the two angles BAG and A B H ; and so on with all the other measurements. To Find, from a Diagram of the Arc and Carbons, a Figure proportional to the Total Amount of Light received from the Crater. Let us first consider the figure that would represent the total light received from the crater if none of it were cut off by the negative carbon. Let A (Fig. 104) be the centre of the mouth of the crater. The distance between the crater and any point at which the light from it is measured is always so great, compared with the diameter of the crater, that the light may all be considered to come from one point. Thus, by Trotter's theorem, we have to find the total light received from a point A, when the quantity of light received in any direction is proportional to the cosine of the angle that that direction makes with the vertical, the unit quantity of light being the light emitted by one square millimetre of crater. With centre A and unit radius describe the circle BCD, cutting the horizontal at B and D and the vertical at C. Draw the tangents B E and C E, and produce C E to F, making * A detailed description of the manner in which these figures are drawn to represent the total light received from an axially symmetrical source is given in the Appendix (p. 448), 338 THE ELECTRIC ARC. EF proportional to the light that would be received from the crater in a vertical direction, i.e., proportional to the area of the crater. Let A G be another direction from which the light is measured, and draw G H K parallel to C F, making H K pro- portional to the light received in the direction A G. Join F K and KB, and draw GM parallel to AC. Then by Trotter's theorem HK_cosGAC E *' cos GM C E FIG. 104. Figure used in finding Total Light received from Crater if none were obstructed by Negative Carbon. Therefore B, K, and F are in one straight line, and B F must be the locus of the ends of all lines drawn in a manner similar to H K, each proportional to the light received from the crater in some given direction between A B and A C. But the figure representing the total light received from the source in one plane is that which is included between B E, E F, and this locus. Hence the triangle B E F must be the figure of which the area is proportional to the whole light that would be received from the crater in one plane if none of it were cut off by the negative carbon, and 2?r x area B E F is the total quantity of light that would be received from the crater in all directions if none were cut off by the negative carbon. We have thus the means of drawing a series of triangles, of which the areas would represent the total light that would be received from the craters of the arcs of which diagrams are AREA PROPORTIONAL TO TOTAL CRATER LIGHT. 339 given in Fig. 103, if none of the light were cut off by the negative carbon. We have only to draw triangles having their bases proportional to the areas of the craters in the diagrams and their heights all equal to B E. In order to compare the quantities of light actually received from the craters, however, this is not sufficient, we must know what part of the light is cut off by the negative carbon. To find this, let BAG (Fig. 105) be the mean of the two angles B AC and ABH in 1, Fig. 103, and let BAN be the mean of the two angles E B D and K A M in the same figure. Then the triangle BHK represents the whole light received from the crater in directions in which the whole crater can be seen, and no light will be received from it at all in any direction nearer to the vertical than AN. Therefore the c E F FIG. 105. Figure proportional to Total Light received from Crater. figure representing the total light received from the crater when part of it is cut off by the negative carbon must be bounded by P B, B K, and a curve which starts at K and ends at P. One point on this curve, if well chosen, will be sufficient to show what the shape of the curve must be, for we know that the occultation produced by the negative carbon must both increase and diminish quite gradually, so that the curve must join both B K and B P quite smoothly. The best point to take is that belonging to the direction in which the occultation begins to be serious, the point corresponding with the direction that just touches the larger shoulder of the negative carbon. Let A Q (Fig. 105) be this direction, then RS is the line representing the total light that would be received from the crater in the direction A Q if none of it were 22 340 THE ELECTRIC AEG. cut off by the negative carbon. To find how much of the light in this direction is cut off, we must turn to Fig. 106. Let AB be the direction in which the light is being received, and let C D be the tangent to the negative carbon that is parallel to A B. Then, since both eye and photometer screen are far from the crater, all the rays of light that reach the eye from the crater will be parallel to A B, and all rays parallel to A B that enter the negative carbon will be cut off from the eye. The outermost of these rays are those that just touch the negative carbon, so that to determine what region of the crater is obscured by the negative carbon from an eye looking at it FIG. 106. To find the Quantity of Light obscured by the Negative Carbon in any one direction. in the direction BA, we must find what is the area of the crater that is cut off by these tangent rays. The true area of this part is that which would be cut off from the crater by the horizontal section of the negative carbon through D, if it were moved parallel to itself along the line D C. The apparent area, to which the light cut off is proportional, is the true area multiplied by cos D C H, where C H is the vertical. As all horizontal sections of the negative carbon are practically circular, this true area would be that cut off from the crater by a circle in the same plane, having C F = D G for its diameter, To find this area, let A E, AC, OF (Fig. 107) be AREA OF. GRATER OBSCURED BY NEGATIVE. 341 equal to the corresponding lengths in Fig. 106, and draw the circle E G H, representing the area of the mouth of the crater, and having B for its centre, and draw F G H equal to the area of the cross-section of the negative carbon at D, and having D for its centre. Then A G C H is the area of that part of the crater from which the rays in the direction A B (Fig. 106) are cut off by the negative carbon. FIG. 107. Geometrical Construction for the Area of Crater obscured by the Negative Carbon in any one direction. To find this area, draw G H meeting A C in K, and join BG, BH, DG, and D H. Let r = A B, the radius of the mouth of the crater. r'= CD ,, horizontal section through D. x = AC y = G K or K H. Let be the angle G B H in degrees, and a' GDH Then the area A G H is - G K, K B ; the area C G H is ~ r ^- G K, D K ; loU /. the area A G C H = a7r r 2 + " %' 2 - G K (B K + K D) 180 180 180 r 2 + aV 2 ) - 342 THE ELECTRIC ARC. Thus the required area has been found in terms of quantities, all of which are easily obtainable for any given arc by drawing such a figure as Fig. 107 from a diagram such as those in Figs. 94 and 106. The ratio of the above area to the area of the crater is the ratio of the part of the crater light cut off in the direction AB (Fig. 106) to the whole light emitted in that direc- tion. If, then, AQ (Fig. 105) represents the direction AB (Fig. 106) i.e., if the angle B A Q (Fig. 105) = the angle E A B (Fig. 106), then, to find what part of the line R S represents the light received from the crater in the direction A B we must take a point T such that S B, ; S T ; \ area of crater (Fig. 106) : area GAHC (Fig. 107), and the curve bounding the figure representing the total light received from the crater must pass through T. We now have four points, B, K, T and P, through which the curved part of the figure must pass, and thus we can draw the figure B K T P R H, of which the area is proportional to the total light received from the crater in one plane. The numerical value of the total light received from the crater in all directions is 2?r x area B K T P R H, when the unit of light is the quantity of light emitted by a square millimetre of crater. If, however, we take as our unit of light the quantity of light emitted by a square millimetre of crater multiplied by 2?r, the area B K T P H (Fig. 105) will then represent the total light received from the crater in all directions in those units. Curves deduced from Diagrams in Fi