thompson jj - electricity and matter

ELECTRICITY AND MATTERCHAPTER I REPRESENTATION OF THE ELECTRIC FIELD BY LINES OF FORCE MY objectin theselecturesis toputbeforeyou in as simple and untechnical a manner as Ican processesg

ELECTRICITY AND

MATTER

"

J J. THOMSON, D.Sc., LL.D., PH.D.,F.R.S

""FELLOW OF TRINITY COLLEGE, CAMBRIDGE; CAVENDISH

PROFESSOR OF EXPERIMENTALPHYSICS,CAMBRIDGE

WITH DIAGRAMS

NEW YORK CHARLES SCRIBNER'S SONS

1904

BY YALE UNIVERSITY

Published, March, 1904

THE SILLIMAN FOUNDATION.

In the year1883a legacyof eightythousanddollars

wasleft tothePresident and Fellows of YaleCollege

in the city of New Haven, to be held in trust, as a

honored motherMrs.HepsaElySilliinan.

On this foundation YaleCollegewas requested and

directed to establish an annual course of lectures

de-signed to illustrate the presence and providence, the

naturaland moralworld These weretobedesignated

asthe Mrs.HepsaElySilliinanMemorialLectures It

the end of this foundation more effectively than anyattempt to emphasize the elements of doctrine or ofcreed; and hetherefore providedthat lectures ondog-matic or polemical theology should be excluded from

the scopeof thisfoundation,andthatthesubjectsshould

chemistry, geology,and anatomy

Itwasfurther directedthateach annual course should

constituting a memorial to Mrs.Sillimau. The

memo-rial fund cameinto the possession of the Corporation

of Yale Universityin the year 1902; and the present

volume constitutes thefirst of the series of memorial

lectures.

In these Lectures given at YaleUniversityin

May, 1903, I have attempted to discuss the

bear-ing of the recent advances made in Electrical

Scienceon our viewsof the ConstitutionofMatter

Electricity; two questions

thesolution of theonewould supplythat of the

other A characteristic feature of recent

Electri-cal Researches, such as the study and discovery

Substances, has been theveryespecial degree in

Inchoosing a subjectforthe Silliman Lectures,

bear-ingofrecent work onthis relationship might be

suitable, especially as such a discussion suggests

multitudes of questions which would furnish

ad-mirablesubjectsforfurther investigation by some

ofmy hearers

J J. THOMSON.

ELECTRICITY AND MATTER

CHAPTER I

REPRESENTATION OF THE ELECTRIC FIELD

BY LINES OF FORCE

MY objectin theselecturesis toputbeforeyou

in as simple and untechnical a manner as Ican

processesgoing on in theelectric field, and ofthe

connectionbetween electricaland ordinarymatter

investigations

The progress of electrical science has been

greatlypromoted byspeculations as tothe nature

overestimate theservicesrendered by twotheories

as old almost as the science itself; I mean the

theories known as the two- and the one-fluid

theoriesofelectricity.

The two-fluid theory explains the phenomena

there are two fluids, uncreatable and

indestruc-2 ELECTRICITY

one of these fluids is called positive, the othernegative electricity, and electrical phenomena

are explained by ascribing to the fluids the

as the squareof thedistance betweenthem,asdo

also the particles of the negative fluid; on theother hand, the particlesof the positive fluidat-tractthoseof the negative fluid. Theattraction

charges, m and m of the same sign, placed in

the sameposition asthe previouscharges In

an-otherdevelopmentof the theory theattraction is

affordabasisforthe explanation ofgravitation.

mo-bileandable topasswithgreat easethroughductors The state of electrificationof abody is

con-determinedby the difference between the

contains more positive fluid than negative it ispositivelyelectrified,if itcontains equal quantities

it is uncharged Since the fluids are uncreatable

and indestructible, theappearanceof the positive

departure of the same quantityfrom some other

place, so that the production of electrificationof

pro-duction of an equal amount of electrification of

the opposite sign

On this view, everybody is supposed to

con-sistofthree things:ordinary matter,positive

each other,but in the earlier formof the theory

no action was contemplated between ordinary

matterandthe electric fluids; itwas not until a

comparatively recent date that Helmholtz

ordinary matterandtheelectricfluids. Hedidthis

to explain what is known as contact electricity,

metals, say zinc and copper, are put in contact

with eachother,thezinc becomingpositively,the

sup-posed that thereare forces between ordinary

kindsof matter, theattraction of zinc for positive

4 ELECTRICITY

that when these metals are put in contact the

zinc robs the copper of some of its

positiveelectricity.

