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. ELECTRONS 


OE 


THE  NATUEE  AND  PROPERTIES 
OF  NEGATIVE  ELECTRICITY 


BY 

SIR   OLIVER  LODGE,  F.R.S. 

D.Sc.  LOND.,  HON.  D.Sc.  OXON.  ET  VICT.,  LI/D.  ST.  ANDREWS,  GLASGOW,  AND 

VICE-PRESIDENT  OF  THE   INSTITUTION   OF  ELECTRICAL   ENGINKERS 

RUMFORD   MEDALLIST  OF  THE   ROYAL  SOCIETY 
EX-PRESIDENT  OF  THE   PHYSICAL  SOCIETY   OF  LONDON 

LATE   PROFESSOR  OF   PHYSICS   IN  THE   UNIVERSITY   COLLEGE   OF  LIVERPOOL 

HONORARY   MEMBER  OF  THE   AMERICAN    PHILOSOPHICAL   SOCIETY   OF   PHILADELPHIA,    OF  THE 

BATAVIAN   SOCIETY   OF   ROTTERDAM,    AND   OF  THE   ACADEMY   OF  SCIENCES   OF  BOLOGNA 

PRINCIPAL   OF  THE   UNIVERSITY   OF  BIRMINGHAM 


LONDON 

GEORGE  BELL  AND  SONS 
1906 


Q-CW 

L7 


GLASGOW  :    PRINTED   AT   THE  UNIVERSITY  PRESS 
BY   ROBERT   MACLEHOSE   AND  CO.    LTD. 


TO   THE 

CAVENDISH   PROFESSORS   OF   PHYSICS 

IN   THE   UNIVERSITY   OF   CAMBRIDGE,   AND   ESPECIALLY 

TO   THE   PRESENT   HOLDER   OF   THE   CHAIR,   THIS   SMALL  BOOK   IS 

DEDICATED   WITH   PROFOUND   ADMIRATION 

BY   THE   AUTHOR 


1  C>2827 


PKEFACE 

IN  1902  I  was  asked  by  the  President  of  the 
Institution  of  Electrical  Engineers  to  give  to  that 
body  a  discourse  on  recent  progress  towards  know- 
ledge of  the  nature  of  Electricity,  especially  con- 
cerning its  discontinuous  or  atomic  structure.  This 
discourse,  greatly  extended,  appeared  in  Vol.  32  of 
the  Journal  of  the  Institution,  and  constitutes  the 
nucleus  of  the  present  book. 

Many  additions  have  now  been  made,  and  some 
of  the  difficulties  recently  promulgated  concerning 
the  possibility  of  an  electric  theory  of  matter  are 
touched  upon.  They  are  of  date  too  recent  to  have 
been  mentioned  even  in  my  "Komanes  Lecture" 
before  the  University  of  Oxford,  published  under 
the  title  Modern  Views  of  Matter  by  the  Clarendon 
Press. 

The  most  important  addition  is  a  more  detailed 
account  of  the  proof  of  the  purely  electrical  nature 
of  the  mass  or  inertia  of  an  electron  :  an  investi- 
gation generally  associated  on  the  experimental 
side  with  the  name  of  Kaufmann,  but  of  course 
based  on  the  work  of  many  predecessors  and  con- 
temporaries. A  proof  that  the  atom  of  matter  is 
essentially  composed  of  such  electrons,  and  that 
its  mass  too  is  of  purely  electromagnetic  nature, 
is  lacking :  the  electromagnetic  theory  of  Matter, 


viii  PREFACE 

unlike  the  electromagnetic  theory  of  Light,  must  be 
regarded  for  the  present  as  no  better  than  a  working 
hypothesis.  It  is  a  hypothesis  of  stimulating  char- 
acter, and  of  great  probability,  but  its  truth  is  still 
an  open  question  that  is  probably  not  going  to  be 
speedily  closed. 

I  am  indebted  to  Professor  Larmor  for  information 
about  some  recent  theoretical  work,  and  for  the 
substance  of  Appendix  M ;  I  have  also  to  thank  Mr. 
Gwilym  Owen,  of  the  University  of  Liverpool,  for 
assistance  in  the  revision  of  the  proof. 

As  "an  introduction  to  an  allied  subject,  the  book 
called  Becquerel  Rays,  by  the  Hon.  K.  J.  Strutt, 
is  to  be  recommended ;  and  the  standard  treatise 
of  Professor  Eutherford  on  Radioactivity  is  well 
known.  I  have  avoided  dealing  at  length  with 
the  topics  so  conveniently  to  be  found  in  these 
writings.  I  have  also  barely  touched  on  the  large 
subject  of  '  ionisation ' :  it  was  difficult  to  do  so 
without  overloading  the  principles  with  detail,  a 
knowledge  of  which  is  nevertheless  necessary  for 
investigators.  The  treatise  of  Prof.  J.  J.  Thomson, 
The  Discharge  of  Electricity  through  Gases,  con- 
tains a  mass  of  information  and  original  work 
highly  valued  by  physicists. 

The  present  book  is  intended  throughout  for 
students  of  general  physics,  and  in  places  for  special- 
ists, but  most  of  it  may  be  taken  as  an  exposition  of 
a  subject  of  inevitable  interest  to  all  educated  men. 

OLIVER  LODGE. 
THE  UNIVERSITY  OF  BIRMINGHAM, 
July,  1906. 


CONTENTS 


I.    PROPERTIES  OF  AN  ELECTRIC  CHARGE,  1 

Charge  in  Uniform  Motion,    -----  3 

Transmission  of  Energy,  -         -         -         -         -         -  6 

Accelerated  Charge,  7 

II.    ELECTRIC  INERTIA,  -       -       -       -       -       -       -  11 

Electrical  Inertia  or  Mass — continued,  12 

Effect  of  Concentration,  -         -         -       ,,-.,-        -  15 

Summary,  16 
Historical  Remarks,         -         -        -         -         --17 

III.  FORESHADOWING  OF  THE  ATOM  OR  INDIVISIBLE 

UNIT  OF  ELECTRICITY,        -       -      ;.    ~  .  19 

IV.  FORESHADOWING  OF  THE  ELECTRON,     -       -       -  24 

Separate  Existence  of  the  Electric  Unit  suggested 

by  Conduction  in  Gases, 24 

Cathode  Bays, --26 

Nature  of  the  Cathode  Rays,  30 

V.    DETERMINATION  OF  SPEED  AND  ELECTROCHEMICAL 

EQUIVALENT  OF  CATHODE  RAYS,       -       -  41 
Further  Measurements  of   Cathode   Ray  Velocity 

and  m/e  Ratio  by  Aid  of  Electrostatic  Deflection,  47 
Measuring    Velocity    by    Combined    Electric    and 

Magnetic  Deflexion  Method,         -      •  -      ''.  •  ,      -  50 

Effect  on  Lenard  Rays,  -         -         -         -                 -  52 
Direct    Determination    of    the   Speed    of    Cathode  . 

Rays, 54 


x  CONTENTS 

CHAP.  PACK 

VI.  DETERMINATION  OF  ELECTROCHEMICAL  EQUIVA- 
LENT IN  THE  CASE  OF  ELECTRIC  LEAKAGE 

IN  ULTRA-VIOLET  LIGHT,    -       -       -       .  58 

Positive  and  Negative  Carriers,  66 

VII.      lONISATION   OF   GASES, 70 

Behaviour  of  Hot  Metals  in  Gases,         -         -         -  71 

Measurements  of  lonisation  Current,  73 

Condensation  of  Moisture  Experiments,  75 

VIII.    DETERMINATION  OF  THE  MASS  OF  AN  ELECTRON,  77 

Aitken  and  Cloud  Nuclei,        -----  79 

J.  J.  Thomson  and  Electrical  Nuclei,  81 

Wilson  and  Metrical  Cloud  Condensation,      -         -  84 

Professor  Stokes  and  Falling  Spheres,  86 

J.  J.  Thomson's  Experiment  of  Counting,  87 

Result,      --.-                           ....  90 

IX.    FURTHER  DETAILS  CONCERNING  ELECTRONS  AND 

IONS, 91 

Confirmatory  Measurements  of  Charge,  9t 

Thomson's  Deductions, 94 

Estimate  of  Size,      -         -        -        -        -         -         -  95 

Penetrability  of  Matter  by  Electrons,  97 

Effects  of  an  Encounter,                                     -        -  100 

X.    THE  ELECTRON  THEORY  OF  CONDUCTION  AND  OF 

EADIATION,    ..      .       -       -       -       -       -  105 

Conduction,      -        -v     -        *        -         -                 -  106 

Radiation, 109 

XL  FURTHER  DISCUSSION  OF  THE  ELECTRON  THEORY 
OF  THE  MAGNETISATION  OF  LIGHT  AND 
DETERMINATION  OF  THE  m/e  RATIO  IN 

