jj-thompson the corpuscular theory of matter

The principle ofthe method usedis as follows: When aparticle carrying a charge e is moving with the velocity vacross the lines of force inamagnetic field, placed so that the lines ofmagn

THE CORPUSCULAR

J. J THOMSON, M.A. F.R.S D.Sc LL.D Ph.D.

PROFESSOR OF EXPERIMENTAL PHYSICS, CAMBRIDGE, AND PROFESSOR

OF NATURAL PHILOSOPHY AT THE ROYAL INSTITUTION, LONDON.

LONDON

ARCHIBALD CONSTABLE & CO LTD.

1907

%^^l^ 3f

BRADBURY, AftNEW, &CO LD.^PRINTERS, LONDON AND TONBRIDGK.

This bookis an expansion of acourse of lectures givenat

the EoyalInstitution inthe Spring of 1906 It contains adescription of the properties of corpuscles and theirapplication tothe explanationof some physical phenomena.

Inthe earlierchapters a considerable amount of attention

is devoted to the consideration of the theory that manyo' the properties of metals are due to the motion of

corpuscles diffused throughout the metal This theory has

received strong support from the investigations of Drude andLorentz;the formerhas shownthat thetheorygivesanapproximately correct value for the ratio of the thermaland electrical conductivities of pure metals and the latter

that it accounts for the long-wave radiation from hot

bodies I give reasons for thinking that the theory in its

usual form requires the presence of so many corpuscles

that theirspecific heat would exceed the actualspecific heat

of the metal I have proposed a modificationof the theorywhich is not open to thisobjection and which makes theratio of the conductivities and the long-wave radiation of

the right magnitude

The later chapters contain a discussion of the properties

of anatom built up of corpusclesand of positive electricity,

the positive electricity being supposed to occupy amuch

larger volume than the corpuscles The properties of anatom of this kind are shown to resemblein many respects

thoseoftheatoms of thechemical elements I thinkthat a

theory which enables us to picture a kind ofmodel atom and to interpret chemical and physical results in terms of

vi PEEFACE.

such model may be useful even though the models are

crude, for if we picture to ourselves how the modelatom,must be behaving in some particularphysical or chemical

process, we not only gain a very vivid conception ofthe

process, but also often suggestions that theprocess underconsideration must be connected with otherprocesses, andthus further investigations arepromoted by this method; italso has theadvantageofemphasisingthe unity ofchemicaland electrical action

In Chapter VII I give reasons for thinking that thenumber of corpuscles in an atom of an element is not

greatly in excess ofthe atomic weight of the element, thus

in particular that the number ofcorpuscles in an atom of

hydrogen is not large. Some writers seemto think that

this makes the conceptionof themodel atom moredifficult.

I am unable to follow this view; it seems to me tomakethe conception easier, since it makes the number of

possible atoms much more nearly equal to the number of

the chemical elements It has, however, an importantbearing on our conception of the origin of the mass of theatom, as if the number of corpuscles in the atom is of thesame order as the atomic weight we cannot regard themass of an atom as mainly or even appreciably due to themass of the corpuscles

I am indebted to Mr G W. C Kave for assisting inrevising theproof sheets

J J. Thomson.Cambridge,

July 1 5, 1907.

I. Introduction—Coepuscles in Vacuum Tubes 1

II. The Origin of the Mass of the Corpuscle 28

III. Properties of a Corpuscle 43

IV Corpuscular Theory of Metallic Conduction 49

V. The Second Theory of Electrical Conduction 86

VI The Arbangement of Corpuscles in the Atoii 103

VII On the Number of Corpuscles in an Atom 142

The theory of the constitution of matter whichI propose

to discuss inthese lectures, is one which supposes that thevarious properties of matter may be regarded as arising

fromelectrical effects. The basisofthe theoryis electricity,

and its object is to construct a model atom, made up of

specified arrangements of positive and negative electricity,

which shall imitate as far as possible the properties of the

real atom We shall postulate that the attractions andrepulsions betweenthe electrical chargesin the atom follow

the familiar law of the inverse square of the distance,

though, of course, we have only direct experimental proof

of this law when the magnitude of the charges and the

distances betweenthem are enormouslygreater than thosewhich can occur in the atom "We shallnot attempt to gobehindthese forces and discuss the mechanism by whichthey might be produced The theory is not an ultimateone; its objectis physicalratherthanmetaphysical Fromthe point of view of the physicist, a theory of matteris apolicy rather than a creed; its object is to connect or

co-ordinate apparently diverse phenomena, and above all

to suggest, stimulate and direct experiment It ought to

furnisha compasswhich, iffollowed, willlead the observer

further and further into previously unexplored regions

2 THE COEPUSCULAK THEOEY OF MATTEE.

Whetherthese regions will be barren or fertile experiencealone will decide; but, at any rate, one who is guided inthis way willtravel onwardin a definite direction, andwill

not wander aimlesslyto andfro.

The corpuscular theory ofmatter withits assumptions of electrical chargesand the forces between them isnot nearly

so fundamental as the vortex atom theory of matter, in

which all that is postulated is an incompressible, less liquid possessing inertia and capable of transmitting

friction-pressure On this theory the difference between matterand non-matter and between one kind of matter andanotheris a difference betweenthe kinds of motion in theincompressible liquid at various places, matter being thoseportions of the liquid in which there is vortex motion.The simplicityofthe assumptionsofthe vortex atom theory

are, however, somewhat dearly purchased atthe costof themathematical difficulties which are met withinits develop-ment ; and for many purposesatheorywhose consequences

are easily followed is preferable to one which is morefundamental but also more unwieldy We shall, however,

often have occasion to avail ourselves of the analogy which

exists betweenthe properties oflines of electric force in the

electric field andlines ofvortexmotioninanincompressible

fluid.

To return to the corpuscular theory Thistheory, as I

have said, supposes that the atom is made up of positive

and negative electricity. A distinctive feature of this

theory—the one from which it derives its name —is the

peculiar wayinwhich the negativeelectricityoccurs both in

the atom and when freefrommatter We supposethat thenegative electricity always occurs as exceedinglyfine par-

ticles calledcorpuscles, and that allthese corpuscles, ever theyoccur, arealwaysofthesamesize and alwayscarrythe same quantity of electricity. Whatever may prove to

when-be the constitution of the atom, we have direct

experi-mental proof ofthe existence ofthese corpuscles, andI will

begin the discussion of the corpuscular theory with a

description of the discovery andproperties ofcorpuscles

COEPUSCLES IN VACUUM TUBES. 3

Corpuscles in Vacuum Tubes

highly exhausted tube throughwhich an electric dischargewas passing When I send an electric discharge through

this highly exhausted tubeyou will notice thatthe sides of

the tube glow with a vivid green phosphorescence That

this is due to something proceeding in straight lines fromthe cathode—the electrode where the negative electricity

enters the tube—can be shown in the following way:

the experimentis one made manyyears ago by Sir WilliamCrookes A Maltese cross made of thin mica is placedbetweenthe cathode and the walls of the tube You will

notice that when I send the discharge through the tube,

the green phosphorescence does not now extend all overthe end ofthe tube as it did inthe tubewithout the cross.