theorywhichmaybeillustrated by thetion of an unelectriEed body All that the two-

containsequalquantitiesofthetwofluids. Itgives

noinformationabouttheamountof either; indeed,

itimpliesthat if equal quantities of the two are

equalquantitiesofthetwofluidsexactlyingeach other. Ifweregardthesefluids as beinganythingmoresubstantial than the mathematical

weregardthemasphysicalfluids,forexample,we

haveto supposethatthemixtureofthetwofluids

in equal proportions is something so devoid of

physical properties that its existence has never

been detected

Theotherfluid theory the one-fluid theory of

On thisview thereis only one electric fluid,the

positive; thepart of the other is taken by

ordi-narymatter,the particles ofwhich are supposed

to repeleach other and attract the positivefluid,

just as the particles of the negative fluid do on

the two-fluid theory. Matter when unelectrified

on a portion of theelectric fluid outside it isjust

thematter Onthis view,ifthe quantity of

mat-ter in a body is known the quantity of electric

Theservices which the fluid theories have

a local habitationto theattractionsandrepulsions

existingbetween electrified bodies, and servedas

the means by which the splendid mathematical

in-versely as the square of the distance which was

inspiredbythe discovery of gravitation could be

longas we confine ourself toquestionswhichonly

involvethelawof forcesbetweenelectrifiedbodies,

andthesimultaneous productionofequalquantities

the same results and there can be nothing to

g ELECTRICITY

decidebetweenthem Thephysicistsand

mathe-maticians who did most to develop the "Fluid

Theories" confinedthemselvestoquestionsof thiskind,and refined and idealized the conceptionofthese fluids until anyreference to theirphysical

propertieswasconsidered almostindelicate It is

notuntilweinvestigatephenomenawhich involvethe physical properties of the fluid that we canhope to distinguish between the rival fluid the-

associated with given charges of electricity ingasesatlowpressures, andithas been foundthatthemass associated with a positivechargeis im-

nega-tive one This difference is what we should

expect on Franklin's one-fluid

theory, if that

theoryweremodifiedby making the electricfluid

correspond to negative instead of positive

great a difference on the two-fluid theory. We

bytheresultsof the most recent researcheswith

those enunciated byFranklin inthe very infancy

ofthe subject.

the idea of action at a distance This idea,

hasmadeitacceptable to manymathematicians,is

one which manyof the greatest physicists have

felt utterly unable to accept, and have devoted

some-thing involving mechanical continuity

Pre-emi-nentamong themisFaraday Faradaywasdeeplyinfluencedbythe axiom, orifyoupreferit,dogma

that mattercannotact where it is not Faraday,

who possessed,I believe, almost unrivalled matical insight, had had no training in analysis,

mathe-so that the convenience of the idea of action at adistanceforpurposesof calculationhad no chance

of mitigating therepugnance hefelttothe ideaof

forces acting far awayfrom their base and with

no physical connection with their origin. Hetherefore castaboutforsome way of picturingto

himself the actions in the electric field which

wouldgetrid of the idea of action ata distance,

and replace it byone which would bring into

the bodies exerting the forces. He was able to

g ELECTRICITY

dothis bythe conceptionof lines of force. As Ishallhavecontinuallytomakeuseof this method,andas I believeitspowers and possibilities have

never been adequately realized, I shall devote

sometime to the discussion and development ofthisconceptionoftheelectricfield.

FIG i.

consideration of the lines of force round a bar

magnet If ironfilingsare scattered on asmooth

surfacenear amagnet they arrange themselvesas

thedirection of these linesatany point coincides

with thedirection of themagneticforce,while the

intensity of the force is indicated bythe

concen-tration of the lines. Startingfrom anypoint in

willnot stopuntil we reach the negative pole of

themagnet; if suchlines are drawnat all points

in thefield,the spacethrough which themagnetic

giving the space afibrous structure like that

pos-sessedbyastackofhayorstraw, the grainofthe

structure being along the lines of force. Ihave

sameconsiderationswillapplytotheelectricfield,

and we mayregard the electric field as full of

lines ofelectric force, which start from positively

thispoint the process has been entirely

geometri-cal, andcouldhave been employed bythosewho

action at a distance; to Faraday, however, the

lines of force were far more than mathematical

abstractions they were physical realities.

