Electricity & Matter - J.J. Thompson

8/8/2019 Electricity & Matter - J.J. Thompson

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SILLIMAN MEMORIAL LECTURESPUBLISHED BY YALE UNIVERSITY PRESSELECTRICITY AND MATTER. By Joseph John Thomson,

D.Sc, LL.D., Ph.D., F.R.S., Fellow of Trinity College. Cambridge;Cavendish Professor of Experimental Physics, Cambridge. {Fourthprinting.) Price $1.25 net.

THE INTEGRATIVE ACTION OF THE NERVOUS SYSTEM.By Charles S. Sherrington, D.Sc, M.D., Hon. LL.D. Tor.,F.R.S., Boll Professor of Physiology, University of Liverpool.{Fourth printing.) Price $3.50 net.

RADIOACTIVE TRANSFORMATIONS. By Ernest Ruther-ford, D.Sc, LL.D., F.R.S., Macdonald Professor of Physics,McGill University. Price $3.50 net.

EXPERIMENTAL AND THEORETICAL APPLICATIONS OFTHERMODYNAMICS TO CHEMISTRY. By Dr. WaltherNernst, Professor and Director of the Institute of Physical Chemistryin the University of Berlin. Price $1.25 net.

PROBLEMS OF GENETICS. By William Bateson, M.A.,F.R.S., Director of the John Inncs Horticultural Institution, MerlonPark, Surrey, England. {Second printing.) Price $4.00 net.

STELLAR MOTIONS. With Special Reference to Motions Deter-mined by Means of the Spectograph. By William WallaceCampbell, ScD., LL.D., Director of the Lick Observatory, Universityof California. Price $4.00 net.

THEORIES OF SOLUTIONS. By Svante Arrhenius, Ph.D.,ScD., M.D., Director of the Physico-Chemical Department of theNobel Institute, Stockholm. Sweden. {Third printing.) Price$2.25 net.

IRRITABILITY. A Physiological Analysis of the General Effect ofStimuli in Living Substances. By Max Verworn, M.D., Ph.D.,Professor at Bonn Physiological Institute. {Second printing.)Price $3.50 net.

PROBLEMS OF AMERICAN GEOLOGY. By William NorthRice, Frank D. Adams, Arthur P. Coleman, Charles D.Walcott, Waldemar Lindgren, Frederick Leslie Ransome,AND William D. Matthew. Price $4.00 net.

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ELECTRICITY ANDMATTER

BYJ. J. THOMSON, D.Sc, LL.D., Ph.D., F.R.S.FELLOW OF TRINITY COLLEGE, CAMBRIDGE; CAVENDISH

PROFESSOR OF EXPERIMENTAL PHYSICS, CAMBRIDGE

WITH DIAGRAMS

Ifcfci.^*^I. II al

NEW UAVEN: YALE UNIVERSITY PRESSMDCCCCIV


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Copyright, igo4By Yale University

8CPublished, March, 1904Second printing, October, 191 2 .Third printing, December, 1913 Fourth printing, November, 1916 \ dX


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THE SILLIMAN FOUNDATION.In the year 1883 a legacy of eighty thousand dollarswas left to the President and Fellows of Yale College

in the city of New Haven, to be held in trust, as agift from her children, in memory of their beloved andhonored mother Mrs. Hepsa Ely Silliman.On this foundation Yale College was requested anddirected to establish an annual course of lectures de-signed to illustrate the presence and providence, thewisdom and goodness of God, as manifested in thenatural and moral world. These were to be designatedas the Mrs. Hepsa Ely Silliman Memorial Lectures. Itwas the belief of the cestator tnat any orderly presenta-tion of the facts of nature or history contributed tothe end of this foundation more effectively than anyattempt to emphasize the elements of doctrine or ofcreed; and he therefore provided that lectures on dog-matic or polemical theology should be excluded fromthe scope of this foundation, and that the subjects shouldbe selected rather from the domains of natural scienceand history, giving special prominence to astronomy,chemistry, geology, and anatomy.

It was further directed that each annual course shouldbe made the basis of a volume to form part of a seriesconstituting a memorial to Mrs. Silliman. The memo-rial fund came into the possession of the Corporationof Yale University in the year 1902; and the presentvolume constitutes the first of the series of memoriallectures.


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PREFACEIn these Lectures given at Yale University in

May, 1903, I have attempted to discuss the bear-ing of the recent advances made in ElectricalScience on our views of the Constitution of Matterand the Nature of Electricity; two questionswhich are probably so intimately connected, thatthe solution of the one would supply that of theother. A characteristic feature of recent Electri-cal Researches, such as the study and discoveryof Cathode and Rontgen Kays and Radio-activeSubstances, has been the very especial degree inwhich they have involved the relation betweenMatter and Electricity.In choosing a subject for the Silliman Lectures,

it seemed to me that a consideration of the bear-ing of recent work on this relationship might besuitable, especially as such a discussion suggestsmultitudes of questions which would furnish ad-mirable subjects for further investigation by someof my hearers.

Cambridge, Aug., 1903.J. J. THOMSON.


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CONTENTSCHAPTER- I PAOB

Representation of the Electric Field by LinesOF Force 1

CHAPTER IIElectrical and Bound Mass 36

CHAPTER IIIEffects Due to the Acceleration of Faraday

Tubes 53

CHAPTER IVThe Atomic Structure op Electricity ... 71

CHAPTER VThe Constitution op the Atom..... 90

CHAPTER VIRadio-activity and Radio-active Substances . . 140


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ELECTRICITY AND MATTERCHAPTER I

EEPEESENTATION OF THE ELECTEIC FIELDBY LINES OF FOECEMy object in these lectures is to put before you

in as simple and untechnical a manner as I cansome views as to the nature of electricity, of theprocesses going on in the electric field, and of theconnection between electrical and ordinary matterwhicli have been suggested by the results of recentinvestigations.The progress of electrical science has been

greatly promoted by speculations as to the natureof electricity. Indeed, it is hardly possible tooverestimate the services rendered by two theoriesas old almost as the science itself ; I mean thetheories known as the two- and the one-fluidtheories of electricity.The two-fluid theory explains the phenomenaof electro-statics by supposing that in the universethere are two fluids, uncreatable and indestruc-


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2 ELECTRICITY AND MATTERtible, whose presence gives rise to electrical effects ;one of these fluids is called positive, the othernegative electricity, and electrical phenomenaare explained by ascribing to the fluids the fol-lowing properties. The particles of the positivefluid repel each other with forces vaiying inverselyas the square of the distance between them, as doalso the particles of the negative fluid; on theother hand, the particles of the positive fluid at-tract those of the negative fluid. The attractionbetween two charges, tr and ??i', of opposite signsare in one form of the theory supposed to beexactly equal to the repulsion between twocharges, w and m of the same sign, placed inthe same position as the previous charges. In an-other development of the theory the attraction issupposed to slightly exceed the repulsion, so as toafford a basis for the explanation of gravitation.The fluids are supposed to be exceedingly mo-

bile and able to pass with great ease through con-ductors. The state of electrification of a body isdetermined by the difference between the quanti-ties of the two electric fluids contained by it ; if itcontains more positive fluid than negative it ispositively electrified, if it contains equal quantities.it is uncharged. Since the fluids are uncreatable


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LINES OF FORCE 3and Indestnictible, the appearance of tlie positivefluid in one place must be accompanied by thedeparture of the same quantity from some otherplace, so that the production of electrification ofone sign must always be accompanied by the pro-duction of an equal amount of electrification ofthe opposite sign.On this view, every body is supposed to con-sist of three things : ordinary matter, positive elec-tricity, negative electricity. The two latter aresupposed to exert forces on themselves and oneach other, but in the earlier form of the theoryno action was contemplated between ordinarymatter and the electric fluids ; it was not until acomparatively recent date that Helmholtz intro-duced the idea of a specific attraction betweenordinaiy matter and the electric fluids. He did thisto explain what is known as contact electricity,i.e.^ the electrical separation produced when twometals, say zinc and copper, are put in contactwith each other, the zinc becoming positively, thecopper negatively electrified. Helmholtz sup-posed that there are forces between ordinary mat-ter and the electric fluids varying for differentkinds of matter, the attraction of zinc for positiveelectricity being greater than that of copper, so


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LINES OF FORCE 5just as the particles of the negative fluid do onthe two-fluid theory. Matter when unelectrifiedis supposed to be associated with just so much ofthe electric fluid that the attraction of the matteron a portion of the electric fluid outside it is justsufficient to counteract the repulsion exerted onthe same fluid by the electric fluid associated withthe matter. On this view, if the quantity of mat-ter in a body is known the quantity of electricfluid is at once determined.The services which the fluid theories have ren-

dered to electricity are independent of the notionof a fluid with any physical properties ; the fluidswere mathematical fictions, intended merely to givea local habitation to the attractions and repulsionsexisting between electrified bodies, and served asthe means by which the splendid mathematicaldevelopment of the theory of forces varying in-versely as the square of the distance which wasinspired by the discovery of gravitation could bebrought to bear on electrical phenomena. Aslong as we confine ourself to questions which onlyinvolve the law of forces between electrified bodies,and the simultaneous production of equal quantitiesof -j- aiid electricity, both theories must givethe same results and there can be nothing to


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6 ELECTRICITY AND JVIATTERdecide between them. The physicists and mathe^maticians who did most to develop the ''FluidTheories " confined themselves to questions of thiskind, and refined and idealized the conception ofthese fluids until any reference to their physicalproperties was considered almost indelicate. It isnot until we investigate phenomena which involvethe physical properties of the fluid that we canhope to distinguish between the rival fluid the-ories. Let us take a case which has actuallyarisen. We have been able to measure the massesassociated with given charges of electricity ingases at low pressures, and it has been found thatthe mass associated with a positive charge is im-mensely greater than that associated with a nega-tive one. This difference is what we shouldexpect on Franklin's one-fluid theory, if thattheory were modified by making the electric fluidcorrespond to negative instead of positive elec-tricity, while we have no reason to anticipate sogreat a difference on the two-fluid theory. Weshall, I am sure, be struck by the similarity be-tween some of the views which we are led to takeby the results of the most recent researches withthose enunciated by Franklin in the very infancyof the subject.