There is a well-defined cross in which there is no

]3hos-phorescence at the end of the tube; the mica cross hasthrown ashadow on the tube, andthe shape of the shadowproves that the phosphorescence is due to something,

travelling from the cathode in straight lines, which is

stoppedbya thin plateofmica Thegreenphosphorescence

iscaused by cathode rays, and at one time therewas akeencontroversy as to the nature of these rays Two viewswere prevalent, one, which was chiefly supported byEnglish physicists, was that the rays are negativelyelectri- fied bodies shotoff from the cathode with great velocity

the other view, which was held by the great majority ofGerman physicists, was that the rays are some kind of

ethereal vibrations or waves

The arguments in favour of the rays being negatively

charged particles are (1) that they are deflected by

a magnet in just the same way as moving negatively

electrified particles. We know that such particles when

a magnet is placed near them are acted upon by aforce whose direction is at right angles to the magnetic

force, and also at right angles to the direction inwhich the

particles are moving Thus, if the particles are moving

b2

4 THE COEPUSCULAR THEORY OF MATTER'.horizontally from east to west, and the magnetic force is

horizontal and from northto south,the force actingonthenegatively electrified particles will be vertical and down-wards

When the magnetis placed so that the magnetic forceis

along the direction in which the particle is moving the

latter will not be affected bythe magnet By placing themagnet in suitable positions I can show you that thecathode particlesmove inthe way indicated bythe theory

The observations that can be made in lecture are sarily very rough and incomplete; but I may add that

neces-elaborate and accurate measurements of the movement of

1.

cathode rays under magneticforces have shownthat in this

respect the rays behave exactly as if they were moving

electrified particles.

Thenext step made inthe proof that the rays are

nega-tively charged particles, was to show that when they are

caught in a metal vessel they give up to it a charge of

negative electricity. This was first done by Perrin I

havehere amodification of his experiment ^ is a metal

cylinder with a hole in it It isplaced so as to be out of

the wayof therays comingfromC,unless theyare deflected

by a magnet, and is connected with an electroscope You

see that when the rays donot pass through the holein the

cylinderthe electroscope does notreceive a charge I now,

by means of a magnet, deflect the rays so that they pass

the You by

COEPUSCLES IN VACUUM TUBES. 5

of the gold-leaves that the electroscope is charged, and on

testingthe sign ofthe charge we find that it isnegative

Deflection op the Eats by a Chaeged Body

If the rays are charged with negative electricity theyought to bedeflected by an electrified body as well as by a

magnet In theearlier experiments made onthis point nosuch deflectionwas observed The reason of this has beenshown to bethat whenthecathode rays pass throughagasthey make it a conductor of electricity, so that if there is

any appreciable quantity of gas in the vessel through

to get rid of this effect and to obtain the electric

deflec-tion ofthe cathoderays The arrangement I used for this

purpose is shown in Fig 2. Theraysontheirway throughthe tube passbetween twoparallelplates,A,B, whichcan beconnected with the poles ofa battery of storage cells. Thepressure in the tube isvery low You will notice that therays are very considerably deflected when I connect the

and

6 THE COEPUSCULAE THEOEY OF MATTEE.

of the deflection shows that the rays are negativelycharged

We can alsoshow theeffect ofmagnetic and electricforce

onthese rays ifwe availourselves of the discoverymade byWehnelt, thatlime when raisedto a red heat emits whennegatively chargedlarge quantitiesof cathode rays Ihavehere atube whose cathode is a strip of platinum on whichthere is a speck of lime "When the piece of platinum is

made very hot, a potential difference of 100 volts or so is

sufficient to make astream of cathode rays start fromthis

speck; youwill be able to trace the course of the rays bythe luminosity they produce as they pass through the gas

PIG 3.

Youcan see the rays as a thin line of bluish light comingfrom apoint on the cathode; on bringing a magnetnear it

the line becomescurved,and I can bend it into acircle or a

spiral, and make it turn round and go right behind thecathode from which it started. This arrangement shows

in a very striking way the magnetic deflection of the rays

To show the electrostatic deflection I use the tube shown inFig 3 I charge up the plateBnegatively so thatit repels

the pencil ofrayswhich approachitfromthe spotoflimeonthe cathode, C You see thatthe pencil of rays is deflected

from the plate and pursues a curved path whose distance

from the plate I can increase or diminishby increasing or

diminishing the negative charge on the plate.

COEPUSCLES IN VACUUM TUBES. 7

We have seen thatthe cathode rays behave under every

test that we have api^Ued as if they are negatively trified particles; we have seen that they carry a negativecharge of electricity and are deflected by electric andmagnetic forces just as negatively electrified particles

elec-would be.

Hertz showed, however,that thecathode particles possess

another property which seemed inconsistent with theideathat they are particles of matter, for he found that theywere able to penetrate very thin sheets of metal, for

example, pieces of gold-leaf placed between them and the

glass,and produce appreciable luminosity onthe glass after

doing so. The ideaof particles as large as themolecules of

agas passingthroughasolid platewasasomewhatstartling

riG 4.

one in an age whichknew not radium—which does projectparticles of this sizethrough jjieces of metal much thicker

than gold-leaf—and this led meto investigatemore closely

the nature ofthe j)articles which form the cathoderays

The principle ofthe method usedis as follows: When aparticle carrying a charge e is moving with the velocity vacross the lines of force inamagnetic field, placed so that

the lines ofmagnetic force areatright anglesto themotion

of the particle, then if H is the magnetic force, themoving particle will be acted on by a force equal toHe r.