Fara-daymaterialized the lines of force and endowed

themwithphysicalproperties so as toexplain the

phenomena of the electric field. Thus he

thattheyrepelled each other. Instead of antangible action atadistance between two electri- fied bodies, Faraday regarded the whole space

repellent springs The charges of electricity to

just the ends of these springs, and an electriccharge,insteadofbeinga portionoffluidconfined

of springs spreading out in all directions to all

parts ofthefield.

To make our ideas clear on this point let us

consider some simple cases from Faraday's point

of view Let usfirst take the case of twobodieswith equal and opposite charges, whose lines offorce are shown in Fig. 2. Younotice thatthe

joining the bodies, and that there are more lines

of force on the side of A nearest to B than on

the opposite side. Consider the effect of the

tension and are pulling away at -4; as there

OF FORCE H

are more pulling at A on the side nearest to B

than onthe opposite side,the pullsonA toward

attraction between oppositely electrified bodies

Letusnow consider the condition of one ofthe

FIG 2.

of tension and will therefore tend to straighten

itself, how is it prevented from doing this and

maintained in equilibrium in a curved position?

We can see the reason for this if we remember

that the lines of force repel each other and that

thelinesaremore concentrated in the region

PQ] thus the repulsion of the lines inside PQ

will be greater than the repulsion of those

out-sideand thelinePQwillbebent outwards

12 ELECTRICITY

Letusnowpassfromthecase oftwooppositely

in Fig 3. Letus supposeA andBare positively

positivelyand end onnegativelyelectrifiedbodies,

to join some body or bodies possessing the

FIG 3.

negative charges corresponding to the positive

charges are a considerable distance away,sothat

present, spreadout, in the partof the field under

consideration,uniformlyinalldirections Consider

force attached toA and Bapproach each other;

sincetheselines repel each other thelines offorce

onthe sideofA nearestB will be pushed to theopposite side of A, sothatthe lines of force will

now be densest on thefar side of A; thus the

pulls exerted on A in the rear by the lines offorce will be greater than those in the frontand

the result will be that A will be pulled away

from B We notice that themechanism ing this repulsion is of exactly the sametype as

pre-vious case,and we may if we please regard the

repulsion betweenAand Bas due to the

charges which must exist in

other parts of the field.

The results of the

repul-sion of the lines of force

areclearlyshowninthecase

represented in Fig 4, that

of two oppositely electrified

plates; you will notice that

the lines of force between

PIG 4.

theplates are straightexcept

near the edges of the plates; this is what we

should expectasthe downward pressure exerted

exerted by those below it. For a line of force

near the edgeof theplate, however, the pressure

press-ure from those above, and the lineof force will

bulge out untilitscurvatureand tension

counter-act the squeeze frominside; thisbulgingisvery

plainlyshownin Fig 4.

So far our use of the lines of force has been

descriptive rather than metrical; it is, however,

easy to develop the method so as to make itmetrical We can do this by introducing the

idea of tubes offorce. If throughtheboundary

ofanysmall closed curve inthe electric fieldwe

tubularsurface,andif wefollow thelinesbackto

thepositivelyelectrified surfacefrom which they

surfaceon whichtheyend, we can provethat the

positive charge enclosed by the tube atits

origin

is equal tothe negative charge enclosed byit at

its end By properly choosing the area of the

small curve through which we draw thelines of

the tubeis equal totheunit charge. Letuscall

such a tube a Faraday tube then each unit of

positive electricity in the field may be regarded

as theorigin andeach unit ofnegative electricity

as the terminationofaFaradaytube. We regard

these Faraday tubes as having direction, their

di-rectionbeingthesame asthat oftheelectric force,

sothatthe positive direction isfrom the positive

tothe negativeend ofthetube Ifwe drawany

closed surface then the difference between the

number of Faradaytubes which pass out of the

surfaceandthosewhichpassin willbeequaltothe

algebraicsumofthe chargesinsidethesurface; this

sumiswhat Maxwell called the electric

pointisthe number of Faraday tubes whichpass

right angles to that direction,the number being

while those which pass through in the opposite

direction are takenas

negative, and the numberpassingthrough the areaisthedifferencebetween

the number passing through positively and the

numberpassingthroughnegatively.