RADIATION, 116 


CONTENTS  xi 

CHAP.  PAGE 

XII.    INCREASE    OF   INERTIA    DUE    TO   VERY   RAPID 

MOTION,         -       .;.-*'•     ...       -       -  122 

XIII.  JUSTIFICATION  FOR  ELECTRIC  THEORY  OF  INERTIA,  129 

Proof  of    the    Purely   Electrical   Nature  of   the 

Inertia  of  the  /?  Particles  shot  out  by  Radium,  131 

XIV.  MORE  ADVANCED  DEVELOPMENT  OF  THE  COM- 

BINED ELECTRIC  AND  MAGNETIC  DEFLEXION 
METHOD  FOR  MEASURING  VELOCITY  AND 
MASS  OF  THE  PARTICLES  IN  COMPOUND 

RAYS,     -              ...       .       .       -  136 

Experimental  Device  used  by  W.  Kaufmann,     -  138 

XV.    ELECTRIC  VIEW  OF  MATTER,                             -  146 

XVI.     ELECTRIC  VIEW  OF  MATTER  (continued),     -       -  152 

Nature  of  Cohesion, 152 

On  Chemical  and  Molecular  Forces,    -         -         -  153 

Molecular  Forces,  Cohesion,          -         -        -  155 

XVII.    FURTHER     CONSIDERATIONS     REGARDING    THE 

STRUCTURE  OF  AN  ATOM,    -       -       -       -  160 

XVIII.  SUMMARY  OF  OTHER  CONSEQUENCES  OF  ELEC- 
TRON THEORY,  -  -  .  *  -  *  -  163 
Radio-activity,  -  .  -  -  -  -  -  "•  163 
Solar  Corona,  Magnetic  Storms,  and  Aurorse,  -  168 
Transformations  of  Radium,  etc.,  -  -  -  169 
Emanations,  *  -  -  -  •••••'  -  '  ">  171 
Deflexion  of  Alpha-rays,  •  -  *  •  -  •;  171 
Activity  of  Radium  at  all  Temperatures,  -  174 

Spectrum  of  Radium, 174 

Electric  Production,      -        -         -        -         -        -176 

Radio-activity  of  Ordinary  Materials,          -         -  177 
Population  Analogy,     -        -  '      -        -        -        -180 


xii  CONTENTS 

CHAP.  PAQE 

XIX.     RADIATION  FROM  A  KING  OF  ELECTRONS,  AND 
ITS  BEARING  ON  THE  CONSTITUTION  OF  AN 

ATOM,     -                                     -       -       -  181 

Instability  of  an  Atom, 183 

.     Cosmic  Analogy, 185 

Another  Account  of  Atomic  Instability,     -         -  185 

Electric  Theory  of  Matter, 186 

XX.    DIFFICULTIES  CONNECTED  WITH  THE  ELECTRIC 

THEORY  OF  MATTER, 188 

1.  Concerning  the  Formation  of  Spectrum  Lines,  188 

2.  Attempt  to  determine  the  Number  of  Effec- 

tive Corpuscles  in  an  Atom,        -         -        -  192 

XXI.    VALIDITY    OF    OLD    VIEWS    OF    ELECTRICAL 

PHENOMENA, 195 

Number  of  Ions  in  Conductors,  -        -        -        -  198 

Conclusion, 200 


APPENDICES 

A.  CALCULATION  OF  THE  INERTIA  OF  AN  ELECTRIC  CHARGE,  -  204 

B.  THE  ELECTRIC  FIELD  DUE  TO  A  MOVING  MAGNET,    -        -  207 

C.  ON  ELECTRICITY  AND  GRAVITATION  AND  DIMENSIONS,        -  209 

D.  DIMENSIONS  OF  SJM  RATIO,         -        -.-        -        -        -211 

E.  ELECTRIC  SATURATION,  ETC.,      -        -        -        -        -  212 

F.  SIZE  OF  ORBIT  OF  RADIATING  ELECTRON,  -        -        -        -  213 

G.  THE  RADIATING  POWER  OF  A  REVOLVING  ELECTRON,         -  214 
H.    FARADAY'S.  PROPHETIC  NOMENCLATURE,      -        -        -        -  217 

J.       ON   THE   /2-RAYS   FROM   RADIUM, 219 

K.  NOTE  ON  THE  BEHAVIOUR  OF  A  CHARGE  MOVING  NEARLY 

AT  THE  SPEED  OF  LIGHT,  -  -  -  -  -  221 

L.  DISTORTION  DUE  TO  HIGH-SPEED  MOTION  THROUGH  THE 

ETHER,  - 226 

M.    CONSTITUTION  OF  ELECTRONS, 227 


UNIVERSITY 


INTRODUCTION 

IN  Maxwell's  Electricity  published  in  1873,  section 
57,  the  following  sentence  occurs  in  connection  with 
the  discharge  of  electricity  through  gases,  especially 
through  rarefied  gases  : 

"  These  and  many  other  phenomena  of  elec- 
trical discharge  are  exceedingly  important,  and, 
when  they  are  better  understood,  they  will 
probably  throw  great  light  on  the  nature  of 
electricity  as  well  as  on  the  nature  of  gases  and 
of  the  medium  pervading  space." 

This  prediction  has  been  amply  justified  by  the 
progress  of  science,  and,  no  doubt,  still  further 
possibilities  of  advance  lie  in  the  same  direction. 
The  study  of  conduction  through  liquids,  first,  and 
the  study  of  conduction  through  gases,  next,  com- 
bined with  a  study  of  the  processes  involved  in 
radiation,  have  resulted  in  an  immense  addition  to 
our  knowledge  of  late  years,  and  have  opened  a  new 
chapter,  indeed  a  new  volume,  of  Physics. 

The  net  result  has  been  to  concentrate  attention 
upon  the  phenomena  of  electric  charge,  and  greatly 


xiv  INTRODUCTION 

to  enhance  the  importance  of  a  study  of  electro- 
statics. Not  long  ago  our  brilliant  and  lamented 
friend,  G.  F.  FitzGerald,  used  chaffingly  to  speak 
of  electrostatics  as  "  one  of  the  most  beautiful  and 
useless  adaptations  of  nature  "  ;  and  it  was  becoming 
the  custom  with  teachers,  who  felt  that  they  must 
attend  exclusively  to  the  practically  useful  and  not 
waste  their  students'  time  on  decoration  and  super- 
fluities, almost  to  ignore,  or  at  any  rate  to  scamper 
through,  the  domain  of  electrostatics,  and  to  begin 
the  study  of  electricity  with  the  phenomena  of 
current,  especially  with  the  connection  between 
electricity  and  magnetism. 

And  certainly  from  the  severely  practical  point 
of  view,  as  well  as  from  many  other  aspects,  this 
part  of  electrical  science  remains  the  most  impor- 
tant ;  but  to  him  who  would  not  only  design 
dynamos  and  large-scale  machinery,  to  him  who,  in 
addition  to  the  training  and  aptitude  of  the 
engineer,  possesses  something  of  the  interests,  the 
instinct,  and  the  insight,  of  a  man  of  science, — to 
such  a  one  the  nature  and  properties  of  an  electric 
charge,  at  "rest  and  in  motion,  constitute  a  fascinat- 
ing study ;  for  there  lies  the  key  to  the  inner 
meaning  of  all  the  occurrences  with  which  his  active 
life  is  so  intimately  concerned — there  lies  the 
proximate  solution  of  problems  which  have  excited 
the  attention  and  taxed  the  ingenuity  of  philo- 
sophers and  physicists  and  chemists  for  more  than 
a  century.  Indeed  it  turns  out  that  subjects 


INTRODUCTION  xv 

broader  and  more  fundamental  than  those  known 
as  '  electric '  are  indirectly  involved ;  and  we  are 
now  beginning  to  have  some  hope  of  obtaining 
unexpected  answers  to  riddles — such  as  those  con- 
cerning the  fundamental  properties  of  matter — which 
have  proposed  themselves  for  solution  throughout 
the  history  of  civilisation.  Problems  of  this  kind 
have  aroused  interest  and  attention  ever  since  men 
began  to  escape  from  the  struggle  for  bare  exist- 
ence— that  most  immediately  practical  of  all  occupa- 
tions— and  felt  free  to  devote  themselves,  some  to 
art,  some  to  literature,  some  to  the  accumulation 
of  superfluous  wealth,  and  some  to  the  gratuitous 
pursuit  of  philosophical  speculation,,  exact  experi- 
ment, and  pure  theory.  To  this  comparatively 
leisured  group  I  now  address  myself. 


MEANING  OF  TERMS  AND  SYMBOLS  AS  USED 
IN  THIS  BOOK.. 

Electron  =  the  unit  electric  charge,  or  atom  of  negative  electricity. 
e     =the  amount  of  this  charge,  whether  positive  or  nega- 
tive; about  3xlO~10  electrostatic  unit. 
E     =an  electromotive  force,  or  the  strength  of  an  electric 

field. 

H     =  the  strength  of  a  magnetic  field. 
m     =  mass  or  inertia,  especially  the  mass  of  an  electron. 
a     =  usually,  the  linear  dimension  of  an  electron  (about  the 

hundred-thousandth  of  b). 

b     =the  linear  dimension  of  an  atom  of  matter  (the  ten- 
millionth  of  a  millimetre). 

ion     =  an  atom  of  matter  with  an  unbalanced  electric  charge, 
either  negative   or   positive,  attached  to  it :    the 
cause  of  chemical  affinity. 
K     =  Faraday's  dielectric  constant,  or  the  specific  inductive 

capacity  of  free  ether. 
P     =  the  magnetic  permeability  of  free  ether. 

[These  two  are  the  great  ethereal  constants,  whose 
value  and  nature  are  not  yet  known.     Only  their 
product  is  known.] 
v     =the  velocity  of  light  in  vacuo 

=  3  x  1010  cm.  per  sec. 
u     =  the  velocity  of  a  particle. 


CHAPTER  I. 

PROPERTIES  OF  AN  ELECTRIC  CHARGE. 

FIRST  I  must  lay  a  basis  of  pure  theory  :  we  must 
consider  the  properties  of  the  ancient  and  long  known 
phenomenon  called  an  electrified  body. 