This force actsin the direction which is atright angles to

the magnetic force and to the direction of motion of the

particle, so that if thejJarticle is moving horizontally as in

thefigure and the magnetic force is at right angles to the

and

8 THE COEPUSCULAE THEOEY OF MATTEE.

electrified particlewill be acted on bya vertical and upward

force. The pencilofrayswillthereforebedeflectedupwardsand with it the patch of green phosphorescence where it

strikesthewallsof thetube Letnowthetwoparallel plates

AandB (Fig.2) betweenwhichthe pencilof rays is moving

be charged withelectricity so thatthe upper plate is

nega-tively andthe lower plate positively electrified, the cathoderays will be repelled from the upper plate with a forceXewhereA' istheelectricforcebetweenthe plates. Thus,ifthe

plates are charged when the magnetic field is acting on the

rays,themagnetic force will tend to sendthe rays upwards,while the charge onthe plates willtend to sendthem down-wards We can adjust the electric and magnetic forcesuntil they balance and the pencil of rays passes horizon-

tally in a straight line between the plates, the green patch

of phosphorescence being undisturbed "When this is the

case, the force Hev due to the magnetic field is equal to

Xe —the force dueto the electric field—and we have

velocity of the rays found in this way is very great; it

varies largely with the pressure of the gas left inthe tube

Inavery highlyexhausted tubeitmaybe 1/3 the velocity of

light or about 60,000 miles per second; in tubes not so

highly exhaustedit maynot be morethan 5,000 miles per

second, butin all cases whenthe cathode rays areproduced

intubes their velocity ismuch greater than the velocity of

any other moving body with which we are acquainted It

is, for example, many thousand times the average velocity

with which the molecules of hydrogen are moving at

ordinary temperatures, or indeed at any temperature yet

COEPUSCLES IN VACUUM TUBES. 9

Determination of e/vH.

Havingfound thevelocity of the rays, let us in the

pre-ceding experiment take away the magneticforce and leavetherays tothe action of the electric force alone Then theparticles forming the rays are acted upon by a constant

vertical downward force andthe problem is practically that

of a bullet projected horizontally with a velocity v and

fall-ing under gravity We knowthat in time t thebody will

fall adepth equal to^gt"^ where g is the vertical tion; inour case the verticalacceleration is equal to A'e/mwhere mis the mass of the particle, the time it is falling

accelera-is l/v where I is the length of path measured horizontally,

and V the velocity of projection Thus, the depth the

particle hasfallen when it reaches theglass, i.e., theward displacement of the patch of phosphorescence wherethe rays strike theglass, is equal to

down-1 Xe l^

We can easily measure d the distance the phosphorescentpatch is lowered, and as we have foundv and Xand Iareeasily measured, we canfind ejiii from the equation :

m X

e-The results of the determinations of the values of ejmmade by this method are veryinteresting, for it is found

that however the cathode rays are produced we always

get the same value of ejm for all the particles in the

rays We may, for example, by altering the shape of thedischarge tube and thepressureofthe gas inthe tube, pro-

ducegreatchangesinthe velocityof theparticles,but unlessthevelocity of the jparticles becomes so great thatthey are

moving nearlyas fast as light, when, as we shall see, otherconsiderations have to be taken into account, the value of

ejm is constant The value of ejin is not merely

inde-pendentof thevelocity. What is even more remarkable isthatit is independent of the kind of electrodes we use and

10 THE COEPUSCULAE THEOEY OF MATTEE.

also of the kind of gas inthe tube The particleswhichform thecathode rays must comeeitherfrom the gas inthetube or from the electrodes ; we may, however, use anykind of substance we please for the electrodes andfill thetube with gas of any kind, and yet the value of ejin will

remain unaltered

This constant value is, when we measure e/m in the

C G S. system ofmagnetic units, equalto about 1"7 x 10''.

If we compare this with the value of the ratio of the mass

to the chargeof electricitycarried byany system previouslyknown, wefind thatit is of quite a different order ofmagni-

tude Before the cathode rayswereinvestigated thechargedatom of hydrogen met with in the electrolysis of liquids

was the system which had the greatest known value forejm, and in this case the value is only 10*; hence for thecorpuscleinthecathode rays the valueof e/in is 1,700 timesthe value of the corresponding quantity for the chargedhydrogen atom This discrepancy must arise in one or

other oftwo ways, eitherthe mass of the corpuscle must bevery small compared with that of the atom of hydrogen,whichuntil quite recentlywas the smallest mass recognised

in physics, or else thecharge on the corpuscle mustbe very

much greater than that on the hydrogenatom Now it hasbeen shown bya methodwhich I shall shortly describe that

the electric charge ispractically the same inthe two cases

hence we are driven to the conclusionthat the mass of thecorpuscle is only about 1/1700 of that of the hydrogenatom Thus the atomis not the ultimatelimit to the sub-

division of matter; we may go further and get to the

corpuscle, and at this stage the corpuscle is the same fromwhatever source it maybe derived

COHPUSCLES VERY WIDELY DISTRIBUTED

It is not onlyfrom what may be regarded as a somewhat

artificial and sophisticated source, viz., cathode rays, that

we can obtain corpuscles "When once they had beendiscovered it was found that they were of very general

CORPUSCLES IN VACUUM TUBES. 11

a red heat: you have already seen what acopious supply

is given out byhot lime Anysubstance whenheated gives

out corpuscles to some extent; indeed, we can detect theemission ofthem from some substances, such as rubidiumand the alloy of sodium and potassium, even when theyarecold; and it is perhaps allowable to suppose that there

is some emission byall substances, thoughour instruments

are not at present sufficiently delicate todetect it unlessit

is unusually large.

Corpuscles are also given out bymetals andother bodies,

but esjjeciallyby the alkalimetals, when these are exposed

to light. They are being continually given out in largequantities, and with very great velocities by radio-active

substances such as uranium and radium ; they are

pro-duced in large quantities when salts are put into flames,

andthere is good reason to suppose that corpuscles reach

us from the sun

The corpuscle is thus very widely distributed,butever it is found it preserves its individuality, e/iii beingalways equal to a certain constant value

where-The corpuscle appears to form a part of all kinds of

matter under themost diverse conditions; itseemsnatural,therefore, to regard it as one of the bricks ofwhich atoms

are built up

Magnitude of the Electric Charge carried by the

Corpuscle

I shall now return tothe proof thatthe very large value

of ejinfor the corpuscle ascompared with thatfor theatom

of hydrogen is dueto the smahness of m the mass, and not

to the greatness of e the charge We can do this by

actually measuring the value of e, availing ourselves for this purpose of a discovery by C T. E Wilson, that a

charged jDarticle acts as a nucleus round which watervapourcondenses,and formsdropsof water Ifwehave air

saturated with watervapour and cool it so thatit would besupersaturated if there were no depositionofmoisture, we

know thatif any dust is present, the particles of dust act

12 THE COEPUSCULAR THEORY OF MATTER.

as nuclei round which the water condenses and we get thetoofamihar phenomenaoffog andrain Ifthe air is quitedust-free wecan,however,cool it very considerably withoutany deposition of moisture taking place If there is no

dust, C. T E Wilson has shown that the cloud does notform until the temperature has been lowered to such apoint that the supersaturation is about eightfold When,however, this temperature is reached, a thick fog forms,even indust-free air. When charged particles are present

FIG O.