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g ELECTRICITY AND MATTERdo this by the conception of lines of force. As Ishall have continually to make use of this method,and as I believe its powers and possibilities havenever been adequately realized, I shall devotesome time to the discussion and development ofthis conception of the electric field.\ifiar;^r-rTTj\ry.-r:- v !,_:: .-.,- r ^i^vs-ss-s.-^-^-^'-^"--'--''- ^ ^w. .._;,. , ^- .f:T,-s'-fj:v.'.'fTi j

V^H'i.v //'/


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10 ELECTRICITY AND ]VIATTERthem witli physical properties so as to explain tliephenomena of the electric field. Thus he sup-posed that they were in a state of tension, andthat they repelled, each other. Instead of an in-tangible action at a distance between two electri-fied bodies, Faraday regarded the whole spacebetween the bodies as full of stretched mutuallyrepellent springs. The charges of electricity towhich alone an interpretation had been given onthe fluid theories of electricity were on this viewjust the ends of these springs, and an electriccharge, instead of being a portion of fluid confinedto the electrified body, was an extensive arsenalof springs spreading out in all directions to allparts of the field.To make our ideas clear on this point let usconsider some simple cases from Faraday's pointof view. Let us first take the case of two bodieswith equal and opposite charges, whose lines offorce are shown in Fig. 2. You notice that thelines of force are most dense along A B, the linejoining the bodies, and that there are more linesof force on the side of A nearest to B than onthe opposite side. Consider the effect of thelines of force on A ; the lines are in a state oftension and are pulling away at A] as there


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LINES OF FORCE 11are more pulling at A on the side nearest to than on the opposite side, the pulls on A towardJ^ overpower those pulling A away from J?, sothat A will tend to move toward B; it was inthis way that Faraday pictured to himself theattraction between oppositely electrified bodies.Let us now consider tlie condition of one of thecurved lines of force, such as I^Q; it is in a state

Fig. 2.

of tension and will therefore tend to straightenitself, how is it prevented from doing this andmaintained in equilibrium in a curved position ?AVe can see the reason for this if we rememberthat the lines of force repel each other and thatthe lines are more concentrated in the region be-tween JPQ and AB than on the other side ofBQ; thus the repulsion of the lines inside BQwill be greater than the rej^ulsion of those out-side and the line PQ will be bent outwards.


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12 ELECTRICITY AND JMATTERLet US now pass from the case of two oppositely

electrified bodies to that of two similarly elec-trified ones, tlie lines of force for which are shownin Fig. 3. Let us suppose A and J^ are positivelyelectrified ; since the lines of force start frompositively and end on negatively electrified bodies,the lines starting from A and i? will travel awayto join some body or bodies possessing the

Fig. 3.

negative charges corresponding to the positiveones on A and ; let us suppose that thesecharges are a considerable distance away, so thatthe lines of force from A would, if I^ were notpresent, spread out, in the part of the field underconsideration, uniformly in all directions. Considernow the effect of making the system of lines offorce attached to A and ^ approach each other ;


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LINES OF FORCE 13since tliese lines repel each other the lines of forceon the side of A nearest J3 will be pushed to theopposite side of A, so that the lines of force willnow be densest on the far side of A ; thus thepulls exerted on A in the rear by the lines offorce will be greater than those in the front andthe result will be that A will be pulled awayfrom . We notice that the mechanism produc-ing this repulsion is of exactly the same type asthat which produced the attraction in the pre-vious case, and we may if we please regard therej)ulsion

between A and JS as due to the attrac-tions on A and of thecomplementary negativecharges which must exist inother parts of the field.The results of the repul- .

sion of the lines of forceare clearly shown in the caserepresented in Fig. 4, thatof two oppositely electrifiedplates; you will notice thatthe lines of force betweenthe plates are straight exceptnear the edges of the plates ; this is what weshould expect as the downward pressure exerted

Fig. 4.


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14 ELECTRICITY AIST) MATTERby the lines of force above a line in this i^art ofthe field will be equal to the upward pressureexerted by those below it. For a line of forcenear the edge of the plate, however, the pressureof the lines of force below will exceed the press-ure from those above, and the line of force willbulge out until its cmn^ature and tension counter-act the squeeze from inside ; this bulging is veryplainly shown in Fig. 4.

So far our use of the lines of force has beendescriptive rather than metrical ; it is, however,easy to develop the method so as to make itmetrical. We can do this by introducing theidea of tubes of force. If through the boundaryof any small closed curve in the electric field wedraw the lines of force, these lines will form atubular surface, and if we follow the lines back tothe positively electrified surface from which theystart and forward on to the negatively electrifiedsurface on which they end, we can prove that thepositive charge enclosed by the tube at its originis equal to the negative charge enclosed by it atits end. By properly choosing the area of thesmall curve through which we draw the lines offorce, we may arrange that the charge enclosed bythe tube is equal to the unit charge. Let us call


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LINES OF FORCE 15sucli a tube a Faraday tubethen each unit ofpositive electricity in the field may be regardedas the origin and each unit of negative electricityas the termination of a Faraday tube. We regardthese Faraday tubes as having direction, their di-rection being the same as that of the electric force,so that the positive direction is from the positiveto the negative end of the tube. If we draw anyclosed surface then the difference between thenumber of Faraday tubes which pass out of thesurface and those which pass in will be equal to thealgebraic sum of the charges inside the surface; thissum is what Maxwell called the electric displace-ment through the surface. What Maxwell calledthe electric displacement in any direction at apoint is the number of Faraday tubes which passthrough a unit area through the point drawn atright angles to that direction, the number beingreckoned algebraically ; i.e., the lines which passthrough in one direction being taken as positive,while those which pass through in the oppositedirection are taken as negative, and the numberpassing through the area is the difference betweenthe luimber passing through positively and thenumber passing through negatively.

For my own part, I have found the conception


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X6 ELECTRICITY AND IMATTERof Faraday tubes to lend itself much more readilyto the formation of a mental picture of the proc-esses going on in the electric field than that ofelectric displacement, and have for many yearsabandoned the latter method.Maxwell took up the question of the ten-

sions and pressures in the lines of force inthe electric field, and carried the problem onestep further than Faraday. By calculating theamount of these tensions he showed that themechanical effects in the electrostatic field couldbe explained by supposing that each Faradaytube force exerted a tension equal to ^, II beingthe intensity of the electric force, and that, inaddition to this tension, there was in the mediumthrough which the tubes pass a hydi'ostaticpressure equal to \NR^ N being the densityof the Faraday tubes; ^.e., the number passingthrough a unit area drawn at right angles tothe electric force. If we consider the effect ofthese tensions and pressure on a unit volume ofthe medium in the electric field, we see thatthey are equivalent to a tension \NR alongthe direction of the electric force and an equalpressure in all directions at right angles to thatforce.