Two  substances  placed  in  intimate  contact  and 
separated  are  in  general  united  more  or  less  per- 
manently by  lines  of  force,  the  region  between  them 
being  in  a  state  of  tension  along  the  lines  and  of 
pressure  at  right  angles.  These  lines  have  direction 
and  '  sense ' — their  two  ends  are  not  alike  :  they 
begin  at  one  body  and  end  at  another,  they  map  out 
a  field  of  electrostatic  force,  and  their  terminations  on 
one  or  other  of  the  bodies  constitute  what  we  call 
an  electric  charge.  Electric  charges  are  of  two  kinds, 
positive  and  negative,  the  former  corresponding  to 
the  beginning  of  the  lines,  the  latter  to  their  ends. 
To  one  class  of  bodies,  called  insulators,  the  lines 
appear  rigidly  attached :  the  charges  cannot  be  dis- 
placed nor  transferred  elsewhere  without  violence  ; 
whereas  in  another  class  they  slip  easily  along,  and 
are  transferred  from  one  such  conducting  body  to 
another  in  contact  with  it,  with  great  ease. 

A  tension  in  the  lines  tends  to  bring  the  ends 
together  as  near  as  possible,  while  laterally  the  lines 
tend  to  drive  each  other  apart :  this  image  sufficing  to 


L.E. 


2     PROPERTIES  OF  AN  ELECTRIC  CHARGE  [CH.  I. 

represent  all  that  is  observed  as  electrical  attractions 
and  repulsions. 

The  field  of  force  mapped  by  the  lines  can  exist 
in  vacuo  perfectly  well,  but  the  lines  never  terminate 
in  vacuo ;  the  charges  are  always  carried  by  matter, 
or  by  something  equivalent  thereto.  In  empty  space 
it  is  probable  that  the  only  way  of  destroying  such  a 
field  of  force  is  to  allow  the  two  bodies  possessing  the 
charges  to  approach  each  other,  and  thus  shorten  up 
the  lines  to  nothing ;  though,  even  so,  it  is  not  prob- 
able that  the  charges  are  destroyed,  but  only  placed 
so  close  together  that  they  have  no  external  effect 
at  any  moderate  distance.  When  matter  is  present, 
however,  it  may  be  able  to  assist  this  collapse  of  the 
lines  in  various  ways,  giving  rise  to  the  various 
phenomena  of  conduction  and  of  disruptive  discharge. 

If  one  of  the  two  oppositely  charged  bodies  is  sent 
away  to  a  considerable  distance,  while  the  other  is 
isolated  and  regarded  alone,  the  lines  of  this  latter 
start  out  in  all  directions  in  nearly  straight  lines, 
giving  rise  to  the  simple  notion  of  a  single  charged 
body.  There  must  however  be  a  complementary 
charge, — the  other  ends  of  the  lines  must  be  some- 
where ;  though  they  may  be  so  far  away  as  to  be 
spoken  of  as,  for  all  practical  purposes,  at  infinity. 

Parenthetical  remark  of  general  application. 
People  often  feel  hesitation  about  the  treatment  of 
things  as  at  infinity,  as  if  it  introduced  a  conception 
of  some  difficulty ;  but  they  should  realise  that  this 
mode  of  expression  is  always  employed  as  a  simplifi- 
cation, whenever  it  happens  that  for  present  purposes 
the  said  things  can  be  ignored.  If  their  existence 
requires  attention,  it  must  be  recognised  that  they 
are  really  at  some  finite  distance,  and  their  location 
must  be  specified ;  but  such  specification  complicates 


CH.  L]  CHARGE   IN   MOTION  3 

both  ideas  and  equations.  Whenever  attention  to 
them  is  unnecessary,  or  their  location  immaterial,  this 
specification  is  avoided  by  treating  them  practically 
as  if  they  were  at  infinity,  that  is  by  ignoring  them. 
Every  now  and  then  this  policy  of  ignoration  must 
be  suspended,  but  for  a  multiplicity  of  purposes  it 
serves. 

Charge  in  uniform  motion. 

Now  consider  how  far  this  field  of  force  belongs  to 
the  body,  and  how  far  it  belongs  to  space,  that  is  to 
the  ether  surrounding  the  body.  The  body  is  the 
nucleus  whence  the  lines  radiate,  but  the  lines  them- 
selves, the  state  of  tension  and  other  properties  which 
they  represent  and  map  out,  do  not  belong  to  the 
body  at  all ;  at  each  point  of  space  there  is  a  peculiar 
etherial  condition  called  an  electric  potential,  and  this 
potential  represents  something  "occurring  in  the  ether 
and  in  the  ether  alone,  though  it  is  originated  and 
maintained  by  the  body. 

Picture  in  the  mind's  eye  such  a  charged  body,  say 
a  charged  sphere,  and  let  it  change  its  position  ;  how 
are  we  to  regard  the  effect  of  the  displacement  on  its 
field  of  force  ?  Few  things  in  physics  are  more  certain 
than  this,  that  when  a  body  moves  along,  the  ether 
in  its  neighbourhood  is  not  dragged  with  it,  as  if  it 
were  in  the  slightest  degree  viscous.*  The  ether,  in 
fact,  as  a  whole — i.e.  when  unmodified  or  in  its 
normal  condition — is  stationary  :  it  is  susceptible  to 
strain,  but  not  to  motion ;  it  is  the  receptacle  of 
potential,  not  of  locomotive  kinetic  energy.  The  only 
generated  motion  to  which  it  is  possibly  susceptible  is 
of  what  is  called  '  irrotational '  character — in  other 
words  it  behaves  as  a  perfect  fluid.  It  may  possess 

*  Lodge,  Phil.  Trans.  1893,  p.  727,  and  especially  1897,  p.  149. 


4     PROPERTIES  OF  AN  ELECTRIC  CHARGE  [CH.  I. 

other  rotational,  or  vortex-like  motion,  but,  if  so,  it  is 
indestructible  and  unproducible  by  any  known  means, 
and  has  not  yet  been  discovered. 

The  effect  of  the  motion  of  the  body,  then,  is  to 
relieve  the  strain  of  the  ether  at  one  place  and  to 
generate  it  at  another ;  the  state  of  strain  travels 
with  the  body,  but  through  the  ether. 

Regarding  the  matter  from  the  point  of  view  of 
the  ether,  we  might  say  that  the  field  of  force  is 
constantly  being  destroyed  and  regenerated  as  the 
body  moves.  Regarding  it  from  the  point  of  view 
of  the  moving  body,  we  should  say  that  it  carries  its 
field  with  it. 

The  question  now  arises — and  it  is  far  from  being 
an  easy  question — what  sort  of  occurrences  go  on  in 
the  ether  when  this  decay  and  regeneration  of  an 
electrostatic  field  is  occurring,  or  when  a  field  of  force 
is  moving  through  it  ?  Can  it  adapt  itself  instantly 
to  the  new  conditions,  or  does  it  require  time  ?  This 
matter  has  been  studied,  closely  and  exhaustively,  by 
Mr.  Oliver  Heaviside. 

Fix  the  eye  upon  a  point  a  mile  distant  from  the 
body ;  does  the  information  about  the  motion  of  the 
body  reach  that  point  instantaneously,  so  that  all  the 
lines  of  force  move  like  absolutely  rigid  spokes,  every 
part  simultaneously  ?  If  so,  how  is  the  communi- 
cation carried  on,  so  that  the  distant  parts  of  the 
medium  can  be  thus  instantaneously  affected  ?  Or 
does  the  disturbance  only  arrive  at  the  distant  point 
after  the  lapse  of  a  small  but  appreciable  time ;  in 
other  words,  has  there  to  be  an  adjustment  to  the 
new  conditions — an  adjustment  which  reaches  the 
nearest  parts  first  and  the  further  parts  later ;  and  if 
so,  what  additional  phenomena  can  be  observed 
during  the  unsettled  period  ? 


CH.L]  CHARGE   IN   MOTION  5 

The  answer  is  that  during  the  motion  of  the 
charged  body,  and  even  after  the  cessation  of  its 
motion, — until  the  disturbance  has  had  time  to  die 
away  and  everything  to  settle  down  into  static  con- 
dition again, — the  phenomena  of  magnetism  make 
their  appearance  :  a  new  set  of  lines  of  force  quite 
different  from  the  electrostatic  lines  (although  they, 
too,  exhibit  a  tension  along  them  and  a  pressure  at 
right  angles)  come  into  temporary  being.  These  do 
not — like  the  electric  ones — originate  at  one  place 
and  terminate  at  another :  they  are  always  and 
necessarily  closed  curves  or  rings,  and  in  the  present 
simple  case  they  are  circles  all  centred  upon  the  path 
of  motion  of  the  charged  body.  At  any  point  of  space 
there  are  now  three  directions  to  consider  :  (l)  there 
is  the  original  direction  of  the  electrostatic  field — the 
original  electric  line  of  force  ;  (2)  there  is  the  direction 
of  the  motion — that  is,  a  direction  parallel  to  the 
movement  of  the  charged  sphere  ;  and  (3)  there  is  the 
direction  at  right  angles  to  these  two ;  this  last  being 
the  direction  of  the  magnetic  lines  of  force — the 
direction  of  the  magnetic  field. 

I  spoke  of  the  magnetic  field  as  temporary,  but 
that  is  on  the  assumption  that  the  charged  body  is 
merely  displaced — merely  shifted  from  one  position  to 
another ;  if  it  is  not  stopped,  but  keeps  on  moving, 
then  the  magnetic  lines  continue  as  long  as  the 
motion  lasts.  The  strength  of  the  magnetic  field, 
at  any  point  with  polar  coordinates  r,  0,  is — 

TT     eu  •    a 

H  =  — r  sin  6. 

r2 

If  we  are  asked  whether  such  a  magnetic  field  is 
weak  or  not,  I  have  to  reply  that  that  depends 
entirely  on  how  strong  the  charge  is  and  how  quickly 


6     PROPERTIES  OF  AN  ELECTRIC  CHARGE  [CH.  I. 

it  is  moving.  There  is,  in  my  opinion,  no  other 
kind  of  magnetic  field  possible  ;  and  so  if  ever  we 
come  across  a  magnetic  field  which  we  feel  entitled 
to  consider  "  strong,"  we  must  conclude  that  it  is 
associated  with  the  motion  of  a  very  considerable 
charge,  at  a  velocity  we  may  properly  style  great. 
But  certainly  it  is  true  that  for  any  ordinary  charged 
sphere,  moving  at  any  ordinary  pace, — even  supposing 
that  it  is  a  cannon-ball  shot  from  the  mouth  of  a 
gun — the  concentric  circular  magnetic  field  sur- 
rounding its  trajectory  is  decidedly  feeble.  Feeble 
or  not,  it  is  there,  and  to  its  existence  we  must  trace 
all  the  magnetic  phenomena  of  the  electric  current. 