inthe gas, Wilson showed tbat a much smaller amount of

cooling is sufficient to produce the fog, a fourfold saturation being all that is required when the charged

super-particles are those which occur in agas when it is in the

state inwhich it conducts electricity. Each of thecharged

particles becomes the centre round which a drop of waterforms; the drops form a cloud, and thus thecharged par-

can be observed The effect ofthe chargedparticles onthe

can shown very by

COEPUSCLES IN VACUUM TUBES. 13

following experiment The vessel A, which is in contactwith water, is saturated with moisture at the temperature

of the room This vessel is in communication with B, acylinderin whicha large piston, C, slides up and down; thepiston, to begin with, is at the top of its travel ; then bysuddenly exhausting the air from below the piston, the

pressure of the air above it will force it down with greatrapidity, and the air in the vessel A will expand very

quickly When,however,air expands itgets cool; thus the

air inA gets colder, and as it was saturated with moisture

before cooling, it is now supersaturated If there is nodust present, no deposition of moisture will take place

unless the airinA iscooledto such a low temperature that

the amount of moisture required to saturate it is onlyabout 1/8 of that actually present Now the amount of

cooling, and thereforeof supersataration, depends upon the

travel of the piston; the greater the travelthe greater the

cooling I can regulate this travel so that the saturation is less than eightfold, and greater than four-

super-fold. We now freethe airfrom dust by forming cloud after

cloud in the dusty air, as the clouds fall they carry the

dust downwith them, just asin nature the air iscleared byshowers Wefind at last thatwhen we makethe expansion

no cloud is visible. We now put the gas in a conducting

state bybringing alittle radiumnear the vesselA; this fills

the gas with large quantities of both positively and

nega-tively electrified particles. On makingthe expansion now,

an exceedingly dense cloud is formed That this is dueto

the electrification in the gas can beshown by the followingexperiment:Alongthe inside wallsofthevesselA wehavetwo

vertical insulated plates which can be electrified; if theseplates are electrifiedtheywilldragthecharged particles out

of thegas asfast as theyare formed, so thatby electrifying

the plates we can get rid of, or at any rate largely reduce,the numberof electrified particles in thegas I now repeat

the experiment, electrifying the plates before bringing upthe radium Yousee that the presenceof theradiumhardly

increases the small amountof cloud Inow discharge the

14 THE COEPUSCULAE THEOEY OP MATTEE.

plates, and on making the expansionthe clond is so dense

as to be quite opaque

We can use the drops to find the chargeon theparticles,

forwhen we know the travel of the pistonwe can deducethe amount of supersaturation, and hence the amount of

water deposited when the cloud forms The water is

deposited in the form of anumberof small drops all ofthesame size ; thus the number of drops will be the volumeof

the water deposited divided by the volume of one of the

drops Hence, ifwe find the volumeof one of the drops

wecan find the number of drops which areformed roundthechargedparticles If theparticlesarenottoonumerous,each will have a drop round it, and we can thus find thenumber of electrified particles.

Ifweobserve therate atwhichthe drops slowlyfall down

we can determine the size ofthe drops Inconsequenceof

theviscosity or friction of the air small bodies donot fall

with aconstantlyaccelerated velocity,butsoonreach a speedwhich remains tiniform forthe rest of the fall ; the smallerthe body the slowerthis speed, and SirGeorge Stokes hasshown thatv, the speed at which a drop of rain falls, is

given by the formula

—

2 g

a-^ ~ 9

H-where a is the radius of the drop, g the acceleration due

to gravity, and /a the co-efiicient ofviscosity ofthe air If

we substitutethe values ofg andfx.,weget

V = 1-28 X 10^a^

Hence, if we measure vwe can determine a, the radius of

the drop We can, inthis way, find the volume of adrop,and maytherefore, asexplained above,calculate thenumber

ofdrops, and therefore the number of electrified particles.

It is asimple matter to find, byelectricalmethods,thetotal

quantity of electricity on these particles; and hence, as we

know the number of particles, we can deduce at once thecharge on eachparticle.

COEPUSCLES IN VACUUM TUBES. 15This was the method by which I first determined thecharge on the particle. H. A AVilson has since used a

simpler method founded on the following principles

C. T E Wilson hasshownthatthedropsofwatercondensemore easily on negatively electrified particles than on

positivelyelectrifiedones Thus,byadjusting theexpansion,

it is possible to get drops of water round the negative

f)articles and not round the positive; with thisexpansion,

therefore, all the drops are negativelyelectrified. The size

of these drops, and therefore their weight, can, as before,

be determined by measuring the speed at which they fall

undergravity Suppose now,that we hold abovethedrops

a positively electrified body, then since the drops are

negatively electrified they will be attracted towards the

positive electricity and thus the downward force on thedrops will be diminished, and they will not fall so rapidly

as they did when free from electrical attraction If we

adjust the electrical attraction so that the upward force oneach drop is equal to the weight ofthe drojJ, thedrojps will

sus-pended between heaven and earth If, then, we adjust the

electricalforce until thedropsare inequilibriumandneither

equal to the weight of the drop, which we have alreadydetermined by measuring the rate of fall when the dropwasnotexposed toanyelectrical force IfXistheelectrical force, ethe charge on the drop, and iv its weight, we have,

when there is equilibrium

—

Xe = IV.

Since Xcan easily bemeasured, andiv is known, we canuse this relation to determine e, the charge on the drop

Thevalueof efound bythese methodsis 3"1 X 10"^°

electro-static units, or 10"^" electromagnetic units. This value is

the same as that of the charge carried by ahydrogen atom

inthe electrolysis of dilute solutions, an approximate value

of whichhas long been known

It might be objected that the charge measured in the

16 THE COEPUSCULAR THEOEY OF MATTEE.

preceding experiments is the charge on a naolecule or

collection of molecules of the gas, and not the charge on

a corpuscle This objection does not, however, apply to

another form in -which I tried the experiment, where thecharges onthe particleswere got, not by exposing the gas

to the effects ofradium, butbyallowing ultra-violetlighttofall on ametal plate in contact with the gas. Inthis case,

as experiments made in a very high vacuum show, the

electrification which is entirely negative escapes from themetal in the form of corpuscles When agas is present*

the corpuscles strike against the molecules of the gas and

stick to them Thus, though it is the moleculeswhich are

charged, the charge on amolecule isequalto the chargeon

a corpuscle, and when we determine the charge on themolecules bythemethods I havejust described, we deter-

minethe charge carried bythecorpuscle The valueofthechargewhen the electrification is produced byultra-violetlight isthe same as when the electrification is producedby

We have just seen that e, the chargeon the corpuscle,is

in electromagnetic units, equal to lO"^, and we have

pre-viously found that elm., m being themass of a corpuscle, is

equal to 1"7 X 10^, hence 7h = 6 X 10"^^ grammes.