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LINES OF FORCE 17

6

Moving Faraday TubesHitherto we have supposed the Faraday tubes

to be at rest, let us now proceed to the study ofthe effects produced by the motion of those tubes.Let us begin with the consideration of a verysimple casethat of two parallelplates,

A and B^ charged, one withpositive the other with negativeelectricity, and suppose that afterbeing charged the plates are con-nected by a conducting wire,EF G.This wire will pass through someof the outlying tubes ; these tubes,when in a conductor, contract tomolecular dimensions and the repul-sion they previously exerted onneighboring tubes will thereforedisappear. Consider the effect ofthis on a tube PQ between theplates ; PQ was originally in equilibrium underits own tension, and the repulsion exei-ted by theneighboring tubes. The repulsions due to thosecut hy

EF G have now, however, disappeared sothat PQ will no longer be in equilibrium, but willbe pushed towards EF G. Thus, more and moretubes will be pushed into EFG, and we shall


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Ig ELECTRICITY AND LIATTERhave a movement of the whole set of tubes be-tween the plates toward EF G. Thus, while thedischarge of the plates is going on, the tubes be-tween the plates are moving at right angles tothemselves. What physical effect accompaniesthis movement of the tubes ? The result of con-necting the plates by ^i^'^'^ is to produce a cur-rent of electricity flowing from the positivelycharged plate through EF G to the negativelycharged plate ; this is, as we know, accompaniedby a magnetic force between the plates. Thismagnetic force is at right angles to the plane ofthe paper and equal to 47r times the intensity ofthe current in the plate, or, if a is the density ofthe charge of electricity on the plates and v thevelocity with which the charge moves, the mag-netic force is equal to 477cru.Here we have two phenomena which do not

take place in the steady electrostatic field, one themovement of the Faraday tubes, the otherthe existence of a magnetic force ; this suggeststhat there is a connection between the two, andthat motion of the Faraday tubes is accompaniedby the production of magnetic force. I have fol-lowed up the consequences of this supposition andhave shown that, if the connection between the


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LINES OF FORCE 19magnetic force and the moving tubes is that givenbelow, this view will account for Ampere's lawsconnecting current and magnetic force, and forFaraday's law of the induction of currents. Max-well's great contribution to electrical theory, thatvariation in the electric displacement in a dielec-tric produces magnetic force, follows at once fromthis view. For, since the electric displacement ismeasured by the density of the Faraday tubes, ifthe electric displacement at any place changes,Faraday tubes must move up to or away from theplace, and motion of Faraday tubes, by hypoth-esis, implies magnetic force.The law connecting magnetic force with the

motion of the Faraday tubes is as follows : AFaraday tube moving with velocity i^ at a pointP^ produces at ^ a magnetic force whose magni-tude is 477 V sin ^, the direction of the magneticforce being at right angles to the Faraday tube,and also to its direction of motion ; Q is the anglebetween the Faraday tube and the direction inwhich it is moving. We see that it is onlythe motion of a tube at right angles to itseKwhich produces magnetic force; no such forceis produced by the gliding of a tube along itslength.


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20 ELECTRICITY AND LIATTERMotion of a Charged 8]^liere

We shall apply these results to a very simpleand important casethe steady motion of acharged sphere. If the velocity of the sphere issmall compared with that of light then the Fara-day tubes will, as when the sphere is at rest, beuniformly distributed and radial in direction.They will be carried along with the sphere. Ife is the charge on the sphere, O its centre, thedensity of the Faraday tubes at P is -np^ 'iso that if V is the velocity of the sphere, d the

Fig. 6.

angle between OP and the direction of motion ofthe sphere, then, according to the above rule, the

G "V sm Vmagnetic force at P will be -^ , the direc-tion of the force will be at right angles to OP^and at right angles to the direction of motion ofthe sphere; the lines of magnetic force will thus


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LINES OF FORCE 21be circles, having tlieir centres on the path of thecentre of the sphere and their planes at rightangles to this path. Thus, a moving charge ofelectricity will be accompanied by a magneticfield. The existence of a magnetic field impliesenergy; we know that in a unit volume of thefield at a place where the magnetic force is Hthere are ^ units of energy, where /x is themagnetic permeability of the medium. In thecase of the moving sphere the energy per unit

LL (?'V^ sin^volume at P is ^-.r^-^, . Takinoj the sum ofthis energy for all parts of the field outside the

sphere, we find that it amounts to - , where ais the radius of the sphere. If m is the mass ofthe sphere, the kinetic energy in the sphere is\ mv^\ in addition to that we have the energyoutside the sphere, which as we have seen is'- ; so that the whole kinetic enero-y of thesystem is Wm -[- "o" "" ) ^^ or the energy isthe same as if the mass of the sphere werem -\^ - instead of m. Thus, in consequence of


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LINES OF FORCE 23wliicli the mass is increased depends upon the di-rection in which the body is moving, being muchsmaller when the body moves point foremostthan when moving sideways. The mass of sucha body depends on the direction in which it ismoving.Let us, however, return to the moving electri-fied sphere. We have seen that in consequence of

its charo'e its mass is increased by ^ ; thus, if itis moving with the velocity v, the momentum is

ni -\- -r^ ) V. The additional mo-O 2mentum -~- v is not in the sphere, but in the spaceoCl/

surrounding the sphere. There is in this spaceordinary mechanical momentum, whose resultant is2u6^-o '^ and whose direction is parallel to the di-rection of motion of the sphere. It is importantto bear in mind that this momentum is not in anyway different from ordinaiy mechanical momen-tum and can be given up to or taken from themomentum of moving bodies. I want to bringthe existence of this momentum before you asvividly and forcibly as I can, because the recogni-tion of it makes the behavior of the electric field


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24 ELECTRICITY AND MATTERentirely analogous to tliat of a mechanical sys-tem. To take an example, according to Newton'sThird Law of Motion, Action and Reaction areequal and opposite, so that the momentum in anydirection of any self-contained system is invariable.Now, in the case of many electrical systems thereare apparant violations of this principle ; thus,take the case of a charged body at rest struck byan electric pulse, the charged body when exposedto the electric force in the pulse acquires velocityand momentum, so that when the pulse has passedover it, its momentum is not what it was origi-nally. Thus, if we confine our attention to themomentum in the charged body, i.e., if we sujoposethat momentum is necessarily confined to what weconsider ordinary matter, there has been a viola-tion of the Third Law of Motion, for the onlymomentum recognized on this restricted viewhas been changed. The phenomenon is, however,brouo-ht into accordance with this law if we recog;-nize the existence of the momentum in the electricfield ; for, on this view, before the pulse reachedthe charged body there was momentum in thepulse, but none in the body; after the pulsepassed over the body there was some momentumin the body and a smaller amount in the pulse,


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LINES OF FORCE 25the loss of momentum in the pulse being equal tothe gain of momentum by the body.We now proceed to consider this momentummore in detail. I have in my " Kecent Researcheson Electricity and Magnetism" calculated theamount of momentum at any point in the electricfield, and have shown that if N is the number ofFaraday tubes passing through a unit area drawnat right angles to their direction, j5 the magneticinduction, 6 the angle between the induction andthe Faraday tubes, then the momentum per unitvolume is equal to JV^ JB sin 6, the direction ofthe momentum being at right angles to the mag-netic induction and also to the Faraday tubes.Many of you will notice that the momentum isparallel to what is known as Poynting's vectorthe vector whose direction gives the direction inwhich energy is flowing through the field.Moment of Momentuin Due to an ElectrifiedPoint and a Magnetic PoleTo familiarize ourselves with this distribution

of momentum let us consider some simple cases indetail. Let us begin with the simplest, that of anelectrified point and a magnetic pole; let A^ Fig. 7,be the point, B the pole. Then, since the momen-


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26 ELECTRICITY AND IMATTERturn at any point P is at right angles to A P, thedirection of the Faraday tubes and also to P jP,the magnetic induction, we see that the momentumwill be perpendicular to the plane A P P \ thus,if we draw a series of lines sue): that their direc-tion at any point coincides with the direction ofthe momentum at that

point,these lines will, form

a series of circles whose planes are perpendicularto the line A P, and whose centreslie along that line. This distributionof momentum, as far as direction

yp goes, is that possessed by a top spin-ning around A P. Let us now findwhat this distribution of momentumthroughout the field is equivalent to.

It is evident that the resultantmomentum in any direction is zero,

' '

but since the system is s]3inninground A P, the direction of rotation being every-where the same, there will be a finite momentof momentum round A P. Calculating the valueof this from the expression for the momentumgiven above, we obtain the very simple expression(9 772. as the value of the moment of momentumabout A P, e being the charge on the point andm the strength of the pole. By means of this


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LINES OF FORCE 27expression we can at once find the moment ofmomentum of any distribution of electrified pointsand magnetic poles.To return to the system of the point and pole,this conception of the momentum of the systemleads directly to the evaluation of the force actingon a moving electric charge or a moving magneticpole. For suppose that in the time 8 t the electri-fied point were to move from A to A'y the ^*moment of momentum is still e7n, but .^its axis is along A' B instead of A B. a\The moment of momentum of the fieldhas thus changed, but the wliole momentof momentum of the system comprisingpoint, pole, and field must be constant, sothat the change in the moment of momen-tum of the field must be accompaniedby an equal and opposite change in themoment of momentum of the pole and ^^^- ^point. The momentum gained by the point mustbe equal and opposite to that gained by thepole, since the whole momentum is zero. If d isthe angle A B A\ the change in the moment ofmomentum is em sin 0, with an axis at rightangles to A B in the plane of the paper. Let8 / be the change in the momentum of A^


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28 ELECTRICITY AND MATTER8 I that of B, tlien 8 / and 8 / must beequivalent to a couple whose axis is at rightangles to ^ -5 in the plane of the paper, andwhose moment is e m sin d. Thus 8 /must be atright angles to the plane of the paper and

bl .AJi = emsin0= -p^Where is the angle A A\ If -y is the

velocity of A,A A^=ivSi and we getThis change in the momentum may be sup-

posed due to the action of a force i^ perpen-dicular to the plane of the paper, /^ being theS /rate of increase of the momentum, or ^" We thus

ernvsind) , . . , ,get jP = J Da ', or the pomt is acted on by aforce equal to e multiplied by the component ofthe magnetic force at right angles to the directionof motion. The direction of the force acting onthe point is at right angles to its velocity andalso to the magnetic force. There is an equaland opposite force acting on the magnetic pole.The value we have found for jP is the ordinary

expression for the mechanical force acting on amoving charged particle in a magnetic field ; it


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LINES OF FORCE 29may be written as ev ^sin


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30 ELECTRICITY AND MATTERhorizontal, then if with a vertical rod I pixshagainst A B horizontally, the point A will notmerely move horizontally forward in the dhectionin which it is pushed, but will also move verti-cally upward or downward, Just as a charged

i.-^ .*.:.Fig. 9,

point would do if pushed forward in the sameway, and if it were acted upon by a magneticpole at B.