For  just  as  there  is  no  electrostatic  field  save  that 
extending  from  one  charged  body  to  another,  so 
there  is  no  electric  current  except  the  motion  of  such 
a  charged  body,  and  no  magnetic  field  except  that 
which  surrounds  the  path  of  this  motion. 

The  locomotion  of  an  electric  charge  is  an  electric 
current,  and  the  magnetic  field  surrounding  that 
current  is  believed  to  be  the  only  kind  of  magnetic 
field  in  existence.  If  any  other  variety  is  possible, 
the  burden  of  proof  rests  on  those  who  make  the 
positive  assertion. 

Transmission  of  Energy. 

While  the  charge  is  stationary  everything  is  steady, 
and  we  have  an  electric  field  only. 

While  the  charge  is  moving  at  constant  speed  the 
current  is  steady,  and  we  have  a  steady  magnetic 
field  superposed  upon  a  steadily  moving  electric  field; 
there  is  likewise  a  certain  conveyance  of  energy  in 
the  direction  of  the  motion. 

This  is  a  special  case  of  the  general  theorem 
known  as  Poynting's :  viz.  that  wherever  an  electric 


CH.  i.]  ACCELERATED   CHARGE  7 

and  a  magnetic  field  are  superposed  there  cannot 
be  static  equilibrium  at  that  place,  energy  must  flow 
through  the  medium ;  and  the  rate  of  transfer  of 
energy — the  amount  conveyed  per  second  through 
unit  area — is  equal  to  1/4 TT  times  the  vector  product  of 
the  intensity  of  the  two  fields  :  that  is  to  say,  it  is 
measured  by  the  area  of  the  parallelogram  bounded 
by  lines  representing  the  two  fields  in  magnitude  and 
direction  ;  a  quantity  commonly  expressed  as 

V(EH),  or  [EH],  or  as  EH  sin  0, 

where  0  is  the  angle  between  E  and  H. 

The  direction  of  propagation  of  energy  is  normal 
to  that  same  area,  and  its  '  sense '  or  sign  depends 
upon  the  sense  of  the  two  fields.  If  both  were 
reversed,  the  sense  of  the  transmission  of  energy 
would  continue  unchanged :  and  its  amount  remains 
constant  so  long  as  the  fields  are  constant,  that  is 
so  long  as  the  current  is  steady.  Another  way  of 
expressing  the  facts  is  to  say  that  the  space  in  which 
two  fields  are  superposed  is  full  of  momentum ;  and 
that  the  moment  of  momentum  ^appropriate  to  a  pole 
m  and  a  charge  e  is  simply  em. 

Accelerated  Charge. 

One  more  statement : 

So  far  we  have  dealt  with  the  case  of  steady  rest  or 
steady  motion ;  but  what  about  the  intermediate 
stages,  the  stages  of  starting  and  stopping  ?  What  is 
the  condition  of  things  after  the  charge  has  begun  to 
move  but  before  it  has  attained  a  constant  speed,  and 
again  when  the  brake  is  applied  and  the  speed  is 
decreasing,  or  when  the  direction  of  motion  is  chang- 
ing? What  phenomena  are  observable  during  the 
epoch  of  acceleration  or  retardation  of  speed  or 


8     PROPERTIES  OF  AN  ELECTRIC  CHARGE  [CH.L- 

curvature  of  path  ?  Something  more*  than  simple 
electrostatics  and  simple  magnetism  is  then  observed. 
For  whenever  a  conductor  is  moved  across  a 
magnetic  field  it  is  well  known  that  an  electromotive 
force  acts  in  that  conductor,  of  magnitude  equal  to 
the  rate  at  which  magnetic  lines  of  force  are  being 

cut ;  or  in  symbols  . 

E=  —dN/dt, 

which  is  the  fundamental  '  dynamo '  equation.  This 
is  called  the  phenomenon  of  magneto-electric  in- 
duction ;  it  is  the  induced  E.M.F.  discovered  by 
Faraday,  and  it  necessarily  occurs  whenever  magne- 
tism and  relative  motion  are  superposed. 

It  is  quite  independent  of  the  conductivity  of 
the  conductor  however,  and  would  have  the  same 
value  if  the  motion  took  place  in  an  insulator, 
though  of  course  it  could  not  then  produce  the 
same  effect  as  regards  conduction-currents. 

The  effect  of  a  conductor  is  to  integrate,  or  add 
up,  the  E.M.F.'S  generated  in  each  element  all  along 
its  length,  and  thus  to  display  the  effect  in  an 
obvious  manner :  especially  when  the  conductor  is 
made  very  long  and  is  compactly  coiled  (as  in  an 
armature).  The  definition  of  electromotive  force 
between  two  points  A  and  B,  or  round  any  closed 
contour,  is — the  line-integral  of  electric  field  from  A 
to  B,  or  round  the  same  contour.  In  the  unclosed- 
path  case  it  is  measured  by  the  difference  of  electric 
potential  between  A  and  B. 

One  of  the  easiest  and  most  ordinary  ways  of 
superposing  motion  and  magnetism,  is  to  allow  or 
cause  a  magnetic  field  to  vary  in  strength  (as  in 
a  Ruhmkorff  coil) ;  for  then  the  lines  of  force  move 
broadside  on,  expanding  or  contracting  as  the  case 
may  be,  and  thus  at  once  we  get  the  phenomenon 


CH.  i.]  ACCELERATED  CHARGE  9 

of  induction — the  generation  of  an  induced  E.M.F., 
of  value  at  any  point  equal  to  the  rate  of  change 
of  the  lines  of  magnetic  force  there.  This  is  what 
happens  whenever  an  electric  charge  is  accelerated ; 
for  then  its  magnetic  field — which,  as  we  have  seen, 
depends  upon  the  velocity — necessarily  changes  in 
strength,  and  so  an  E.M.F.  is  induced.  There  being 
no  conductor,  this  E.M.F.  will  propel  no  current,  but  it 
will  represent  an  electric  force  which  was  not  there 
before,  and  the  new  force  will  be  in  a  new  direc- 
tion ;  the  direction  of  an  induced  electric  force  is 
perpendicular  to  the  direction  in  which  the  grow- 
ing magnetic  lines  are  moving,  which  in  the 
present  case  is  outwards  from  the  charge.  Con- 
sequently the  new  or  induced  E.M.F.  points  in  the 
direction  of  motion,  though  in  the  sense  opposed 
to  any  change  in  it ;  and  the  effect  of  the  super- 
position of  this  new  E.M.F.  upon  the  already  existing 
magnetic  field  is  to  cause  a  certain  small  transmission . 
of  energy  in  a  radial  direction  out  and  away  from 
the  accelerated  charge.  Some  energy  therefore  flashes 
away  with  the  speed  of  light ;  and  although  in 
ordinary  cases  it  may  be  an  exceedingly  small  amount 
which  is  thus  radiated  into  space,  yet  it  is  the  only 
mode  of  generating  radiation  with  which  we  are 
acquainted. 

It  is  from  an  electric  charge  during  its  epochs  of 
acceleration  or  retardation  that  we  get  the  pheno- 
menon called  radiation ;  it  is  this  and  this  alone 
which  excites  ethereal  waves,  and  gives  us  the 
different  varieties  of  light. 

The  energy  radiated  per  second  has  been  shown 
by  Larmor  to  be 


10  PROPERTIES  OF  AN  ELECTRIC  CHARGE  [CH.  i. 

where  v  is  the  speed  of  light  and  u  is  the  acceleration 
of  the  charge  e. 

After  this  manner,  though  of  course  by  means  of 
a  very  extensive  development  of  these  fundamental 
ideas,  are  all  the  phenomena  of  electricity  and  mag- 
netism and  optics  summarised,  and,  so  to  speak, 
accounted  for. 


NOTE. 

Let  it  be  said  here,  once  for  all,  that  in  every  case  one  or  other 
of  the  two  etherial  constants,  p  and  K,  should  be  exhibited 
explicitly  wherever  it  rightly  occurs.  If  this  be  not  done  the 
dimensions  of  most  expressions  are  necessarily  wrong;  and 
words  have  to  be  added  about  whether  the  units  intended  are 
c.g.s.  or  some  other  system,  and  likewise  whether  they  are 
electrostatic  or  electromagnetic.  This  latter  double  system  of 
measurement  has  served  its  turn,  and  still  serves  it  ;  but  intrinsi- 
cally it  is  confusing,  and  has  been  only  rendered  necessary 
because  we  do  not  yet  know  the  values,  or  even  for  certain  the 
tnature,  of  p  and  K.  It  is  to  be  hoped  that  no  third  system  — 
'devised  as  an  attempted  escape  from  confusion,  but  really  an 
intensification  of  fog  —  will  ever  be  successfully  attempted  ;  though 
there  are  threats  in  that  direction,  owing  to  lack  of  clear  thinking. 