We can realise more easily wBat this meansifweexpressthe mass of the corpuscle interms ofthe mass of the atom

of hydrogen We have seen that for the corpuscle

atom ofhydrogen inthe electrolysis ofdilute solutions, and

M the mass of the hydrogen atom, E\M = 10*; hence

e\tn = 1700 Fj\M We have already stated that thevalue of e found by the preceding methods agrees well

with the value of H, which has long been approximatelyknown Townsend has used a method in which the value

of e/-E is directlymeasured and has showed in thiswayalso

that e isequal to -E ; hence,sinceelm = 1700EIM, wehave

M = 1700 )/(, i.e., the mass of a corpuscle is only about1/1700j)art ofthe mass ofthe hydrogen atom

Inall known cases in whichnegative electricity occurs in

CORPUSCLES IN VACUUM TUBES. 17gases at very low pressures it occurs in the form of

corpuscles, small bodies with an invariable charge andmass Thecaseisentirelydifferentwithpositive electricity.

The Caekiers of Positive Elbctbicity

We getexamplesof positivelycharged particles invariousphenomena One of the first cases to beinvestigated was

thatofthe"Canalstrahlen" discoveredbyGoldstein Ihavehere a highly exhausted tube with a cathode, throughwhich a large number of holes has been bored When I

send a discharge throughthis tube youwillsee thecathoderays shooting out in front of the cathode In addition tothese, you see other rays streaming through the holes in

the cathode, and travelling throughthegas at the back of

FIG 6.

the cathode Theseare called " Canalstrahlen." Younotice

that, like the cathoderays, they make the gas luminous as

they passthrough it, but the colour of the luminosity due

to the canalstrahlen is not the same as that due to thecathode rays The distinctionis exceptionally well marked

in helium, where the luminosity due tothe canalstrahlen is

tawny, and that due to the cathode rays bluish The

luminosity, too, produced when the rays strike against a

solid is also of quite a different character This is well

shown by allowing both cathode rays and canalstrahlen to

strike against lithium chloride Under the cathode raysthe salt gives out a steely blue light, and the spectrum is acontinuous one; underthe canalstrahlen the salt gives out

a brilliant red light, and the spectrum shows the lithium

line It is a very interesting fact that the lines in thespectra of the alkali metals are very much more easily

18 THE COEPUSCULAE THEOEY OF MATTEE.

obtained when the canalstrahlen fall on salts of the metalthan when theyfallon themetal itself. Thus when apool

oftheliquid alloyofsodium and potassiumisbombarded bycanalstrahlen the specks of oxide on the surface shine with

a bright yellow light, while the untarnished part of the

surface is quite dark

The canalstrahlen are deflected by a magnet, though not

to anything likethe same extent asthe cathoderays Their

deflection, too, is in the opposite direction, showing that

theyare positively charged

Value of e/m foe the Particles in the Canalstrahlen

W Wien has applied themethodsdescribedinconnectionwith the cathode raysto determine the value of e/vifor the

particles in the canalstrahlen The contrast between the

results obtained for the two rays is very interesting Inthe caseof the cathode rays thevelocity of different rays

inthe same tube maybe different, but the value ofe/m for

these rays is independent of the velocity as well as of thenature of the gasand the electrodes In the caseof thecanalstrahlen we getin the same pencil of rays not merely

variations in the velocity, but also variations in the value

of e/m Thedifference between the values of e/m for thecathode rays and the canalstrahlen is also very remarkable.For the cathode rays e/m always equal to l"7XlO^; while

for canalstrahlen the greatest value ever observed is 10*,

which is also the value of e/m for the hydrogenions in the

electrolysis of dilute solutions When the canalstrahlenpass throughhydrogenthe value of e/mfor a large portion

of the rays is 10*. There are, however, some rays presentevenin hydrogen, forwhich e/m is muchless than 10*, andwhich are but slightly deflected even by very intensemagnetic fields. When the canalstrahlen pass throughvery pure oxygen, Wien found that the value of e/m for

the most conspicuous rays was about 750,which isnot far

from what it would be if the charge were the same as for

the canalstrahlen in hydrogen, while the mass was greater

mass an atom

CORPUSCLES IN VACUUM TUBES. 19

of an atom of hydrogen Alongwith these rays in oxygen

there were others having still smaller values ol^ejin, andsome having ejm equal to 10*.

As the canalstrahlen or rays of positive electricity are

a very promising field for investigations on the nature

of positive electricity, I have recently made a series of

experiments on these rays in different gases, measuring

the deflections they experience when exposed to electric

and magnetic forces and thus deducing the values of «/mand V I find, when the pressure of thegas is nottoo low

that the bright spot produced by the impact of these

rays on the phosphorescent screen is deflected by electric

and "magnetic forces into acontinuous band extending, as

shown in Fig 7, on both sides of the undeflected portion,

the portion on one side {cc) isverymuchfainter than that

on the other, and also somewhat shorter The direction

of the deflection of the band cc shows that it is produced

by particles charged with negative electricity, while the

brighter band hh is due to particles charged with positive

electricity. The negatively charged particles which

pro-duce the bandcc are not corpuscles,forfrom thedeflections

in this band we can find the value of ej'm ; as this value

20 THE COEPUSCULAR THEOEY OF MATTEE.

comes out of the order 10*, we see thpt the mass of the

carrier is comj)arable with that of an atom, and therefore

immensely greater than that of a corpuscle When the

pressure is very low the portion of the phosphorescence

deflectedin the negative direction disappears and the phorescent spot, instead of being stretched bythe electric

phos-and magnetic forces into a continuous band, is broken up

into two patches, as in the curved parts of Figs 8 and 9.Fig 8is the appearance atexceedinglylow pressures Fig 9thatatasomewhathigherjpressure. Foroneofthesepatches

about5X10^. The appearanceof thepatches andthe values

of e/m at these very low jDressures are the same whether

o

oo

The curved patches represent the

and magnetic force.

the tube is filled originally with air, hydrogen, or helium.Another experimentI tried was to exhaust the tube until

the pressurewas too lowfor the discharge to pass,and then

to introduce into thetube avery small quantity of gas, thisincreases the pressure and the discharge is able to passthrough the tube The following gases were admitted intothe tube: air, carbonic oxide, oxygen, hydrogen, helium,argonand neon, butwhatever the gas the appearanceofthe

phosphorescence was the same In everycase there weretwo 23atches,one havinge/m = 10*,the other ejm = 5 X lO''.

At these very low pressures the intensity of the electric field in the discharge tube is very great.

When the 23ressure inthe tubeis not verylowthe nature

rays depends very considerable

COEPUSCLES IN VACUUM TUBES. 21uponthe kind of gas withwhich thetubeis filled. Thus,

for example, in air at these pressures the phosphorescentspot is stretched out into a straight band as in Fig 7; the

at suitable pressures we getthe spot stretched out into twobands as in Fig 10; for one of these bands the maximum

FIG 10.

value of e/m is 10*, while for the other it is 5X 10^. Inhelium we also get two bands as in Fig 11, but while the

same as for the corresponding band in hydrogen, the

maximum value of e/ni in the otherband is only2'5 X 10^.