MaxweWs Vector PotentialThere is a very close connection between the

momentum arising fi'om an electrified point and a


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LINES OF FORCE 31magnetic system, and tlie Vector Potential of tliatsystem, a quantity whicli plays a very large partin Maxwell's Theory of Electricity. From tlie ex.pression we have given for tlie moment of mo-mentum due to a charged point and a magneticpole, we can at once find that due to a charge e ofelectricity at a point P, and a little magnet A B ;let the negative pole of this magnet be at A^ thepositive at B^ and let mi be the strength of eitherpole. A simple calculation shows that in thiscase the axis of the resultant moment of momen-tum is in the planePA B 2X right angles to P O,being the middle point of A B, and that themagnitude of the moment of momentum is equal

- to e. m. A B jfj^2-> ^vhere


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32 ELECTRICITY AND ]\LA.TTERCalling this Vector Potential I, we see tliat the

momentum due to the charge and the magnet isequivalent to a momentum el 2X P and a momen-tum e 1 2X the magnet.We may evidently extend this to any complexsystem of magnets, so that if / is the Vector Po-tential at P of this system, the momentum in thefield is equivalent to a momentum e I 2A> P to-gether with momenta at each of the magnetsequal to e (Vector Potential atP due to that magnet).If the magnetic field arises entirely fi'om electriccurrents instead of from permanent magnets, themomentum of a system consisting of an electrifiedpoint and the currents will differ in some of itsfeatures from the momentum when the magneticfield is due to permanent magnets. In the lattercase, as we have seen, there is a moment of mo-mentum, but no resultant momentum. When,however, the magnetic field is entirely due toelectric currents, it is easy to show that there is aresultant momentum, but that the moment of mo-mentum about any line passing through the elec-trified particle vanishes. A simple calculationshows that the whole momentum in the field isequivalent to a momentum e I oX the electrified


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LINES OF FORCE 33point / being the Vector Potential at P due tothe currents.

Thus, whether the magnetic field is due to per-manent magnets or to electric currents or partlyto one and partly to the other, the momentumwhen an electrified point is placed in the field atP is equivalent to a momentum e I Sit P where 1is the Vector Potential at P. If the magneticfield is entirely due to currents this is a completerepresentation of the momentum in the field ; ifthe magnetic field is partly due to magnets wehave in addition to this momentum at P othermomenta at these magnets ; the magnitude of themomentum at any particular magnet is 6 timesthe Vector Potential at P due to that magnet.The well-known expressions for the electro-

motive forces due to Electro-magnetic Inductionfollow at once from this result. For, from theThird Law of Motion, the momentum of any self-contained system must be constant. Now themomentum consists of (1) the momentum in thefield ; (2) the momentum of the electrified point,and (3) the momenta of the magnets or circuitscarrying the currents. Since (1) is equivalent toa momentum e 1 at the electrified particle, we seethat changes in the momentum of the field must


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34 ELECTRICITY AND INIATTERbe accompanied by changes in tlie momentum ofthe particle. LetM be the mass of the electrifiedparticle, w, f, w the components parallel to theaxes of a?, y, z of its velocity, F^ G, H, the com-ponents parallel to these axes of the Vector Po-tential at P^ then the momentum of the field isequivalent to momenta e F, e G, eH at P parallelto the axes of x, y, z] and the momentum of thecharged point at P has for components Mu, Mo^Mw. As the momentum remains constant, Mu +e F\'^ constant, hence if Sw and 8^ are simulta-neous changes in ii and F^

M^u-\-ehF=z 0;dti dllor w-=- = ^ _- .(it at

From this equation we see that the point with thecharge behaves as if it were acted upon by a me.chanical force parallel to the axis of x and equal todF . -i ix'j? li. dll e -r-, ^.e., by an electric lorce equal to -^dt ^ dt'In a similar way we see that there are electricforces T -_, parallel to v and z respec-dt' dt' ^ ^ ^tively. These are the well-known expressions ofthe forces due to electro-magnetic induction, andwe see that they are a direct consequence of the


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LINES OF FORCE 35principle tliat action and reaction are equal andopposite.

Keaders of Faraday's Experimental Researcheswill remember that he is constantly referring towhat he called the " Electrotonic State " ; thus heregarded a wire traversed by an electric currentas being in the Electrotonic State when in amagnetic field. No effects due to this state can bedetected as long as the field remains constant ; itis when it is changing that it is operative. ThisElectrotonic State of Faraday is just the momeri'turn existing in the field.


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CHAPTER nELECTRICAL AND BOUND MASS.

I WISH in this chapter to consider the connec*tion between the momentum in the electric fieldand the Faraday tubes, by which, as I showed inthe last lecture, we can picture to ourselves thestate of such a field. Let us begin by consideringthe case of the moving charged sphere. The linesof electric force are radial ; those of magnetic forceare circles having for a common axis the line of mo-tion of the centre of the sphere ; the momentum

at a pointP is at rightangles to each of thesedirections and so is atright angles to P \x^the plane containingi^and the line of motion

^^^' 10- of the centre of thesphere. If the number of Faraday tubes passingthrough a unit area at P placed at "right anglesto O P \^ N^ the magnetic induction at P is,if /A is the magnetic permeability of the medium


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ELECTRICAL MASS 37surrounding tlie sphere, iiTT^xN'V sin 6, v beingthe velocity of the sphere and d the angleO P makes with the direction of motion ofthe sphere. By the rule given on page 25 themomentum in unit volume of the medium at P isJV^X 4:TTixNv sin 6, or 4:TriJLJV^v sin 0, and isin the direction of the component of the veloc-ity of the Faraday tubes at right angles to theirlength. Now this is exactly the momentum whichwould be produced if the tubes were to carrywith them, when they move at right angles totheir length, a mass of the surrounding mediumequal to 47r [x J^^ per unit volume, the tubes pos-sessing no mass themselves and not carrying anyof the medium with them when they glidethrough it parallel to their own length. Wesuppose in fact the tubes to behave very much aslong and narrow cylinders behave when movingthrough water ; these if moving endwise, i.e., par-allel to their length, carry very little water alongwith them, while when they move sideways, i.e., atright angles to their axis, each unit length of thetube carries with it a finite mass of water. Whenthe length of the cylinder is very great comparedwith its breadth, the mass of water carried l)y itwhen moving endwise may be neglected in com-


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38 ELECTRICITY AND MATTERparison witli that carried by it when moving side*ways ; if the tube had no mass beyond that whichit possesses in virtue of the water it displaces, itwould have mass for sideways but none for end-wise motion.We shall call the mass ^ir fiN^ carried by thetubes in uuit volume the mass of the bound ether.It is a very suggestive fact that the electrostaticenergy ^ in unit volume is proportional to M themass of the bound ether in that volume. This caneasily be proved as follows : E = , whereIC is the specific inductive capacity of themedium ; while M =^ 4:Tr fx, JV^, thus,but j^= V^ \vhere V is the velocity with whichlight travels through the medium, hence

thus E is equal to the kinetic energy possessedby the bound mass when moving with the veloc-ity of light.The mass of the bound ether in unit volume is

47rjaiV^^ where iV^is the number of Faraday tubes ;thus, the amount of bound mass per unit length of


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ELECTEICAL MASS 39eacli Faraday tube is 47r/aiV^ We have seen tLatthis is proportional to the tension in each tube, sothat we may regard the Faraday tubes as tightlystretched strings of variable mass and tension ; thetension being, however, always proportional to themass per unit length of the string.