The  explicit  retention  of  the  constants  keeps  everything  clear 
and  easy.  For  instance,  the  expression  just  above  quoted  is 
essentially  what  it  purports  to  be,  an  energy  divided  by  a  time 

FL 


and  is  therefore  true  as  it  stands  in  every  complete  system  of 
units  whatever.  So  also  the  expression  quoted  near  the  be- 
ginning of  the  next  chapter  is  essentially  what  it  purports  to  be, 
namely,  a  mass  or  inertia  ;  and  the  same  may  be  said  of  all  other 
expressions  in  this  book. 

The  ordinary  convention  for  numerical  specification  is,  —  for 
electromagnetic  c.g.s.  units,  to  consider  /*  =  1,  for  electrostatic 
units,  to  consider  K  =  I  \  and  this  convention  must  hold  until  we 
learn  the  real  facts,  by  future  discovery  :  for  which  discovery 
continual  familiarity  with  the  unknown  constants  undoubtedly 
serves  to  pave  the  way. 


CHAPTER  II. 
ELECTEIC   INERTIA. 

WHATEVER  a  charge  may  be,  and  whatever  the 
physical  constitution  of  the  ether,  it  must  be  able 
to  maintain  electric  lines  and  magnetic  lines 
separately,  and  to  transmit  energy  wherever  both 
sets  of  lines  coexist  and  cross  each  other. 

An  accelerated  charge  is  equivalent  to  a  changing 
current,  for  dC/dt  may  be  written  d2e/dt2.  When- 
ever a  current  changes  it  is  well  known  that  an  E.M.F. 
of  self-induction  is  set  up,  equal  to  LdC/dt;  and 
this  electrical  equation  E  =  L  e  corresponds  to  the 
mechanical  equation  F  =  ra  x, — Newton's  second  law. 

Considered  from  the  point  of  view  of  a  current  as 
constituted  by  a  moving  charge,  this  self-induced  or 
reaction  E.M.F.  corresponds  or  is  analogous  to  a  mass- 
acceleration.  And  the  electrical  acceleration  is 
opposed  by  the  E.M.F.,  just  as  the  acceleration  of 
matter  is  opposed  by  its  mechanical  inertia.  The 
coefficient  of  the  electric  acceleration — commonly 
denoted  by  L — represents  therefore  an  inertia  term, 
and  is  properly  called  'electric  inertia.' 

By  Lenz's  law  the  effect  of  induction  is  always 
to  oppose  the  cause  which  is  producing  it.  In  the 
present  case  the  *  cause'  is  the  acceleration  or  retarda- 
tion of  the  moving  charge ;  and  so,  in  each  case,  this 


12  ELECTRIC   INERTIA  [CH.  n. 

is  opposed  by  the  reaction  of  the  magnetic  lines 
generated  by  it. 

Motion  is  opposed  while  it  is  increasing  in  speed, 
and  it  is  assisted  while  it  is  decreasing  in  speed  — 
an  effect  precisely  analogous  to  ordinary  mechanical 
inertia  ;  —  and  therefore  force  is  necessary,  and  work 
must  be  done,  either  to  start  or  to  stop  the  motion 
of  a  charged  body.  An  extra  force,  that  is,  by 
reason  of  its  charge.  Whatever  ordinary  inertia 
the  body  may  have,  considered  as  a  piece  of  matter, 
it  has  a  trifle  more  by  reason  of  its  being  charged 
with  electricity  —  no  matter  what  the  sign  of  its 
charge  may  be. 

The  value  of  this  imitation  or  electrical  inertia, 
for  the  case  of  a  charged  sphere  of  radius  a,  was 
calculated  by  J.  J.  Thomson  in  1881,  and  is 


3a 


Electrical  Inertia  or  Mass,  continued. 

Since  this  is  very  important,  I  repeat  :  — 
Just  as  a  changing  magnetic  field  affects  an  electro- 
static charge,  —  that  is  to  say  generates  a  feeble  field 
of  electric  force,  into  the  intensity  of  which  the 
velocity  of  light  enters  squared  in  the  denominator 
(see  Lodge,  Phil.  Mag.,  June  1889,  p.  472),  —  so  it 
is  with  a  changing  electric  field,  it  generates  a 
magnetic  field  proportional  to  its  velocity  of  change. 
And  if  it  is  being  accelerated,  the  magnetic  field 
itself  varies,  and  in  that  case  generates  an  E.M.F. 
which  reacts  upon  the  accelerated  moving  charge, 
—  always  in  such  a  way  as  to  oppose  its  motion  — 
by  what  is  called  Lenz's  law,  or  simply  by  the  law 
of  conservation  of  energy  :  for  if  it  assisted  the 


CH.  II.]  ELECTRIC   INERTIA  13 

motion,  the  action  and  reaction  would  go  on  in- 
tensifying themselves,  until  any  amount  of  violence 
was  reached. 

The  magnetic  lines  generated  by  a  rising  current, 
that  is  by  a  positively  accelerated  charged  body, 
react  back  upon  the  motion  which  produced  them 
in  such  a  way  as  to  oppose  it ; — to  oppose  it 
actively  or  elastically,  not  passively  or  sluggishly 
as  by  friction.  The  reaction  ceases  the  instant  the 
motion  becomes  steady :  it  is  not  analogous  to 
friction  therefore,  but  to  inertia ;  it  is  the  coeffi- 
cient of  an  acceleration  term. 

The  magnetic  lines  generated  by  a  falling  current, 
that  is  by  a  negatively  accelerated  or  retarded 
charged  body,  react  oppositely,  and  tend  to  con- 
tinue the  motion  :  thus  here  also  we  have  a  term 
corresponding  to  inertia.  And  the  charged  body 
may  be  said  to  have  extra  momentum,  by  reason 
of  its  charge,  while  it  is  moving.  The  value  of 
the  momentum  is  proportional  to  the  velocity,  so 
long  as  the  velocity  is  not  excessively  great ;  and 
accordingly  the  inertia  term  is  constant,  i.e.  inde- 
pendent of  speed,  under  the  same  restriction.  It 
may  therefore  be  considered  to  be  in  existence 
even  when  the  charge  is  stationary,  and  thus  it 
simulates  exactly  the  familiar  mechanical  inertia 
of  a  lump  of  ordinary  matter. 

In  Appendix  A,  is  given  the  simplest  form  of 
the  quantitative  relations  here  indicated,  and  the 
inertia  due  to  an  electric  charge  is  there  calculated. 
It  is  to  be  understood  that  whatever  inertia  a 
material  sphere  may  possess,  considered  as  matter, 
it  will  possess  more  when  it  is  charged  with  elec- 
tricity, and  this  no  matter  whether  the  charge 
be  positive  or  negative.  The  amount  of  extra  or 


14  ELECTRIC   INERTIA  [CH.  n. 

electrical  inertia  is  proportional  to  the  electrostatic 
energy  of  the  charge  :  that  is  to  say,  it  is  pro- 
portional to  the  charge  and  its  potential  conjointly. 
Call  the  charge  e,  and  the  radius  of  the  sphere  a, 
the  potential  will  be  e/Ka  (K  being  Faraday's 
dialectric  constant)  ;  and  the  appropriate  inertia  is 


where  v  is  the  velocity  of  light.     (See  Note  at  end 
of  chap,  i.) 

Another  way  of  putting  it  is  to  say  that  if  a 
real  mass  of  this  amount  were  moving  with  the 
speed  of  light,  its  kinetic  energy  would  be  half  as 
great  again  as  the  potential  energy  of  the  electric 
charge  thus  reckoned  as  mechanically  equivalent 
to  it; 

for  ~mv2  =  -e  .  —  =  —  charge  x  potential 

4  2      KCI     2 

=  potential  energy. 

Now  any  appreciable  quantity  of  matter,  even  a 
milligramme,  moving  with  the  speed  of  light,  must 
have  a  prodigious  amount  of  energy  ;  for,  on  the 
ordinary  assumption  that  mass  is  quite  constant, 
the  energy  of  one  milligramme  rushing  along  with 
the  light-speed  would  amount  to  no  less  than 
fifteen  million  foot-tons.  Or  as  Sir  William  Crookes 
has  expressed  it  :  a  gramme,  or  fifteen  grains,  of 
matter,  moving  with  the  speed  of  light,  would  have 
energy  enough  to  lift  the  British  Navy  to  the  top 
of  Ben  Nevis. 

Consequently  the  inertia  of  any  ordinary  quantity 
of  electric  charge  must  be  exceedingly  minute. 
Notwithstanding  this,  it  is  quite  doubtful  whether 


CH.  ii.]  ELECTRIC   INERTIA  15 

or  not  there  really  exists  any  other  kind  of  inertia. 
The  question  whether  there  does  or  not  is  at 
present,  strictly  speaking,  an  open  one. 

Effect  of  Concentration. 

The  only  way  of  conferring  upon  a  given  electric 
charge  any  appreciable  mass,  is  to  make  its  potential 
exceedingly  high,  that  is  to  concentrate  it  on  a 
very  small  sphere. 

A  coulomb  at  the  potential  of  a  volt  has  an  elec- 
trostatic energy  of  half  a  Joule,  that  is  ^  x  10r  ergs. 

The  mass  equivalent  to  this  would  be 

2      10^          2 

39xl020  =  27  X  10~13  gramme=  10~8  milligramme. 

Kaise  the  potential  to  a  million  volts,  and  the 
mass-equivalent  to  a  coulomb  at  that  potential 
would  be  the  hundredth  part  of  a  milligramme ; 
still  barely  appreciable  therefore. 

The  charge  on  an  atom  as  observed  in  electrolysis 
is  known  to  be  10~10  electrostatic  units.*  If  this 
were  distributed  uniformly  on  a  sphere  the  nominal 
size  of  an  atom,  viz.,  one  10~8  centimetre  in  radius, 
its  potential  would  be  one  hundredth  of  an  elec- 
trostatic unit,  or .  about  3  volts.  The  energy  of 
such  a  charge  would  be  10~12  erg,  and  the  inertia 
of  a  body  which  would  possess  this  energy  if  moving 
at  the  speed  of  light  would  be  10~33  gramme ;  which 
would  therefore  be  its  electrical  inertia  or  extra  mass. 