We see fromthis that theratio ofthemasses ofthecarriers

—

The rays on their way to the screen have to passthrough gas which is ionised by the passage through it of

22 THE COEPUSCULAE THEOEY OF MATTEE.

the rays; this gas will therefore contain free corpuscles

The particleswhich constitutethe rays start with a charge

of positive electricity ; some of these in their journeythrough the gas may attract a corpuscle, the negativecharge onwhich will neutralise the positive charge on the

particle. The particles when in this neutral state may be

ionised by collision and reacquire a positive charge, or by

attracting another corpuscle they may become negativelycharged, andthis process maybe repeated several times intheir journeyto the screen Thus, some of the particles,

instead of being positively charged for the whole of thetime they are exposed to electric and magnetic forces, may

befor a partof thattime without a charge or even have anegative charge Now the deflection of a particle will beproportional to the average value of its charge whileunder the action of electric and magnetic forces; if the

particle is without chargefor a 23art of the time, its

deflec-tion will be less thanthat of ajDarticle which has retained

its positive charge for the whole of the journey, while thesmall number of particles, which have a negative charge

for a longer timethan theyhave apositive, will be deflected

in the opposite direction and produce the faint tail of

phosphorescence which is deflectedinthe opposite direction

to the main portion

It is remarkable and suggestive that even when greatcare is takento eliminate hydrogen from the tube, we get

at all pressures a large quantity of rays for which e/m is

equal to IC, the value for the hydrogen atom; and in

manj^ cases this is the only definite value of ejin to beobserved, for the continuous band in which we have all

values of e/in is due, as we have seen, notto changes inm,but to changes inthe average value of e.

If the presence of rays for which e/m = 10"^was entirely

due to hydrogen present as an impurityin the gas withwhichthe tubeis filled,the positive particlesbeinghydrogen

ionised by the corpuscles projected from the cathode, weshould have expected, since the ionisation consists in thedetachment of a corpuscle from the molecule, that the

COEPUSCLES IN VACUUM TUBES. 23

positively charged particles would be molecules and n-ot

atoms of hydrogen

Again, at very low pressures, when the electric field is

veryintense, we get the same two types of carriers ever kind of gas is in the tube For one of these typese/m=10* and for the other ejm=5X10^; the second valuecorresponds tothe positive particles which are given out by

what-radio-active substances The most obvious interjjretation

of this result is that under the conditions existing in thedischarge tube at these very low|)ressures all gases give

off positive particles which resemble corpuscles, in so far

as they are indej)endent of the nature of the gas fromwhich they are derived,butwhich difi'er fromthe corpuscles

in having masses comjDarable with themass of an atom of

hydrogen, while the mass of acorpuscle is only 1/1700 of

this mass One type of positive jDarticle has amass equal

to that of an atom of hydrogen, the other type has a massdouble this ; and the experiments I have just describedindicate thatwhen the |3ressure is verylow andthe electric

ofone or other ofthesetypes

We have seen that for the positively charged particles

in the canalstrahlen the value of ejm dejpends, when thepressure is nottoo low, onthe kind ofgas inthe tube, and

is such that the least value of vi is comparable with the.

massof anatomofhydrogen,and isthus alwaysimmensely

greater than the carriers of the negative charge in thecathode rays We know of no case where the mass of the

positively charged particle is less than that of an atom of

hydrogen

Positive Ions from Hot Wires

When a metallic wire is raised to a red heat itgives out

positively electrified particles I have investigated thevalues of e/?ft for these particles, and find that they showthe same peculiarities as the positively chargedparticles in

the canalstrahlen The particlesgiven off bythe wire are

not all alike. Some have one value of ejm, othersanother,

24 THE COEPUSCULAE THEOEY OF MATTEE.

but the greatest value I found in my experiments wherethe wire was surrounded by air at a low pressurewas 720,

and there were many particles for which ejm was very

much smaller, and which werehardly affected even byverystrong magnetic fields.

Positive Ions feom Eadio-activb Substances.The various radio-active substances, such as radium,polonium, uranium, and actinium, shoot out with^great

velocitypositivelyelectrifiedparticleswhichare calledSrays

The values ofejm for theseparticleshavebeenmeasured byEutherford, Des Coudres, Mackenzie, andHuff, and for all

the substances hitherto examined— radium and its

trans-formation products, polonium, and actinium—the value of

e/m is the same and equal to 5 X 10^ the same as for onetype of ray in the vacuum tube The velocity with whichthe particles move varies considerably from one substance

to another As these substances all give off helium, there

is prima jacie evidence that the a particles are helium.For a helium atom with a single charge, e\m is 2"5 X 10^,

hence if the a particles are helium atoms they must carry,

a double charge; the large value of e\m shows that the

carriers of the positive charge must be atoms, or molecules

of some substance with a small atomic weight Hydrogenand helium arethe only substances with an atomic weightsmall enoughto be compatible with so large avalue ofe\m

as 5,000, and of these, helium is known to be given off

by radio-active substances, whereas we have as yet noevidence thatthere is any evolutionof hydrogen

Positive particles having e/»i = 5 X 10^ are found,

as we have seen, in all vacuum tubes carrying an electric

discharge when the pressure in the tube is very lowthe velocity of these particles is very much less thanthat of the a particles. From the researches of

Bragg, Kleeman, and Eutherford, it ajDpears that the aparticles lose their power of ionisation and of producingphosphorescencewhen their velocity isreduced by passingthrough absorbing substances to about 10' cm/sec The

COEPUSCLES IN VACUUM TUBES. 25

interesting point about this result is that the positively

electrified particles in a discharge tube can produce tion and phosphorescence whentheir velocity is verymuchsmaller thanthis.

ionisa-This may possibly be due to the « particles beingmuchfewerinnumber than the positively charged particles in a

discharge tube; andthat as the a particles are so few and

far between, a particle in its attempts at ionisation or at

producing phosphorescence receives no assistance from its

companions Thus,ifionisationorphosphorescencerequires

a certain amount of energy to be communicated to a

system, all that energy has to come from one particle.