Since the mass of ether imprisoned by a Faradaytube is proportional to iVthe number of Faradaytubes in unit volume, we see that the mass andmomentum of a Faraday tube depend not merelyupon the configuration and velocity of the tubeunder consideration, but also upon the numberand velocity of the Faraday tubes in its neigh-borhood. We have many analogies to this in thecase of dynamical systems ; thus, in the case of anumber of cylinders with their axes parallel, mov-ing about in an incompressible liquid, the momen-tum of any cylinder depends upon the positionsand velocities of the cylinders in its neighborhood.The following hydro-dynamical system is one bywhich we may illustrate the fact that the boundmass is proportional to the square of the numberof Faraday tubes per unit volume.

Suppose we have a cylindrical vortex column ofstrength m placed in a mass of liquid whose ve-locity, if not disturbed by the vortex column, would


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40 ELECTRICITY AND MATTERbe constant botli in magnitude and direction, andat right angles to the axis of the vortex column.The lines of flow in such a case are representedin Fig. 11, where A is the section of the vortex

Fig. 11.

column whose axis is supposed to be at right an-gles to the plane of the paper. We see that someof these lines in the neighborhood of the columnare closed curves. Since the liquid does not crossthe lines of flow, the liquid inside a closed curvewill always remain in the neighborhood of the col-umn and will move with it. Thus, the columnwill imprison a mass of liquid equal to that en-closed by the largest of the closed lines of flow.If m is the strength of the vortex column and a thevelocity of the undisturbed flow of the liquid, wecan easily show that the mass of liquid imprisoned


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ELECTRICAL JkL^SS 41

by the column is proportional to ^. Thus, if^we take m, as proportional to the number ofFaraday tubes in unit area, the system illustratesthe connection between the bound mass and theetrenirth of the electric field."Ci"

Effective of Velocity on the Bound MassI will now consider another consequence of the

idea that the mass of a charged particle arises fromthe mass of ether bound by the Faraday tube as-sociated with the

charge.These tubes, when theymove at right angles to their length, carry with

them an appreciable portion of the ether throughwhicli they move, while when they move parallelto their length, they glide through the fluid with-out settinc: it in motion. Let us consider how along, narrow cylinder, sliaped like a Faraday tube,wouhl behave when moving through a liquid.

Such a body, if free to twist in any direction,will not, as you might expect at first sight, movepoint foremost, but will, on the contrary, set itselfbroadside to the direction of motion, setting itselfso as to carry with it as much of the fluid throughwhich it is moving as possible. Many illustra-tions of this principle could be given, one very


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42 ELECTRICITY AND IklATTERfamiliar one is that falling leaves do not fall edgefirst, but flutter down witli their planes more orless horizontal.

If we apply this principle to the charged sphere,we see that the Faraday tubes attached to thesphere will tend to set themselves at right anglesto the direction of motion of the sphere, so that ifthis principle were the only thing to be consideredall the Faraday tubes w^ould be forced up into theequatorial plane, i.e., the j)lane at right angles tothe direction of motion of the sphere, for in thisposition they would all be moving at right anglesto their lengths. We must remember, however,that the Faraday tubes repel each other, so thatif they were crowded into the equatorial regionthe pressure there would be greater than thatnear the pole. This would tend to thrust theFaraday tubes back into the position in which theyare equally distributed all over the sphere. Theactual distribution of the Faraday tubes is a com-promise between these extremes. They are notall crowded into the equatorial plane, neither arethey equally distributed,

for they are more in theequatorial regions than in the others ; the excess ofthe density of the tubes in these regions increasingwith the speed with which the charge is moving.


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ELECTRICAL MASS 43When a Faraday tube is in the equatorial regionit imprisons more of the ether than when it isnear the poles, so that the displacement of theFaraday tubes from the pole to the equator willincrease the amount of ether imprisoned by thetubes, and therefore the mass of the body.

It has been shown (see Heaviside, Phil. Mcig.^April, 1889, ^^Eecent Researches," p. 19) that theeffect of the motion of the sphere is to displaceeach Faraday tube toward the equatorial plane,i.e., the plane through the centre of the sphere atright angles to its direction of motion, in such away that the projection of the tube on this planeremains the same as for the uniform distribution oftubes, but that the distance of every point in thetube from the equatorial plane is reduced in theproportion of V F^-y'^ to FJ where T^ is the veloc-ity of light through the medium and v the velocityof the charged body.From this result we see that it is only when the

velocity of the charged body is comparable withthe velocity of light that the change in distribu-tion of the Faraday tubes due to the motion ofthe body becomes appreciable.

In "Recent Researches on Electricity and Mag-netism," p. 21, 1 calculated the momentum ij in the


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44 ELECTRICITY AND MATTERspace siuTounding a spliere of radius a, having itscentre at the moving charged body, and showed thatthe value of /is given by the following expression :J=

(l + i^cos2^)| ; . . (1)where as before v and F'are respectively the ve-locities of the particle and the velocity of light,and Q is given by the equation

sm V j^'The mass of the sphere is increased in conse-

quence of the charge by - , and thus we see fromequation (1) that for velocities of the chargedbody comparable with that of light the mass ofthe body will increase with the velocity. It isevident from equation (1) that to detect the influ-ence of velocity on mass we must use exceed-ingly small particles moving with very high ve-locities. Now, particles having masses far smallerthan the mass of any known atom or moleculeare shot out from radium with velocities ap-proaching in some cases to that of light, and theratio of the electric charge to the mass fur parti-


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ELECTRICAL MASS 45cles of this kind has lately been made the subjectof a very interesting investigation by Kaufmann,with the results shown in the following table ; thefirst column contains the values of the velocitiesof the particle expressed in centimetres per sec-ond, the second column the value of the fraction where e is the charsje and m the mass of them particle :


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ELECTRICAL MASS 47about one-fourth of the whole mass. He was care-ful to point out that this fraction depends uponthe assumption we make as to the nature of themoving body, as, for example, whether it is spheri-cal or ellipsoidal, insulating or conducting; andthat with other assumptions his experiments mightshow that the whole mass was electrical, which heevidently regarded as the most probable result.

In the present state of our knowledge of theconstitution of matter, I do not think anything isgained by attributing to the small negativelycharged bodies shot out by radium and otherbodies the property of metallic conductivity, andI prefer the simpler assumption that the distribu-tion of the lines of force round these particles isthe same as that of the lines due to a chargedpoint, provided we confine our attention to thefield outside a small sphere of radius a having itscentre at the charged point ; on this suj^positionthe part of the mass due to the charge is the valueof in equation (1) on page 44. I have calcu-lated from this expression the ratio of the massesof the rapidly moving particles given out by ra-dium to the mass of the same particles when atrest, or moving slowly, on the assumption that tlie


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48 ELECTRICITY AND lilATTERloliole of tlie mass is due to the charge and have com-pared these results with the values of the sameratio as determined by Kaufmann's experiments.These results are given in Table (II), the first col-umn of which contains the values of v, the veloci-ties of the particles ; the second p, the number oftimes the mass of a particle moving with this ve-locity exceeds the mass of the same particle whenat rest, determined by equation (1) ; the thirdcolumn p\ the value of this quantity found byKaufmann in his experiments.


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ELECTRICAL IkLiSS 49confine our attention to tlie part of tlie field wliicliis outside a spliere of radius a concentric with thecharge, the mass m due to the charge e on theparticle is, when the particle is moving slowly,given by the equation m =i -k

In a subsequent lecture I will explainhow the values of m e and e have been deter-mined ; the result of these determinations is that^ = 10-^ and 6 = 1.2 X 10"'" in C. G. S. elec-etrostatic units.

Substituting these values in theexpression for m we find that a is about 5 X10"" cm, Si length very small in comparison withthe value 10"^ c m, which is usually taken as a goodapproximation to the dimensions of a molecule.We have regarded the mass in this case as dueto the mass of ether carried along by the Faradaytubes associated with the charge. As these tubesstretch out to an infinite distance, the mass of theparticle is as it were diffused through space, andhas no definite limit. In consequence, however, ofthe very snuill size of the particle and the factthat the mass of etlier carried by the tubes (beingproportional to the square of the density of theFaraday tubes) varies inversely as the fourth


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50 ELECTRICITY AND MATTERpower of tlie distance from the particle, we findby a simple calculation that all but the most insig-nificant fraction of mass is confined to a distancefrom the particle which is very small indeed com-pared with the dimensions ordinarily ascribed toatoms.

In any system containing electrified bodies apart of the mass of the system will consist of themass of the ether carried along by the Faradaytubes associated with the electrification. Nowone view of the constitution of mattera view, Ihope to discuss in a later lectureis that theatoms of the various elements are collections ofpositive and negative charges held together mainlyby their electric attractions, and, moreover, thatthe negatively electrified particles in the atom(corpuscles I have termed them) are identicalwith those small negatively electrified particleswhose properties we have been discussing. Onthis view of the constitution of matter, partof the mass of any body would be the mass ofthe ether dragged along by the Faraday tubesstretching across the atom between the positivelyand negatively electrified constituents. The viewI wish to put before you is that it is not merely apart of the mass of a body which arises in this


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ELECTRICAL IVIASS 51way, but that the ivJiole mass of any body is justthe mass of etlier surrounding the body which iscarried along by the Faraday tubes associatedwith the atoms of the body. In fact, that all massis mass of the ether, all momentum, momentum ofthe ether, and all kinetic energy, kinetic energyof the ether. This view, it should be said, requiresthe density of the ether to be immensely greaterthan that of any known substance.