But  this  is  incomparably  smaller  than  the  mass 
of  a  hydrogen  atom,  which  is  approximately  10~25 
gramme.  Consequently  the  ionic  charge  distributed 
uniformly  over  an  atom  would  add  no  appreciable 
fraction  to  its  apparent  mass. 

*  More  exactly,  according  to  Cambridge  measurements,  3*3  x  10 ~10. 


16  ELECTRIC   INERTIA  [CH,  n. 

If,  however,  the  atomic  charge  were  concentrated 
into  a  sphere  of  dimension  10~13  centimetre,  its 
potential  would  be  1000  electrostatic  units,  or 
300,000  volts;  its  energy  would  then  be  10~7  erg, 
and  its  inertia  10 ~28  gramme,  or  about  YTHJIT  °f  the 
mass  of  a  hydrogen  atom. 

Summary. 

All  this  is  a  preliminary  statement  of  undeniable 
fact :  that  is  to  say  of  fact  which  follows  from  the 
received  and  established  theory  of  Electricity, 
whether  such  things  as  electrons  have  ever  been 
found  to  exist  or  not. 

All  that  we  have  stated  is  true  of  an  ordinary 
charge  on  any  ordinary  sphere  which  can  be  made 
to  move  by  mechanical  force  applied  to  it. 

It  gives  us  the  phenomena 

of  electrostatics  when  at  rest, 
of  magnetism  when  in  motion, 
of  radiation  when  its  motion  is  altered ; 
and  it  incidentally,  by  reason  of  the  known  laws  of 
electromagnetic  induction,  exhibits  a  kind  of  imitation 
inertia,  and  in  that  way  simulates  the  possession  of 
the  most  fundamental  property  of  matter.  > 

I  will  add  a  few  more  closely  connected  assertions, 
for  later  application : 

Apply  a  sufficiently  violent  E.M.F.  to  a  charged 
sphere,  and  the  charge  may  be  wrenched  off  it. 

Insert  an  obstacle  in  the  path  of  a  violently  moving 
charged  sphere,  so  as  to  stop  it  mechanically  with 
sufficient  suddenness,  and  again  it  is  possible  for  the 
charge,  or  something  like  it,  to  be  jerked  off  it  and 
passed  on.  But  to  do  this  the  speed  of  the  material 
sphere,  as  well  as  the  suddenness  of  stoppage,  must  be 


CH.II.]  HISTORICAL  REMARKS  17 

excessive.  Usually  the  charge  is  merely  thrown  into 
oscillation,  when  the  sphere  is  suddenly  stopped ;  and 
it  then  emits  a  solitary  wave  or  spherical  shell  of  thick- 
ness equal  to  the  diameter  of  the  sphere  :  or  greater 
than  that  diameter  by  the  amount  the  sphere  has 
moved  during  its  retardation.  When  the  acceleration 
is  moderate,  however,  the  radiation  is  less  energetic 
and  also  less  intense  :  less  energetic  because  its  power 
depends  on  the  square  of  the  acceleration,  less  intense 
because  it  is  spread  over  a  thicker  ethereal  shell. 
Rontgen  rays  are  perceptible  only  when  the  speed  was^ 
great  and  the  stoppage  so  sudden  that  the  wave  or 
pulse- shell  is  strong  and  thin  (see  chap.  viii.).  The 
thinner  the  pulses  or  wave  shells  the  more  penetrating 
they  are.  If  thin  enough  they  could  traverse  matter 
without  affecting  it  or  being  affected  by  it. 

Historical  Remarks. 

The  doctrine  of  the  behaviour  of  a  charged  sphere 
in  motion,  and  the  calculation  of  the  value  of  the 
quasi  inertia  of  an  electric  charge,  was  begun  by 
Professor  J.  J.  Thomson  in  an  epoch-making  paper 
published  in  the  Philosophical  Magazine  for  April, 
1881 — one  of  the  most  remarkable  physical  memoirs 
of  our  time. 

The  stimulus  to  this  investigation  was  supplied  by 
those  brilliant  experiments  of  Crookes,  published  in 
the  Philosophical  Transactions  for  1879,  which  were 
preceded  by  observations  of  Pliicker  and  Hittorf,  and 
related  to  other  observations  by  Goldstein,  Spottis- 
wood  and  Moulton,  and  others,  about  the  same  period. 

In  1891  Sir  William  Crookes  was  President  of 
the  Institution  of  Electrical  Engineers,  and  in  his 
inaugural  address  he  expounded  further  some  of  these 
brilliant  experimental  investigations,  to  which  Schuster 


L.E. 


18  ELECTRIC   INERTIA  [CH.  n. 

and  many  others  had  contributed.  It  is  not  too  much 
to  say  that  up  to  the  time  of  Crookes  the  phenomena 
of  the  vacuum  tube  were  shrouded  in  darkness,  not- 
withstanding much  laborious  and  painstaking  work 
done  both  in  this  country  and  on  the  Continent  in 
connection  with  them  ;  but  that  since  the  researches 
of  Crookes  in  the  seventies,  the  theoretical  luminosity 
of  the  vacuum  tube  has  steadily  increased,  until  now, 
as  Maxwell  predicted,  it  is  shedding  light  upon  the 
whole  domain  of  electrical  science,  and  even  upon  the 
constitution  of  matter  itself. 


CHAPTEK   III. 

FORESHADOWING  OF  THE  ATOM   OR  INDIVISIBLE 
UNIT  OF  ELECTRICITY. 

So  far  we  have  dealt  with  the  fundamental  laws  of 
electricity  in'  general.  It  is  now  time  to  begin  to 
consider  the  possibly  atomic  or  molecular  condition  in 
which  it  is  associated  with  atoms  of  matter. 

Quoting  again  from  the  great  Treatise  of  Clerk 
Maxwell,  1st  Edition  (1873),  we  find  on  page  312, 
in  the  chapter  on  electrolysis,  the  following  sentence  : 

"  Suppose,  however,  that  we  leap  over  this 
difficulty  by  simply  asserting  the  fact  of  the 
constant  value  of  the  molecular  charge,  and 
that  we  call  this  constant  molecular  charge,  for 
convenience  in  description,  one  molecule  of 
electricity."  .  .  . 

Thus  some  idea  of  the  conception  of  the  atomic 
nature  of  electricity  was  long  ago  forced  upon  men  of 
genius  by  the  facts  of  electrolysis  and  a  knowledge  of 
Faraday's  laws.  But  Maxwell  went  on,  after  a  few 
more  paragraphs  : 

"It  is  extremely  improbable  that  when  we 
come  to  understand  the  true  nature  of  electrolysis 
we  shall  retain  in  any  form  the  theory  of  molecular 


20  FORESHADOWING  OF  THE  ATOM     [CH.  in. 

charges,  for  then  we  shall  have  obtained  a  secure 
basis  on  which  to  form  a  true  theory  of  electric 
currents,  and  so  become  independent  of  these 
provisional  theories." 

It  is  rash  to  predict  what  may  ultimately  happen, 
but  the  present  state  of  electrical  science  seems  hostile 
to  this  latter  prediction  of  Maxwell.  The  theory  of 
molecular  charges  looms  bigger  to-day,  and  has  taken 
on  a  definiteness,  largely  as  the  outcome  of  his 
own  work,  that  would  have  pleased  and  surprised 
him. 

The  unit  electric  charge,  the  charge  of  a  monad 
atom  in  electrolysis,  whatever  else  it  is,  is  a  natural 
unit  of  electricity,  of  which  we  can  have  multiples, 
but  of  which,  so  far  as  we  know  at  present,  it  is 
impossible  to  have  fractions. 

I  will  extract  the  following  sentence  from  Section 
32  of  my  little  book  called  Modern  Views  of 
Electricity  (1889.  See  also  Brit.  Assoc.,  Aberdeen, 
1885,  p.  763): 

"  This  quantity,  the  charge  of  one  monad 
atom,  constitutes  the  smallest  known  portion  of 
electricity,  and  is  a  real  natural  unit.  Obviously 
this  is  a  most  vital  fact.  This  unit,  below  which 
nothing  is  known,  has  even  been  styled  an 
'  atom  of  electricity,'  and  perhaps  the  phrase 
may  have  some  meaning.  .  .  .  This  natural 
unit  of  electricity  is  exceedingly  small,  being 
about  the  hundred-thousand-millionth  part  of 
the  ordinary  electrostatic  unit,:  or  less  than  the 
hundred- trillionth  of  a  coulomb." 

The  atom  with  its  charge  is  called  an  "  ion."  The 
charge  considered  alone,  without  attending  to  its 


CH.IIL]  OF   ELECTRICITY  21 

atom,    was    called    by    Dr.    Johnstons    Stoney    an 
"  electron  "  or  natural  electrical  unit. 

What  we  learn  with  great  accuracy  from  electro- 
lysis is  the  ratio  of  the  charge  to  the  mass  of 
substance  with  which  it  is  associated.  It  matters 
nothing  how  much  substance  is  chosen,  whether  100 
atoms  or  one,  whether  an  atom  or  a  gramme  or  a  ton, 
— the  amount  of  electricity  associated  with  it  in 
electrolysis,  and  liberated  when  the  substance  is 
decomposed,  increases  in  the  same  proportion  ;  the 
ratio  is  constant  for  each  material,  and  if  determined 
for  one  is  known  for  all. 