When, however, as in a discharge tube, the stream of

particles is much more concentrated, the energy required

bythe system maybe derived from more than one jsarticle,

the energy given to the systemby one particle not havingbeen entirely lost before additional energyis supplied byanother particle. Thusthe effectsproduced bythe particles

might be cumulative and the system might ultimately

receivethe requiredamountofenergybycontributions from

several particles. Thus, although the contribution fromany one particle might beinsufficient to produce ionisation

or phosphorescence, thecumulative effects of several might

escapefrom anegatively charged corj)uscle when it passes

close to it, butretainsthe corpuscle as a kind of satellite,

the two forming an electrically neutral system, and that

inasmuch as the chanceofionisationbycollisiondiminishes

as the velocity increases, whenthevelocityexceedsa certainvalue, such a neutral systemis not so likely to be ionised

and again acquire a chargeof electricity asthe more slowlymoving j)articles in adischarge tube

These investigations on the properties of the carriers of

26 THE COEPUSCULAE THEOEY OF MATTEE.

positive electricity prove: (1) that whereas ingases atverylow pressures the carriers ofnegative electricityhave an ex-

ceedingly small mass, oiily about 1/1700 of that of thehydrogen atom, the mass of the carriers of positive elec- tricity is never less than that of the hydrogen atom

(2) that while the carrier of negative electricity, the

cor-puscle, has the same mass from whatever source it maybe

derived, the mass of the carrier of the positive charge may

be variable: thus in hydrogenthe smallest of the positiveparticles seems to be the hydrogen atom, while in helium,

atnottoolowapressure,thecarrierofthepositiveelectricity

is partly, at anyrate, the helium atom All the evidence

atour disposal shows that even in gases at the lowest suresthe positive electricity is always carried by bodies at

pres-least as large as atoms; the negativeelectricity,onthe otherhand,isunderthesamecircumstancescarried bycorpuscles,

bodies with aconstant and exceedingly smallmass

The simplest interpretation of these results is that the

positive ions are the atoms or groups of atoms of variouselements from which one or more corpuscles have beenremoved That, infact, the corpuscles are the vehicles bywhich electricity is carried from one body to another, a

positively electrified body differing from the same body

whenunelectrified inhavinglostsomeof itscorpuscles whilethe negative electrified body is onewith more corpusclesthan the unelectrified one

In the old one-fluid theory of electricity, positive ornegative electrificationwas due to an excess or deficiency

of an " electric fluid." On the view we are considering

positive or negative electrification is due to a defect or

excess in the number of corpuscles The two views havemuch in commonif we suppose that the "electric fluid"

is built up ofcorpuscles

In the corpuscular theoryof matterwe supposethat theatoms ofthe elementsare madeuj) ofpositive andnegative

electricity, the negative electricity occurring in the form of

corpuscles Inanunelectrifiedatomthereare asmanyunits

ofpositive electricityasthereareofnegative; an atom with

COEPUSCLES IN VACUUM TUBES. 27

a unit positive charge is a neutral atom which has lostone

corpuscle, while an atom with a unit negative charge is a

neutral atom to which an additional corpuscle has been

attached No positivelyelectrified bodyhas yet been foundwithamassless than thatof ahydrogenatom Wecannot,however, without further investigation infer from this that

the mass ofthe unit charge of positive electricity is equal

tothemassofthehydrogenatom,for all we know about the

electrified systemis, thatthe positive electricity is in excess

by one unit over the negative electricity ; any system

con-taining n units of positive electricity and {u

-1) corpuscles

would satisfy this condition whatever might be the 'value

of n. Beforewe can deduceanyconclusions as to the mass

ofthe unit ofpositive electricity we must know somethingabout the number of corpuscles in the system We shall

give, later on, methods by which we can obtain this

infor-mation; we may, however, state here that these methods

indicate thatthe number of corpuscles in an atom of anyelement is proportional to the atomic weightof the element

—it is a multiple, andnota large one,oftheatomic weightof

the element If this result is right,there cannot be a large

number of corpuscles and therefore of units of positive

electricity in an atom of hydrogen, and as the mass of acorpuscle is very small compared with that ofan atom of

hydrogen,it followsthat onlya small fraction of themass

of the atom can be due to the corpuscle The bulk of themass must be due to thepositive electricity, and therefore

the mass of unit positive chargemust be large compared

'withthat of the corjDuscle—the unit negativecharge.From the experiments described on p. 19 we conclude

that positiveelectricity is made up of units,which are

inde-pendent of thenature of the substance which is the seat of

the electrification.

CHAPTEE II.

THE ORIGIN OF THE MASS OF THE CORPUSCLE.The originofthe massofthe corpuscleisveryinteresting,for it has been shown that this mass arises entirely fromthe charge of electricity on the corpuscle We can see

how this comes about in the following way If I take

an uncharged body of mass M at rest and set it movingwith the velocity V, the work I shall have to do onthe body is equal to the kinetic energy it has acquired,

electricity I shall have to do more work to set it movingwith the same velocity, for a moving charged body pro-duces magnetic force, it is surrounded by a magnetic field

and this field contains energy; thus when I set the body

inmotion I haveto supplythe energy for thismagnetic aswell as forthe kinetic energy of the body If the chargedbodyis moving along theline OX, the magnetic forceat apointPis at rightangles tothe plane POX; thus the lines

of magneticforces are circles havingOXfor theiraxis. Themagnitudeof the forceat Pis equal to ^ ^^2"' where 6

denotes the anglePOX Nowinamagneticfield the energyper unit volume at anyplace where the magneticforce is

OEIGIN OF THE MASS OF THE CORPUSCLE. 29equalto H is H'^/Stt. Thus the energy per unit volume at

P arisingfrom themagnetic force produced by themovingcharge is / ," , and by taking the sum of theenergythroughout the volume surrounding the charge, we

find the amount of energy in the magnetic field If themoving bodyis a conducting sphere of radiusa, asimple

calculation showsthat the energyin the magnetic field is

Thusthe apparent massof theelectrified body isnot in but

m 4- - —. The seat of this increase in mass isnot in the

electrified bodyitself but in the space around it, just as if

the etherin that space were set in motion by the passagethroughit ofthelines of force proceedingfrom the chargedbody, and that the increase in the mass of the chargedbodyarose fromthe massofthe ether set in motion by the

lines of electric force It may make the considerationof

this increase in massclearer if we take a case which is not

electrical but in which an increase in the apjDarent massoccursfrom causes which are easily understood Suppose

that we start a sphere of mass M with a velocity Vin avacuum, the work which has to be done on the sphere is

I M V^ Let us now immerse the sphere in water: thework required to start the sphere with the samevelocity

willevidentlybegreater thanwhen itwas inthevacuum,for

motion

30 THE COEPUSCULAE THEOEY OF MATTEE.

motion Thewater will have kinetic energy, and this, aswell as the kinetic energy of the sphere, has to be suppliedwhen the sphere is moved It has been shown by Sir

George Stokes that the energy in the water is equal to

^ Ml F^ where Mi is the mass of half the volume of thewater displaced bythe sphere Thus the energy required

to start the sphere is ^ (M + Mi) F^ and the spherebehaves as if its mass were M + Mi and not M, and formany purposeswe could neglect the effect of the water if

we supposed the mass ofthe sphere to be increased in theway indicated If we suppose the lines of electric force

proceeding from the charged body to set the ether in

motion andassumethe etherhasmass,then theoriginoftheincrease ofmass arising from electrification would be veryanalogous to the case just considered The increase in

mass due to the charge is - — ; thus for agivenchargethe intrease in the mass is greater for asmall bodythanfor

a large one Now for bodies of ordinary size this increase

ofmass due to electrification is for anyrealisable charges

quite insignificant in com23arisonwith the ordinary mass.But since this addition to the mass increases rapidly as

the body gets smaller, the question arises, whether inthecase of these charged and exceedingly small corpusclesthe electrical mass, as we may call it, maynot be quite

appreciableincomparisonwith the other (mechanical) mass

We shall now show that this is the case; indeed for

corpuscles there is no other mass: all the mass is

electrical.