It might be objected that since the mass has tobe carried along by the Faraday tubes and sincethe disposition of these depends upon the relativeposition of the electrified bodies, the mass of acollection of a number of positively and negativelyelectrified bodies would be constantly changingwith the positions of these bodies, and thus thatmass instead of being, as observation and experi-ment have shown, constant to a very high degreeof approximation, should vary with changes inthe physical or chemical state of the body.

These objections do not, however, ap])ly to sucha case as that contemplated in the preceding theory,where the dimensions of one set of the electrifiedbodiestlie negative ones are excessively smallin comparison with the distances separating thevarious members of the system of electrified bodies.


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52 ELECTRICITY AND MATTERWhen this is the case the concentration of thelines of force on the small negative bodiesthecorpusclesis so great that practically the wholeof the bound ether is localized around thesebodies, the amount depending only on their sizeand charge. Thus, unless we alter the number orcharacter of the corpuscles, the changes occurringin the mass through any alteration in their rela-tive positions mil be quite insignificant in com-parison with the mass of the body.


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CHAPTER IIIEFFECTS DUE TO ACCELERATION OF THEFARADAY TUBES

Montgen Rays and LightWe have considered the behavior of the linesof force when at rest and when moving uniformly,we shall in this chapter consider the phenomenawhich result when the state of motion of the linesis changing.

Let us begin with the case of a moving chargedpoint, moving so slowly that the lines of force areuniformly distributed around it, and consider whatmust happen if we suddenly stop the point. TheFaraday tubes associated with the sphere haveinertia ; they are also in a state of tension, thetension at any point being proportional to the massper unit length. Any disturbance connnunicatedto one end of the tube will therefore travel alouffit with a constant and Unite velocity ; the tube infact having very considerable analogy witli astretched string. Suppose we have a tightlystretched vertical string moving uniformly, from


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54 ELECTRICITY AND MATTERright to left, and tliat we suddenly stop one end,A, what will happen to the string ? The end Awill come to rest at once, but the forces calledinto play travel at a finite rate, and each part ofthe string will in virtue of its inertia continue tomove as if nothing had happened to the end Auntil the disturbance starting from A reaches it.Thus, if V is the velocity with which a disturb-ance travels along the string, then when a time, t,has elapsed after the stoppage of A, the parts ofthe string at a greater distance than Vt from Awill be unaffected by the stoppage, and will havethe position and velocity they would have hadif the string had continued to move uniformlyforward. The shape of the string at successiveintervals will be as shown in Fig. 12, the length of

A A AFig. 12.the horizontal portion increasing as its distancefrom the fixed end increases.


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RONTGEN RAYS AND LIGHT 55Let US now return to tlie case of the movingcharged particle wMcli we shall suppose suddenly-

brought to rest, the time occupied by the stoppagebeing r. To find the configuration of the Faraday-tubes after a time t has elapsed since the beginningof the process of bringing the charged particle torest, describe with the charged particle as centretwo spheres, one having the radius Vt, the otherthe radius V(t r), then, since no disturbance canhave reached the Faraday tubes situated outsidethe outer sphere, these tubes will be in the posi-tion they would have occupied if they had movedforward with the velocity they possessed at themoment the particle was stopped, while inside theinner sphere, since the disturbance has passedover the tubes, they will be in their final positions.Thus, consider a tube which, when the particlewas stopped was along the line OPQ (Fig. 13) ;this ^vill be the final position of the tube ; hence atthe time t the portion of this tube inside the innersphere wall occupy the position (9P, while theportion ^'^' outside the outer sphere will be in theposition it would have occupied if the particle hadnot been reduced to rest, i.e.^ if 6^' is the positionthe particle would have occupied if it had notbeen stopped, F' Q' will be a straight line pass-


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56 ELECTRICITY AND MATTERing througli 0'. Thus, to preserve its continuitythe tube must bend round in the shell between thetwo spheres, and thus be distorted into the shapeOFP'Q'. Thus, the tube which before the stop-

Fig. 13.

page of the particle was radial, has now in theshell a tangential component, and this tangentialcomponent implies a tangential electric force.The stoppage of the particle thus produces aradical change in the electric field due to the par-ticle, and gives rise, as the following calculationwill show, to electric and magnetic forces muchgreater than those existing in the field when theparticle was moving steadily.If we suppose that the thickness 8 of the shellis so small that the portion of the Faraday tubeinside it may be regarded as straight, then if T is


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RONTGEN RAYS AND LIGHT 57the tangential electric force inside the pulse, Rthe radial force, we LaveT P'R 00' sin


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5g ELECTRICITY AND MATTERpulse produced by tlie stoppage of the particle isthe seat of intense electric and magnetic forceswhich diminish inversely as the distance from thecharged particle, whereas the forces before theparticle was stopped diminished inversely as thesquare of the distance ; this pulse travelling out-ward with the velocity of light constitutes in myopinion the Rontgen rays which are producedwhen the negatively electrified particles whichform the cathode rays are suddenly stopped bystriking against a solid obstacle.The energy in the pulse can easily be shown

to be equal to 2 ^3 8 'this energy is radiated outward into space.The amount of energy thus radiated dependsupon 8, the thickness of the pulse, i. e., uponthe abruptness with which the particle isstopped; if the particle is stopped instantaneouslythe whole energy in the field will be absorbed inthe pulse and radiated away, if it is stopped grad-ually only a fraction of the energy will be radiatedinto space, the remainder will appear as heat atthe place where the cathode rays were stopped.

It is easy to show that the momentum in the


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RONTGEN RAYS AND LIGHT 59pulse at any instant is equal and opposite to themomentum in the field outside the pulse ; as thereis no momentum in the space through which thepulse has passed, the whole momentum in the fieldafter the particle is stopped is zero.The preceding investigation only applies to the

case when theparticle

was movingso slowly that

the Faraday tubes before the stoppage of thepulse were uniformly distributed; the sameprinciples, however, will give us the effect ofstopping a charged particle whenever the dis-tribution of the Faraday tubes in the state ofsteady motion has been determined.

Let us take, for example, the case when theparticle was initially moving with the velocity oflight; the rule stated on page 43 shows thatbefore the stoppage the Faraday tubes wereall congregated in the equatorial plane of themoving particle. To find the configuration ofthe Faraday tubes after [i time t we proceed asbefore by finding the configuration at that timeof the tubes, if the particle had not been stopped.The tubes would in that case have been in a planeat a distance Vt in front of the particle. Drawtwo spheres having their centres at the particle andhaving radii respectively e(ual to Vt and V (t r),


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60 ELECTRICITY AND MATTERwhere r is the time occupied in stopping theparticle; outside the outer sphere the configura-tion of the tubes will be the same as if the par-ticle had not been stopped, i. e., the tubes will bethe plane at the distance Vt in front of the par-ticle, and this plane will touch the outer sphere.Inside the inner sphere the Faraday tubes will beuniformly distributed, hence to preserve continuitythese tubes must run round in the shell to join thesphere as in Fig. 14. We thus have in this case

two pulses, one aplane pulse propa-gated in the direc-tion in which theparticle was mov-ing before it wasstopped, the other aspherical pulse trav-elling outward in alldirections.The preceding

method can be ap-plied to the case

when the charged particle, instead of beingstopped, has its velocity altered in any way ; thus,if the velocity v of the particle instead of being

Fig. 14.


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RONTGEN RAYS AND LIGHT Qlreduced to zero is merely diminislied by A v, wecan show, as on page 57, that it will give rise toa pulse in which the magnetic force H is given bythe equation ^ eAv sinJi = 5^ ,roand the tangential electric force T by^ _


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62 ELECTRICITY AND MATTERsuch a way that its acceleration went throughperiodic changes, periodic waves of electric andmagnetic force would travel out from the chargedbody. These waves would, on the Electromag-netic Theory of Light, be light waves, providedthe periodic changes in the acceleration of thecharged body took place with sufficient rapidity.The method we have been investigating, in whichwe consider the effect produced on the configura-tion of the Faraday tubes by changes in the mo-tion of the body, affords a very simple way ofpicturing to ourselves the processes going on dur-ing the propagation of a wave of light throughthe ether. We have regarded these as arisingfrom the propagation of transverse tremors alongthe tightly stretched Faraday tubes; in fact, weare led to take the same view of the propagationof light as the following extracts fi'om the paper,"Thoughts on Ray Vibrations," show to havebeen taken by Faraday himself. Faraday says," The view which I am so bold to put forwardconsiders therefore radiations as a high species ofvibration in the lines of force which are knownto connect particles and also masses together."