This  ratio  is  the  reciprocal  of  what  is  technically 
known  as  the  "  electrochemical  equivalent "  of  a  sub- 
stance. In  the  light  of  Faraday's  laws,  if  this  quantity 
is  measured  for  one  substance  it  is  known  for  all, 
because  the  charge  is  the  same  for  every  kind  of 
atom,  up  to  a  simple  multiple ;  and  hence  in  specify- 
ing electrochemical  equivalents  there  is  nothing 
to  consider  but  the  atomic  weight,  or  combining 
proportion,  of  the  substance.  Thus  the  electro- 
chemical equivalent  of  oxygen  is  8  times  that  of 
hydrogen,  that  of  zinc  is  32|-  times,  and  that  of  silver 
108  times  that  of  hydrogen.  The  substance  chosen 
for  a  determination  of  the  electrochemical  equivalent 
may  be  the  one  which  can  be  most  accurately  experi- 
mented on ;  and  Lord  Rayleigh  has  shown  that  such  a 
substance  is  nitrate  of  silver,  and  has  ascertained  that 
if  a  current  of  one  ampere  is  passed  from  a  silver  anode 
to  a  platinum  cathode  through  a  nitrate  of  silver  solu- 
tion, the  cathode  gains  in  weight  by  4*025  grammes 
every  hour.  Hence  the  electrochemical  equivalent  of 
silver  is 

4*025  grammes  f 

1  ampere-hour  ' 


22  FORESHADOWING  OF  THE  ATOM    [CH.  HL 

the   electrochemical   equivalent   of  hydrogen,    being 
Y^-gth  of  this  quantity,  is 

4*025  grammes  4*025 

108  ampere-hours  =  108  x  360  C'g'S* 

=  '0001035  c.g.s.  =  Qggnn  grammes  per  coulomb. 


Hence  the  ratio  of  an  atom  of  electricity  to  an  atom 
of  hydrogen  is  9,660  M~^  c.g.s.  units,  or  approximately 

centimetres\ 


{    // 
V 


*  grammes/ 

the  unknown  constant  M  necessarily  making  its 
appearance,  because  we  are  comparing  quantities  of 
different  nature,  or  at  any  rate  quantities  measured 
in  different  ways,  viz.,  'electricity'  and  'matter'  (see 
Appendix  D). 

The  numerical  part  of  this  quantity  is  known 
with  comparative  exactitude,*  that  is  to  say  up  to 
the  limits  of  error  of  experiment  :  to  proceed 
further,  we  must  make  an  estimate  of  the  mass  of 
an  atom.  That  can  be  done,  and  has  been  done,  in 
many  ways,  and  we  have  been  taught  both  by  Dr. 
Johnston  e  Stoney  and  by  Loschmidt,  originally  even 
by  Dr.  Thos.  Young,  but  with  greatest  force  and  range 
by  Lord  Kelvin,  that  the  mass  of  an  atom  of  water  is 
approximately  10~24  of  a  gramme;  wherefore  an  atom 
of  hydrogen  will  be  approximately  10  ~25  gramme; 
whence  the  unit  of  electric  charge  is  10~21  c.g.s. 
magnetic  unit,  or  10~10  of  an  electrostatic  unit  or 
10-20  of  a  coulomb. 

*The  decimal  places  are  correctly  printed  above  ;  though  the  fact 
that  1  coulomb,  or  1  ampere-second,  is  one-tenth  of  a  c.g.s.  unit  —  owing 
to  the  ohm  and  volt  having  been  inadvertently  defined,  one  as  109,  and 
the  other  as  108  c.g.s.,  instead  of  both  the  same  —  always  stands  ready  to 
introduce  confusion  and  error. 


CH.  in.]  OF   ELECTRICITY  23 

I  have  emphasised  this  matter  of  the  ratio  m  to  e, 
or  e  to  ra,  because  it  plays  a  considerable  part  in 
what  follows.  The  absolute  values  are  of  less 
consequence  to  us  than  the  ratio,  and  are  only  known 
approximately,  but  the  ratio  is  known  with  fair 
accuracy ;  and  the  ratio  e  :  m  for  hydrogen  is  very 
nearly  104  magnetic  units,  or  more  exactly  9,660. 

Thus  what  we  learn  from  electrolytic  conduction, 
briefly  summarised,  is  that  every  atom  carries  a 
certain  definite  charge  or  electric  unit,  monads 
carrying  one,  diads  two,  triads  three,  but  never  a 
fraction  ;  that  in  liquids  these  charges  are  definitely 
associated  with  the  atoms,  and  can  only  be  torn  away 
from  them  at  the  electrodes ;  that  the  current 
consists  of  a  procession  of  such  charges  travelling 
with  the  atoms, — the  atoms  carrying  the  charges,  or 
the  charges  dragging  the  atoms,  according  to  the 
point  of  view  from  which  we  please  to  regard  the 
process. 


CHAPTEE  IV. 
FORESHADOWING  OF  THE  ELECTRON. 

Separate  Existence  of  the  Electric    Unit  suggested 
by  Conduction  in  Gases. 

WE  will  now  leave  liquids  and  proceed  to  conduction 
by  ratified  gases,  that  is  to  say  to  the  phenomena 
seen  in  vacuum  tubes.  If  a  long  glass  tube,  say  a 
yard  long  and  two  inches  wide,  with  an  electrode  at 
each  end,  and  full  of  common  air,  is  connected  to  an 
induction  coil  and  attached  to  an  air-pump, — the 
ordinary  spark-gap  of  the  coil  being,  say,  two  or 
three  inches  wide, — we  find  that  for  some  time  after 
working  the  pump  the  electric  discharge  prefers  the 
inch  or  two  of  ordinary  air  to  a  long  journey  through 
the  partially  rarified  air  in  the  tube ;  but  that  at  a 
certain  stage  of  exhaustion,  one  which  any  rough 
air-pump  ought  to  reach,  this  preference  ceases.  A 
flickering  light  appears  in  the  tube,  readily  visible  in 
the  dark,  which  very  soon  takes  on  the  appearance  of 
red  streamers  like  the  Aurora  Borealis ;  and  soon  the 
sparks  outside  in  the  common  air  cease,  showing  that 
the  rarified  air  is  now  the  better  conductor  and  the 
preferable  alternative  path.  Let  the  exhaustion 
proceed  further— the  axis  of  the  tube  becomes 
illumined  with  a  glow,  which  is  now  much  brighter, 


CH.IV.]  VACUUM   TUBE  25 

forming  a  band  or  thread  of  light,  while  the  original 
spark-gap  may  be  shortened  down  gradually  to  one- 
eighth  of  an  inch,  or  even  less,  without  any  spark 
taking  place  across  it, — showing  that  rarified  air  is 
a  very  good  conductor.  When  the  best  conducting 
stage  is  reached  the  tube  is  filled  with  a  glow,  called 
the  positive  column  ;  and  both  ends  of  the  tube  are 
apt  to  look  alike.  If  we  exhaust  still  further — and 
to  exhaust  even  as  far  as  this  something  better  than 
an  ordinary  air-pump  is  necessary,  an  oil  or  mercury 
pump  being  the  most  suitable — the  column  of  light 
is  seen  to  fill  the  whole  tube,  to  gradually  lose  its 
bright  red  or  crimson  tint,  and  to  break  up  into  a 
number  of  very  narrow  discs,  like  pennies  seen  edge- 
ways. At  the  same  time  the  spark-gap  must  be 
widened  to  something  more  like  a  quarter  or  half  an 
inch,  to  prevent  the  discharge  from  taking  that  path, 
and  a  dark  space  near  the  cathode  now  begins  to  be 
visible,  the  cathode  itself  being  covered  all  over  with 
a  glow,  while  the  anode  is  usually  only  illuminated 
at  a  point  or  two.  The  striae,  into  which  the  positive 
column  has  been  broken  up,  thicken  and  separate  as 
exhaustion  proceeds.  The  dark  space  near  the 
cathode  also  enlarges,  driving  as  it  were  the  positive 
column  before  it  into  the  anode,  and  looking  as  if  it 
would  presently  fill  the  tube ;  but  before  it  can  do 
this  it  is  noticed  that  the  glow  on  the  cathode  itself 
is  coming  off  as  a  kind  of  shell,  leaving  another  dark 
space,  a  narrower  and  much  darker  space,  inside  it. 
The  first  dark  space  has  been  called  Faraday's  dark 
space ;  the  second  is  generally  known  by  the  name  of 
Crookes'.  This  second  dark  space  now  increases  in 
thickness,  pushing  the  glow  before  it  as  the  vacuum 
gets  better  and  better ;  but  the  terminals  of  the 
spark-gap  must  now  be  pulled  still  further  apart,  else 


26  FORESHADOWING  OF  THE  ELECTRON  [CH.  IV. 

the  discharge  will  prefer  to  take  a  reasonably  long 
path  through  the  air.  Exhausting  further  still,  the 
glow  all  disappears  and  the  second  dark  space  fills 
the  whole  of  the  tube ;  and  now  is  noticed  a  new 
phenomenon,  the  sides  of  the  glass  have  begun  to 
glow  with  a  phosphorescent  light,  the  colour  of  the 
light  depending  on  the  kind  of  glass  used,  but 
generally  in  practice  with  a  greenish  light ;  a  result 
evidently  of  being  the  boundary  of  the  dark  space. 
If  exhaustion  proceeds  further,  the  resistance  of  the 
tube  becomes  very  high,  and  the  spark  may  prefer  to 
burst  through  an  equal,  and  ultimately  even  a  greater, 
length  of  ordinary  air.  This  is  the  condition  of  the 
tube  so  much  investigated  by  Crookes,  by  Lenard 
and  Rontgen,  and  by  many  other  observers.  It  is 
the  phenomena  occurring  in  this  dark  space  which 
have  proved  of  the  most  intense  interest. 

Cathode  Rays. 