The method by which this result has been arrived at is

as follows: The distribution of magnetic force near a

moving electrified particle depends upon the velocity of

the particle,and when thevelocity approaches thatof light,

is' of quite a different character from that near a slowlymovingparticle. Perhaps the clearest wayof seeingthis is

to follow the changes which occur in the distribution ofthe

electric force round a charged body as its velocity is

graduallyincreased When the body is at rest the electric

OEIGIN OF THE MASS OF THE COEPUSCLE. 31

force isuniformly distributed round the body, i.e., as long

as we keep at the same distance from the charged bodythe electric forceremainsthe same whether we are to the

east,west,north or south of theparticle ; the lines of force

which come from the body spread out uniformly in alldirections When thebody ismoving this is no longer the

case, for ifthe body ismoving along theline OA (Fig 13),

the lines of electric force tend to leave the regions in theneighbourhood of OA and OB, which we shall call the

23olar regions, and crowd towards a plane drawn through

O at rightangles toOA ; theregionsin the neighbourhood

riG 13

of this plane we shall call the equatorial regions Thiscrowding ofthelines of forceisexceedinglyslightwhen the

velocity ofthe bodyis onlya small fractionof thatof light,

butit becomes verymarked when the velocityof the body

is nearly equalto that velocity; and whenthe bodymoves

atthe same speed as light all the lines of force leave theregionround OA and crowd into the plane through at

rightangles to OA,i.e.,the lines of forcehave swung round

until they are all at right angles to the direction in whichthe particle ismoving The effect of this crowding of the

lines offorce towards theequatorial j^lane is to weaken themagnetic force in thepolarandincrease

32 THE COEPUSCULAE THEOEY OF MATTEE.

regions Thepolar regions are those where the magnetic

force was originally weak, the equatorial regions thosewhere it was strong Thus the effect of the crowding is

to increase relatively the strengthof the field inthe strongparts ofthe field and to weakenit in theweak parts. Thismakes the energy in the fieldgreaterthan if there were nocrowding, in which case the energy is — where e is

the charge, v the velocity and a the radius of the sphere

When we allow for the crowding, the energy will be

-, where a is a quantity which willbe equal to

— a

unity when v is small compared with c the velocity of

light, but becomes very large when v approaches c. The

part of the mass arising from the charge is — a —, thus

since adepends upon r—the velocity of the particle— the

electrical mass will dei^end upon v,and thus this part of

the mass has the peculiarity that it is not constant butdepends upon the velocity of the particle. Thus if anappreciable part of the mass of the corpuscle is electrical

in origin, the mass of rapidly moving corpuscles will be

greaterthan that of slow ones, while if the mass were in

the main mechanical, it would be independent of the

velocity. Eadium gives out corpuscles which move with

velocities comparable with that of light and which are

therefore very suitable for testing whether or not thisincrease in the mass of a corpusclewith its velocity takes

place This test has been apjplied byKaufpaann, who hasmeasuredthe valueofmjeforthe various corpuscles movingwith different velocities given out by radium We can

calculate the value of the coefficienta—the quantitywhich

exjDresses the effect of the velocity on themass Thevalue

of this quantity depends to some extent on the view wetake as to the distribution of electricity on the corpuscle

we get slightly different values according as we supposethe electricity to be distributed over the surface of a con-ducting sphere of radius a, or rigidly distributed over the

OKIGIN OF THE MASS OF THE COEPUSCLE. 33

surface of anon-conducting sphere of the same radius, or

uniformly distributed throughout the volume of such a

sphere Incalculating thesedifferenceswehaveto supposethe charge on the sphere divided up into smaller parts and

that each of these smallparts obeys the ordinary laws of electrostatics If we suppose that the charge on thecorpuscles is the unit of negative electricity, it is notpermissible to assume that smaller portions will obey theordinary laws of electrostatic attraction

Perhaps the simplest assumption we can make is that

the energy is the sameas that outside a sphere of radius amoving with the velocity V and with a charge e at itscentre Ihavecalculatedthevalue of aon thissupposition;the results are given in the following Table The first

column ofthe Table contains thevelocityofthecorpuscles,

which were the object of Kaufmann's experiments; thesecond column, the valuesfound by Kaufmannfor theratio

of the mass of corpuscles moving with this velocity to

the mass of a slowly moving corpuscle, and the third

column the value of a calculated on the precedinghypothesis

34 THE COEPUSCULAE THEOEY OF MATTEE.

andis not resident inthe corpuscleitself ; hence, from ourpointofview,eachcorpusclemaybe saidtoextend through-out the whole universe, a result which is interesting in

connection with the dogma that two bodies cannot occupythesame space

From the result that thewhole of the massis electrical

we are able to deduce the size of the corpuscle, for if m

isthe mass,

2 e2

m = — —

Now we have seen that e/ni = 1'7 X 10^, and that in

electromagneticmeasuree =10^°. Substituting these values

wefindthat athe radius ofthe corpuscle = 10"^^ cm Theradius ofthe atom is usuallytakenasabout 10"'cm., hencethe radius of acorpuscle is only about the one-hundred-thousandth partof the radius of the atom The potential

energy due to the charge is - , if Vis thevelocity of

amount as the kinetic energy possessed by an « particle

movingwith a velocity aboutone-fiftieth thatof light.

Evidence of the Existence of Corpuscles afforded by

THE Zeeman Effect

The existence of corpuscles is confirmed in a very

striking way by the effect produced by a magnetic field

on the lines of the spectrum and known as the Zeeman

giving out the spectrum is placed in a strong magnetic

application of the field are resolved into three or morecomponents The simplest case is whena line originallysingle is resolvedinto three components,theluminousbodybeing looked at in a direction at rightangles to the lines of

magnetic force; the middle line of the three occupies itsold position, and the side lines are separatedfrom itby an amount proportional to the magnetic force. All the lines