For my own part, Ihave found the conception

to the formationof a mental picture ofthe

proc-esses going on in theelectric field than that of

Maxwell took up the question of the

ten-sions and pressures in the lines of force in

step further than Faraday. By calculating the

amount of these tensions he showed that themechanicaleffects in the electrostatic field could

be explained by supposing that each Faraday

tube forceexerted a tension equaltoR, Hbeing

the intensity of the electric force, and that, inaddition tothis tension, there was in themedium

pressure equal to \NR, N being the density

right angles to

these 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 equal

pressure in all directions at right anglestothatforce.

Moving Faraday Tubes

Hithertowe have supposedthe Faraday tubes

Let us begin with the consideration of a very

simple case that of two parallel

positive the other with negative

con-nectedbyaconductingwire,EFG.

of the outlying tubes; these tubes,

when in a conductor, contract to

moleculardimensionsandthe

repul-sion they previously exerted on

disappear Consider the effect of

plates; PQ was originally in equilibrium under

its own tension, and the repulsion exertedbythe

neighboring tubes. The repulsions duetothose

thatPQwill nolongerbeinequilibrium,butwill

tubes will be pushed into E FG, and we shall

F

FIG 5.

jg ELECTRICITY

have a movement of the whole set of tubes

discharge of theplates is going on, the tubes

right angles to

themselves What physical effect accompanies

thismovementofthe tubes? The result of

con-necting the plates by EF Gistoproducea

charged plate through E F Gtothe negativelychargedplate; this is,as we know, accompanied

magnetic force is at right anglestothe plane of

the current in the plate, or,if a- is the density of

the charge of electricity onthe plates and v the

velocity with which the charge moves,the

mag-neticforceisequaltokiro-v.

Here we have two phenomena which do not

take placeinthe steady electrostaticfield,onethemovement of the Faraday tubes, the other

the existence of a magnetic force; this suggests

that there is a connection between the two, and

bythe productionofmagnetic force Ihave

have shown that, if the connection between the

below, thisview will account for Ampere's laws

connecting current and magnetic force, and for

Faraday'slaw of the induction of currents

Max-well'sgreat contribution to electricaltheory,that

variation inthe electric displacement ina

this view For, since theelectric displacementis

the electric displacement at any place changes,

place, and motion of Faraday tubes, by

hypoth-esis, impliesmagneticforce.

The law connecting magnetic force with the

magni-tude is 4?rv sin 0, the direction of themagnetic

force beingat rightangles to the Faraday tube,

andalso toitsdirection of motion; 6isthe angle

length

We shallapply theseresults to a very simple

and important case the steady motion of a

charged sphere Ifthe velocity of the sphere is

small compared withthat oflight then the

Fara-day tubes will, as whenthe sphereis at rest,be

uniformly distributed and radial in direction

Theywill be carried alongwith the sphere If

e is the charge on the sphere, its centre,the

density of the Faraday tubes at P is

TTp*'

sothat if v is the velocity of the

sphere, 6 the

anglebetween OPandthedirection ofmotion of

thesphere, then,

according totheabove rule,the

magnetic force at P will be 6V *

, the tion of the force will be at

direc-right angles to OP,

rightanglesto the direction of motion ofthe sphere; the linesof magnetic force will thus

centre of the sphere and their planes at

right

angles to this path Thus, a moving charge of

electricity will be accompanied by a magnetic

field. The existence of a magnetic field implies

energy; we know that in a unit volume of the

there are ~ units of energy, where /x is the

O7T

case of the moving sphere the energy per unit

D . a^v*sin2 ,- ,

Typr- Taking the sum of

sphere,wefindthat it amounts to

3a

isthe radius of the sphere. If m is themassof

the sphere, the kinetic energy in the sphere is

mv9

; in addition to thatwe have the energy

outside the sphere, which as we have seen is

-zod ; so that the whole kinetic energy of the

22 ELECTRICITY

~&^L^AAoL_ 9,1$

charged sphereisdueto its charge I shall later

showthatit isnot impossible that thewhole mass

ofabody mayarise intheway

Before passing on to this point, however, I

shouldlike to illustrate the increase which takesplaceinthemassofthe sphere by someanalogiesdrawnfromotherbranchesof physics Thefirstoftheseis the case of a sphere moving through a

propor-tionedtoits own,so thatto move the sphere we

sphere itself, but also theliquid around it; theconsequence of thisis,that the sphere behavesas