This view of light as due to the tremors intightly stretched Faraday tubes raises a question


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RONTGEN RAYS AND LIGHT 63wliicli I have not seen noticed. The Faradaytubes stretchino: throus-h the ether cannot beregarded as entirely filling it. They are ratherto be looked upon as discrete threads embeddedin a continuous ether, giving to the latter a fibrousstructure ; but if this is the case, then on the viewwe have taken of a wave of light the wave it-self must have a structure, and the front of thewave, instead of being, as it were, uniformly illu-minated, will be represented by a series of brightspecks on a dark ground, the bright specks cor-responding

to the places where the Faradaytubes

cut the wave front.Such a view of the constitution of a light wave

would explain a phenomenon which has alwaysstruck me as being very remarkable and difficultto reconcile with the view that a light wave, orrather in this case a Rontgen ray, does not possessa structure. AVe have seen that the method ofpropagation and constitution of a Rontgen rayis the same as in a light wave, so that anygeneral consideration a]:)out structure in Ront-gen rays will apply also to light waves. Thephenomenon in question is this : Rontgen raysare able to pass very long distances throughgases, and as they pass through the gas they


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64 ELECTRICITY AND MATTERionize it, splitting up tlie molecules into posi-tive and negative ions ; the number of moleculesso split up is, however, an exceedingly small frac-tion, less than one-billionth, even for strong rays, ofthe number of molecules in the gas. Now, if theconditions in the front of the wave are uniform, allthe molecules of the gas are exposed to the sameconditions ; ho^v is it then that so small a propor-tion of them are split up ? It might be argued thatthose split up are in some special conditionthatthey possess, for example, an amount of kineticenergy so much exceeding the average kineticenergy of the molecules of the gas that, in accord-ance with Maxwell's Law of Distribution ofKinetic energy, their number would be exceedinglysmall in comparison with the whole number ofmolecules of the gas ; but if this were the case thesame law of distribution shows that the numberin this abnormal condition would increase veryrapidly with the temperature, so that the ioniza-tion produced by the Rontgen rays ought to in-crease very rapidly as the temperature increases.Recent experiments made by Mr. McClung in theCavendish Laboratory show that no appreciableincrease in the ionization is produced by raisingthe temperature of a gas from 15C. to 200 C,


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RONTGEN RAYS AND LIGHT 65whereas the number of molecules

possessingan

abnormal amount of kinetic energy would beenormously increased by this rise in temperature.The difficulty in explaining the small ionization isremoved if, instead of supposing the front of theKontgen ray to be uniform, we suppose that it con-sists of specks of great intensity separated byconsiderable intervals where the intensity is verysmall, for in this case all the molecules in the field,and probably even different parts of the samemolecule, are not exposed to the same conditions,and the case becomes analogous to a swarm ofcathode rays passing through the gas, in whichcase the number of molecules which get into col-lision with the rays may be a very small fractionof the whole number of molecules.To return, however, to the case of the charged

particle whose motion is accelerated, we haveseen that from the particle electric and magneticforces start and travel out radially with the ve-locity of light, both tlie radial and magnetic forcesbeins; at rio;ht anc-les to the direction in whichthey are travelling ; but since (see page 25)each unit volume of the electro-magnetic field hasan amount of momentum equal to the product ofthe density of the Faraday tube and the magnetic


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66 ELECTRICITY AND MATTERforce, the direction of the momentum being atright angles to both these quantities, there will bethe wave due to the acceleration of the chargedparticle, and indeed in any electric or light wavemomentum in the direction of propagation of thewave. Thus, if any such wave, for example awave of light, is absorbed by the substance throughwhich it is passing, the momentum in the wavewill be communicated to the absorbing substance,which will, therefore, experience a force tending topush it in the direction the light is travelling.Thus, when light falls normally on a blackened ab-sorbing substance, it will repel that substance.This repulsion resulting from radiation was shownby Maxwell to be a consequence of the Electro-magnetic Theory of Light ; it has lately been de-tected and measured by Lebedew by some mostbeautiful experiments, which have been confirmedand extended by Nichols and Hull.The pressure experienced by the absorbing sub-

stance will be proportional to its area, while theweight of the substance is proportional to its vol-ume. Thus, if we halve the linear dimensions wereduce the weight to one-eighth while we only re-duce the pressure of radiation to one-quarter ; thus,by sufficiently reducing the size of the absorbing


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KONTGEN RAYS AND LIGHT 67body we must arrive at a stage when the forcesdue to radiation exceed those which, like weight,are proportional to the volume of the substance.On this principle, knowing the intensity of theradiation from the sun, Arrhenius has shown thatfor an oj^aque sphere of unit density 10"^ cm. indiameter the repulsion due to the radiation fromthe sun would just balance the sun's attraction,while all bodies smaller than this would be re-pelled from the sun, and he has applied this prin-ciple to explain the phenomena connected withthe tails of comets. Poynting-has recently shownthat if two spheres of unit density about 39 cm.in diameter are at the temperature of 27 C. andprotected from all external radiation, the re-pulsion due to the radiation emitted from thespheres will overpower their gravitational at-traction so that the spheres ^vill repel eachother.

Again, ^vhen light is refracted and reflectedat a transparent surface, the course of the lightand therefore the direction of momentum ischanged, so that the refracting substance musthave momentum communicated to it. It is easyto show that even when the incidence of the lightis oblique the momentum communicated to the


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RONTGEN RAYS AND LIGHT 69does not at once attain the acceleration as itmwould if there were no loss of energy by radia-tion; on the contrary, the acceleration of the parti-cle is initially zero, and it is not until after thelapse of a time comparable with -ta that theparticle acquires even an appreciable fraction ofits final acceleration. Thus, the rate at which theparticle loses energy is during the time -y verysmall compared with the ultimate rate. Thus, ifthe particle were acted on by a wave of electricforce which only took a time comparable with -y^to pass over the particle, the amount of energy ra-diated by the particle would be avery much smallerfraction of the energy in the wave than it would beif the particle took a time equal to a considerable

e"multiple of tt to pass over the particle. This hasan important application in exj)laining the greaterpenetrating power of " hard " Kontgen rays thanof " soft " ones. The " hard " rays correspond tothin pulses, the " soft " ones to thick ones ; so thata smaller proportion of the energy in the "hard"rays will be radiated away by the charged particles


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70 ELECTRICITY AND lilATTERover whicli tliey pass than in the case of the "soft"rays.By applying the law that the rate at which en-

1 ^V2ergy is radiating is equal to ^ "r/^ to the case ofa charged particle revohang in a circular orbit un-der an attractive force varying inversely as thesquare of the distance, we find that in this casethe rate of radiation is proportional to the eighthpower of the velocity, or to the fourth power ofthe energy. Thus, the rate of loss of energy byradiation increases very much more rapidly thanthe energy of the moving body.


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CHAPTER IVTHE ATOMIC STRUCTURE OF ELECTRICITYHitherto we have been dealing chiefly with the

properties of the lines of force, with their ten-sion, the mass of ether they carry along with them,and with the propagation of electric disturbancesalong them ; in this chapter we shall discuss thenature of the charges of electricity which form thebeginnings and ends of these lines. We shall showthat there are strong reasons for supposing thatthese changes have what may be called an atomicstructure ; any charge being built up of a numberof finite individual charges, all equal to each other :just as on the atomic theory of matter a quantityof hydrogen is built up of a number of small par-ticles called atoms, all the atoms being equal toeach other. If this view of the structure of elec-tricity is correct, each extremity of a Faraday tubewill be the place from ^vhich a constant fixed num-ber of tubes start or at which they arrive.

Let us first consider the evidence given by thelaws of the electrolysis of liquids. Faraday


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72 ELECTRICITY AND MATTERshowed that when electricity passes through aliquid electrolyte, the amount of negative electric-ity given up to the positive electrode, and of posi-tive electricity given to the negative electrode, isproportional to the number of atoms coming upto the electrode. Let us first consider monovalentelements, such as hydrogen, chlorine, sodium, andso on ; he showed that when the same number ofatoms of these substances deliver up theircharges to the electrode, the quantity of electricitycommunicated is the same whether the carriersare atoms of hydrogen, chlorine, or sodium, in-dicating that each atom of these elements carriesthe same charge of electricity. Let us now go tothe divalent elements. We find again that the ionsof all divalent elements carry the same charge,but that a number of ions of the divalent ele-ment carry twice the charge carried by the samenumber of ions of a univalent element, showingthat each ion of a divalent element carries twiceas much charge as the univalent ion ; again, a tri-valent ion carries three times the charge of a uni-valent ion, and so on. Thus, in the case of the elec-trolysis of solutions the charges carried by theions are either the charge on the hydrogen ion ortwice that charge, or three times the charge, and


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THE ATOMIC STRUCTURE OF ELECTRICITY 73SO on. The charges we meet with are always anintegral multiple of the charge carried by the hy-drogen atom ; we never meet with fractional partsof this charge. This very remarkable fact shows,as Helmholtz said in the Faraday lecture, that" if we accept the hypothesis that the elementarysubstances are composed of atoms, we cannot avoidthe conclusion that electricity, positive as well asnegative, is divided into definite elementary por-tions which behave like atoms of electricity."When we consider the conduction of electricitythrough gases, the evidence

in favor of the atomiccharacter of electricity is even stronger than it isin the case of conduction through liquids, chieflybecause we know more about the passage of elec-tricity through gases than through liquids.