if itsmass were increasedbythat ofacertain

In the case ofa cylinder movingat rightanglesto

itslength,its massis increasedby themassof an

equal volume of the liquid. In the case of an

elongated body like a cylinder, the amount by

di-rection in which the body is moving, beingmuch

smaller when the body moves point foremost

than when moving sideways. The mass of such

moving

electri-fiedsphere We haveseen thatinconsequence of

its chargeits massisincreased by-(* ;thus,if it

oa

is moving with the velocityv, themomentum is

-f-"^ jv. The additional

mo-mentum - visnotinthesphere,butinthe space

space

v and whose direction is parallel to the

di-rectionof motion of the sphere. It isimportant

tobearin mindthat thismomentumisnot inany

way different from ordinary mechanical

momen-tum andcan begiven up to or taken from the

momentum of moving bodies I want to bring

the existence of this momentum before you as

vividlyand

forciblyas Ican, because the

recogni-tion of itmakesthebehaviorof the electric field

entirely analogous to that of a mechanical tem Totakeanexample, accordingtoNewton's

equalandopposite, sothat themomentum in any

direction ofanyself-containedsystemisinvariable

Now, inthecase of manyelectricalsystems there

are apparant violations of this principle; thus,

take thecase ofachargedbodyat rest struck by

andmomentum, sothat whenthe pulse has passedover it, its momentum is notwhat it was origi-

momentuminthechargedbody,i.e., ifwesuppose

thatmomentumis necessarilyconfinedtowhat weconsider ordinary matter,there has been a viola-

momentum recognized on this restricted view

hasbeenchanged. The phenomenonis, however,

recog-nizethe existence ofthemomentumintheelectric

pulse, but none in the body; after the pulsepassed over the bodythere was some momentum

in the body and a smaller amount in the pulse,

25theloss of momentuminthe pulsebeingequalto

the gainofmomentum bythe body

We now proceed to consider this momentum

on Electricity and Magnetism" calculated the

amount of momentumat anypointin the electric

field,and have shown thatifNis thenumberof

at

right anglesto their direction, Bthemagnetic

induction, the angle between the inductionand

volume is equal to N B sin 0, the direction of

the momentum being at right anglesto the

mag-netic induction and also to the Faraday tubes

Many of you will notice that the momentum is

parallel towhatis known as Poynting's vector

the vectorwhose direction gives the direction in

which energyisflowing throughthefield.

Moment of Momentum Due to cm Electrified

Point and a Magnetic Pole

To familiarizeourselves with this distribution

ofmomentumletus considersomesimple cases in

be thepoint,Bthepole. Then,sincethe

momen-26 ELECTRICITY

turn atanypointPisat right anglestoA P, the

direction of the Faraday tubes andalso toB P,

the magneticinduction,weseethat themomentum

will be perpendiculartothe plane A B P; thus,

direc-tion at anypointcoincideswith the direction ofthe momentumatthatpoint,theselineswillform

to the lineA 12,and whosecentres

liealong that line. Thisdistribution

of momentum, as far as directiongoes, is that possessedbya top spin-

what thisdistribution of momentum

It is evident that the resultant

momentum in any direction is zero,

but since the system is spinning

ofmomentumroundA B. Calculating the value

of this from the expression for the momentum

given above,weobtain theverysimple expression

em as the value of the moment of momentum

m the strength of the pole. By means of this

expression we can at once find the moment of

momentumofanydistributionofelectrifiedpoints

Toreturntothesystem of the pointandpole,

thisconception of the momentum of the system

leads directly tothe evaluation of theforceacting

onamoving electriccharge or a movingmagnetic

pole Forsuppose thatinthetime 8tthe

electri-fiedpointweretomovefromAtoA!',the ^

moment of momentum is still em, but

ifc/

its axis is alongA!IB instead of A B ^

The moment of momentum of the field \

has thus changed, butthe whole moment \

of momentum of the system comprising \

point, pole,and field mustbe constant, so \

by an equal and opposite change inthe j

moment of momentum of the pole and FlGt 8

-point The momentumgained bythe pointmust

be equal and opposite to that gained by the

pole, since the whole momentumis zero. If is

the angle A A, the change in the momentof

momentum is em sin 0, with an axis at

right

angles to A B in the plane of the paper Let

equivalent to a couple whose axis is at

rightangles to A B in the plane of the paper, and

rightangles tothe planeofthepaper and

perpen-dicular to the plane of the paper, Fbeing the

g2

rate of increase ofthemomentum,or -r' Wethus

get Jb= A rea ; orthe point isacted on bya

force equal to e multiplied by thecomponent ofthe magneticforce at right anglestothedirection

ofmotion The direction of the force actingon

the point is at

right angles to its velocity and

and oppositeforceactingon themagneticpole

Thevalue wehave found forFis the ordinaryexpression for the mechanical force acting on amoving charged particle in a magnetic field; it

may bewritten as ev Hsm<, where H's is the

strength of the magnetic field. The forceacting

on unit charge is therefore vHsm<f>. This

me-chanical force may be thus regarded as arising

from an electric force vHsin

<f>, and we may

express theresult bysaying that whenacharged

body is moving in a magnetic field an electric

force vIfsin

<f> is produced This force is the

The forces called into play are due to the

relativemotionofthe pole andpoint; iftheseare

moving with the same velocity, the line joining

them will not alter in direction,themoment of

momentum of the systemwillremain unchanged

and therewill not be anyforces actingeitheron

the pole or thepoint

The distribution of momentum in the system

of pole and point is similar in some respectsto

thatin a top spinning about the lineA B We

letFig.9 represent a balancedgyroscope spinning

horizontal, then if with a vertical rod I push

against A B horizontally, the point A will notmerelymovehorizontallyforward inthedirection

verti-cally upward or downward, just as a charged

FIG 9.

point would do if pushed forward in the same

pole atB.

momentumarisingfrom an electrifiedpoint anda

system, a quantitywhichplays a very

large part

ex-pression we have given for the moment of

mo-mentum due to achargedpoint and a magnetic

pole, we can atonce findthat duetoa charge eof

magnet A B;

letthe negative poleof thismagnetbe at A, the

positive atB, and letmbe the strength of either

pole A simple calculation shows that in this

casetheaxis of the resultantmoment of

momen-tumis inthe planeP A Bat rightanglestoPO,

makeswith O P. Thismomentofmomentum is

equivalentin direction andmagnitudeto thatdue

to a momentum e in. A B

-Qjk atPdirected

at right anglestothe planeP A B,and another

momentum equal in magnitude and opposite in

at right anglestothe plane P A Bis the vector

called by MaxwelltheVectorPotentialatP due

to theMagnet

32 ELECTRICITY

CallingthisVectorPotentialI, wesee that the

momentum due to the chargeandthe magnet is

equivalenttoamomentum eIatP anda tum eTat the magnet

momen-We mayevidentlyextend this to anycomplex

systemof magnets, sothatif/is theVector

Po-tential atPof this system, themomentum inthe

to-gether with momenta at each of the magnets

equalto

e(VectorPotential atP duetothat magnet)

currents instead of from permanent magnets, the

momentumofa systemconsistingof anelectrified

pointandthe currentswill differ in some of itsfeaturesfromthe momentum when the magnetic

mo-mentum, but no resultant momentum When,

entirely due to

easy toshow that thereisa

resultant momentum,butthat the momentof

mo-mentum about anylinepassing through the

equivalent to a momentumeIat the electrified

pointIbeing the Vector Potential atP due to

thecurrents

per-manent magnets or to electric currents or partly

to one and partly to the other, the momentum

when anelectrified pointisplacedin the fieldat

Pisequivalentto amomentum eTat P where I

field is

entirely duetocurrentsthis is a complete

representation of the momentum in the field; if

have in addition to this momentum at P other

momentaat thesemagnets;themagnitude of the

momentum at any particular magnetis etimes

follow at once from this result. For, from the

self-contained system must be constant Now the

momentumconsists of (1) the momentum in the

and (3) themomentaof the magnets or circuits

carrying thecurrents. Since (1)is equivalent to

amomentume1attheelectrified particle, wesee

com-ponents parallel to these axes of the Vector

equivalenttomomenta eF,e G,eHat Pparallel

to the axesof a?, y,z; and themomentum of the

Mw Asthemomentumremainsconstant,Mu

-f-eF\* constant,henceif 8w and F are

simulta-neous changesinu andF,

In a similar way we see that there are electric

theforces due to electro-magnetic induction, and

weseethat theyare a direct consequence of the

principle thataction and reaction are equal and

opposite

willremember that he is constantlyreferring to

whathecalledthe "Electrotonic State"; thushe

as being in the Electrotonic State when in a

detectedaslongas thefield remains constant; it

Electrotonic State of Faraday is

just the tumexisting inthe field.