Let us consider for a moment a few of the prop-erties of gaseous conduction. When a gas hasbeen put into the conducting statesay, by expos-ure to Rontgen raysit remains in this state fora sufficiently long time after the rays have ceasedto enable us to study its properties. We find thatwe can filter tlie conductivity out of the gas bysending the gas througli a plug of cotton-wool, orthrough a water-trap. Thus, the conductivity isdue to something mixed with the gas whicli can


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74 ELECTRICITY AND [MATTERbe filtered out of it; again, the conductivity istaken out of the gas when it is sent through astrong electric field. This result shows that theconstituent to which the conductivity of the gas isdue consists of charged j^articles, the conductivityarising from the motion of these particles in theelectric field. We have at the Cavendish Labora-tory measured the charge of electricity carried bythose particles.The principle of the method first used is as fol-

lows. If at any time there are in the gas n of theseparticles charged positively and n charged nega-tively, and if each of these carries an electric chargee, we can easily by electrical methods determine n e,the quantity of electricity of our sign present inthe gas. One method by which this can be doneis to enclose the gas between two parallel metalplates, one of which is insulated. Now suppose wesuddenly charge up the other plate positively to avery high potential, this plate will now I'epel thepositive particles in the gas, and these before theyhave time to combine with the negative particleswill be driven

againstthe insulated plate. Thus,

all the positive charge in the gas will be drivenagainst the insulated plate, where it can be meas-ured by an electrometer. As this charge is equal


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THE ATOMIC STRUCTURE OF ELECTRICITY 75to w. e we can in this way easily determine n e: iitlien we can devise a means of measuring 7^- weshall be able to find e. The method by which Idetermined n was founded on the discovery byC. T. R. Wilson that the charged particles act asnuclei round which suiall drops of water condense,when the 2:)articles are surrounded by damp aircooled below the saturation point. In dust-freeair, as Aitkeu showed, it is very difficult to get afog when damp air is cooled, since there are nonuclei for the drops to condense around ; if thereare

charged particlesin the dust-free air, however,a fog \vill be deposited round these by a supersat-

uration far less than that required to produce anyappreciable effect when no charged particles arepresent.

Thus, in sufficiently supersaturated damp air acloud is deposited on these charged particles,and they are thus rendered visible. This is thefirst step toward counting them. The drops are,however, far too small and too numerous to becounted directly. AVe can, however, get theirnumber indirectly as follows : suppose we have anumber of these particles in dust-free air in aclosed vessel, the air being saturated with watervapor, suppose now that we produce a sudden


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76 ELECTRICITY AND MATTERexpansion of the air in the vessel; this will coolthe air, it will be supersaturated with vapor, anddrops vnll be deposited round the charged parti-cles. Now if we know the amount of expansionproduced we can calculate the cooling of the gas,and therefore the amount of water deposited.Thus, we know the volume of water in the form ofdrops, so that if we know the volume of one dropwe can deduce the number of drops. To find thesize of a drop we make use of an investigationby Sir George Stokes on the rate at which smallspheres fall through the air. In consequence ofthe viscosity of the air small bodies fall exceedinglyslowly, and the smaller they are the slower theyfall. Stokes showed that if a is the radius of adrop of water, the velocity v with which it fallsthrough the air is given by the equation

2 qa^9 '

when g is the acceleration due to gravity = 981and ju, the coefficient of viscosity of air = .00018;thus


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THE ATOMIC STRUCTURE OF ELECTRICITY 77But V is evidently tlie velocity witli which thecloud round the charged particle settles down, andcan easily be measured by observing the move^ment of the top of the cloud. In this way Ifound the volume of the drops, and thence n thenumber of particles. As n e had been determinedby electrical measurements, the value of e couldbe deduced when n was known ; in this way Ifound that its value is

3.4 X 10-'" Electrostatic C. G. S. units.Experiments were made with air, hydrogen,and carbonic acid, and it was found that theions had the same charge in all these gases ; astrong argument in favor of the atomic characterof electricity.We can compare the charge on the gaseous ionwith that carried by the hydrogen ion in the elec-trolysis of solutions in the following Avay: Weknow that the passage of one electro-magneticunit of electric charge, or 3 X 1^^ electrostaticunits, through acidulated water liberates 1.23 c.c.of hydrogen at the temperature 15C. and pressureof one atmosphere ; if there are N molecules in ac.c. of a gas at this temperature and pressure thenumber of hydrogen ions in 1.28 c.c. is 2.46 iV,


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78 ELECTRICITY AND MATTERSO that if 1 is tlie charge on the hydrogen ion inthe electrolyis of solution,

2.46 NE= 3 X 10'",or ^= 1.22 X lO'^-^iV:

Now, e, the charge on the gas ion is 3.4X10"'",hence if ^=3.6X10'^ the charge on the gaseousion will equal the charge on the electrolytic ion.Now, in the kinetic theory of gases methods areinvestigated for determining this quantity N, orAvogadro's Constant, as it is sometimes called ; thevalues obtained by this theory vary somewhatwith the assumptions made as to the nature ofthe molecule and the nature of the forces which onemolecule exerts on another in its near neighbor-hood. The value 3.6X10'*' is, however, in goodagreement with some of the best of these deter-minations, and hence we conclude that the chargeon the gaseous ion is equal to the charge on theelectrolytic ion.

Dr. H. A. Wilson, of the Cavendish Laboratory,by quite a different method, obtained practicallythe same value for e as that given above. Hismethod was founded on the discovery by C. T. E,.Wilson that it requires less supersaturation todeposit clouds from moist air on negative ions


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THE ATOMIC STRUCTURE OF ELECTRICITY 79than it does on positive. Thus, by suitablychoosing the supersaturation, we can get thecloud deposited on the negative ions alone, sothat each drop in the cloud is negatively charged ;by observing the rate at which the cloud falls wecan, as explained above, determine the weight ofeach drop. Now, suppose we place above thecloud a positively electrified plate, the plate willattract the cloud, and we can adjust the charge onthe plate until the electric attraction just balancesthe weight of a droj), and the drops, like Mahomet'scoffin, hang stationary in the air; if X is theelectric force then the electric attraction on thedrop is Xe, when e is the charge on the drop. AsX e m equal to the weight of the drop which isknown, and as we can measure X, e can be at oncedetermined.Townsend showed that the charge on the

gaseous ion is equal to tliat on the ion of hydrogenin ordinary electrolysis, by measuring the coeffi-cient of diffusion of the gaseous ions and com-paring it with the velocity acquired by the ionunder a given electric force. Let us consider thecase of a volume of ionized gas between twohorizontal planes, and suppose that as long as wekeep in any horizontal layer the number of ions


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80 ELECTRICITY AND AIATTERremains the same, but that the number varies aswe pass from one layer to another; let x be thedistance of a layer from the lower plane, ??-the number of ions of one sign in unit volumeof this layer, then if D be the coefficient ofdiffusion of the ions, the number of ions whichin one second pass downward through unit areaof the layer is

axso that the average velocity of the particles down-ward is

n dx'The force which sets the ions in motion is the

variation in the partial pressure due to the ions ; ifthis pressure is equal to^, the force acting on theions in a unit volume is -7-' and the averaaie forceax ^per ion is - -r-. Now we can find the velocityfv (Jj JLwhich an ion acquires when acted upon by aknown force by measuring, as Rutherford andZeleny have done, the velocities acquired by theions in an electric field. They showed that thisvelocity is proportional to the force acting on theion, so that if A is the velocity when the electric


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THE ATOMIC STRUCTURE OF ELECTRICITY glforce is JTand when the force acting on tlie ion istherefore X e, the velocity for unit force will be-==r-y and the velocity when the force is^ willXe n axtherefore be

\ dp A ^n dx Xe^this velocity we have seen, however, to be equal toD dn

n dx^hence we have

dp A ^ dn ^-xdx Xe dx 'Now if the ions behave like a perfect gas, the

pressure p bears a constant ratio to n, the numberof ions per unit volume. This ratio is the samefor all gases, at the same temperature, so that ifN is Avogadro's constant, i.e., the number of mol-ecules in a cubic centimetre of gas at the atmos-plieric pressure P

p nand equation (1) gives us

PA Xe.XDThus, by knowing D and a we can find the valueof Ne. In this way Townsend found that

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Electricity & Matter - J.J. Thompson