So  far  we  have  supposed  that  the  cathode  is  a 
brass  knob  or  other  convenient  terminal  introduced 
into  the  tube ;  but  if  we  now  proceed  to  use  other 
shapes, — as  Plucker  did  first  in  1859,  followed  by 
Hittorf  (1869),  Goldstein  (1876),and  Crookes  (1879)— 
using  a  flat  disc  or  a  saucer-shaped  piece  of  metal,  and 
if  we  then  introduce  into  the  dark  space  various  sub- 
stances, we  shall  find  that  shadows  are  thrown,  and 
that  the  dark  space  is  full  of  properties  which  are 
most  clearly  expressed  by  saying  that  it  is  a  region 
of  cathode  rays — that  is  to  say,  of  something  shot 
off  in  straight  lines  from  the  cathode.  There  is 
evidently  something  being  thus  shot  off — though  what- 
ever it  is,  it  is  invisible  until  it  strikes  an  obstacle — 
something  which  seems  to  fly  in  straight  lines  and  to 
produce  a  perceptible  effect  only  when  it  stopped. 


CH.  iv.]  CATHODE    RAYS  27 

Such  a  *  something'  might  be  a  bullet  from  a  gun, 
which  is  quite  invisible  when  looked  at  sideways,  but 
may  produce  a  flash  of  flame  when  it  strikes  a  target, 
or  may  do  other  damage.  So  it  is  with  these  cathode 
rays  :  the  region  of  their  flight  is  the  dark  space  ;  the 
boundaries  of  that  space,  where  the  projectiles  strike, 
are  illuminated.  A  substance  with  phosphorescent 
power,  such  as  many  minerals,  or  even  glass,  phos- 
phoresces brightly ;  and  the  path  of  the  rays  can 
be  traced  by  smearing  a  sheet  of  mica  with  some 
phosphorescent  powder  and  placing  it  edgeways 
along  their  path.  In  this  way  it  can  be  shown 
that  the  rays  are  like  particles  travelling  definitely 
in  straight  lines,  not  colliding  against  each  other, 
but  each  shot  like  bullets  from  an  immense  number 
of  parallel  guns.  Where  they  strike  the  sides  of 
the  glass  they  make  it  phosphoresce;  where  they 
strike  residual  air  in  the  tube,  as  they  do  if  the 
exhaustion  is  not  high  enough,  they  make  it  phos- 
phoresce also,  and  give,  in  fact,  the  ordinary  glow 
surrounding  the  dark  space. 

These  rays  possess  a  considerable  amount  of 
energy,  as  can  be  shown  by  concentrating  them,  by 
means  of  a  curved  saucer-shaped  cathode,  and 
bringing  them  to  a  focus.  The  rays  can  be  brought 
to  a  focus  in  consequence  qf  the  fact  that  they 
are  projected  from  the  cathode  initially  normal  to 
its  surface,  though  the  focus  is  further  from  the 
cathode  than  the  centre  of  curvature  because  of 
something  equivalent  to  mutual  repulsion  of  the 
rays.  A  piece  of  platinum  put  at  that  focus  will 
(if  the  exhaustion  is  not  too  high)  show  evident 
signs  of  being  red-hot — that  is  to  say,  will  emit 
light.  If  the  exhaustion  proceeds  further,  less  heat 
is  produced,  though  a  phosphorescent  light  is 


28    FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

now  emitted  from  suitable  substances,  like  alumina 
and  most  earths ;  and  if  the  exhaustion  is  pressed 
further  still,  the  bombarded  target  emits  no  visible 
light  but  only  that  higher  kind  of  radiation  known 
as  Rontgen  or  X-rays.  It  may  be  doubted,  however, 
whether  the  target  itself  emits  these  rays,  whether  its 
function  is  not  rather  to  stop  the  projectiles,  as 
suddenly  as  possible,  by  the  massiveness  of  its  atoms. 
Thus  the  best  target  would  be  a  substance  with 
the  heaviest  atoms.  X-rays  are  emitted  by  the 
suddenly  stopped  projectiles,  in  a  manner  which  has 
been  investigated  both  by  Sir  G.  Stokes  and 
Professor  J.  J.  Thomson,  and  which  is  intelligible 
to  anyone  who  has  studied  the  properties  of  moving 
electric  charges  moving  at  or  near  the  speed  of  light : 
a  matter  on  which  Mr.  Heaviside  has  written  with 
great  clearness  in  his  volume  called  Electromagnetic 
Theory. 

Cathode  rays  have  a  remarkable  penetrating 
power;  for  Hertz  found  that  a  thin  metal  diaphragm, 
especially  if  it  were  of  aluminium,  was  powerless  to 
stop  their  passage  completely ;  as  could  be  demon- 
strated by  the  phosphorescence  and  other  effects 
appearing  in  the  further  half  of  the  tube  beyond  the 
diaphragm. 

The  position  of  the  anode  in  such  experiments  is  of 
small  consequence.  There  must  be  one  somewhere, 
and  the  easiest  plan  is  to  make  it  a  cylinder  through 
which  the  cathode  ray  bombardment  goes.  The 
bombarding  particles  fly  in  straight  lines  and  decline 
to  turn  a  corner,  taking  no  apparent  notice  of  the 
position  of  the  anode,  and  exhausting  themselves  by 
bombarding  the  side  of  the  glass  opposed  to  them ; 
as  can  be  well  shown  by  having  the  tube  bent  into 
a  V  shape,  for  instance. 


CH.  IV.] 


LENARD  RAYS 


29 


Lenard  extended  Hertz's  discovery  in  a  remarkable 
way  by  skilfully  constructing  a  tube  with  an  outer 
window  of  very  thin  aluminium,  so  arranged  as  to  be 
able  to  stand  the  atmospheric  pressure  outside.  He 
then  directed  the  cathode  ray  bombardment  on  to  this 
window  or  aluminium  film,  and  showed  that  the  rays 
can  penetrate  it  and  actually  come  outside  into  the 
ordinary  atmosphere,  where  they  are  called  Lenard 
rays,  in  honour  of  this  indefatigable  investigator,  a 
friend  and  disciple  of  Hertz.  (See  Fig.  1.) 


FlG.  1. — Lenard  tube  for  the  production  of  Lenard  rays,  which  were 
discovered  before  Rontgen  rays.  C  is  a  cathode  in  high  vacuum ;  the 
anode  A  is  a  metal  cylinder  behind  it ;  the  whole  is  screened  in  metal, 
and  the  cathode  rays  impinge  on  a  minute  hole  W  covered  with  ex- 
ceedingly thin  aluminium  foil,  through  which  it  would  seem  the  rays 
emerge  into  the  air,  radiating  in  all  directions  from  the  aluminium 
window  as  Lenard  rays  L,  where  they  are  rapidly  diffused  and  absorbed. 

These  Lenard  rays  make  the  air  phosphoresce  and 
produce  the  other  effects  which  cathode  rays  can 
produce,  but  they  are  stopped  within  a  moderate 
range  by  the  immense  obstruction  they  meet  with 
from  a  substance  of  the  density  of  ordinary  air. 
Substances  seem  to  stop  them  simply  in  proportion 
to  the  quantity  of  matter  which  they  encounter, 
without  regard  to  its  nature.  A  thick  layer  of  air 
would  be  about  as  opaque  as  a  layer  of  water  -^^  as 
thick  ;  and  even  if  the  body  put  in  their  way  is 


30     FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

an  opaque  solid  such  as  a  sheet  of  metal,  provided 
it  is  thin  enough  and  not  too  massive,  it  will  be 
penetrated  by  the  rays;  and  phosphorescent  effects 
will  be  produced  on  the  other  side  of  it.  The  rays 
can  also  affect  photographic  plates,  and  indeed  do 
nearly  all  the  things,  though  on  a  smaller  scale  and 
with  much  less  penetrating  power,  that  the  later 
discovered  Rontgen  rays  can  do. 

The  Lenard  rays  are  clearly  cathode  rays  emerged 
from  the  tube ;  and  it  was  the  custom,  at  the  date  of 
their  discovery,  to  think  of  them  as  flying  charged 
particles  of  matter ;  though  the  extraordinary  dis- 
tance they  could  travel  through  common  air,  a 
distance  comparable  to  an  inch,  was  a  manifest 
objection  to  such  a  hypothesis,  seeing  that  things  as 
big  as  atoms  of  matter  cannot  travel  so  much  as  xeVfy 
of  an  inch  in  ordinary  air  without  many  collisions. 

Lenard  accordingly  adhered  to  the  view,  advanced 
first  by  Goldstein,  that  they  were  not  material  but 
ethereal ;  and  although,  in  the  sense  he  probably 
intended,  this  is  not  a  tenable  view — for  they  are 
not  Qthereal  waves  or  anything  of  the  nature  of 
radiation — yet,  as  we  shall  see,  neither  are  they 
ordinary  material  particles,  any  more  than  the 
cathode  rays  are.  But  that  is  just  the  point  which 
we  are  now  considering,  and  we  will  return  to  them 
as  observed  by  Crookes  in  1879.* 

Nature  of  the  Cathode  Rays. 

We  have  seen  that  the  impact  of  the  cathode  rays, 
speaking  in  language  appropriate  to  the  assumption 

*  The  biographical  history  of  this  subject  is  set  out  largely  in  the 
contemporary  letters  that  passed  between  Crookes  and  Stokes  :  these 
have  been  supplied  by  Sir  William  Crookes,  and  will  shortly  be 
published  in  the  Scientific  Correspondence  of  Sir  George  Stokes. 


CH.  iv.]  BY   CATHODE   RAYS  31 

that  they  are  charged  particles,  will  result  partly  in 
heat,  or  vibration  of  the  impacted  molecules  ;  partly 
in  light  or  phosphorescence,  due  to  the  quiver  of 
electrically  charged  atoms  (or  rather  of  electrical 
charges  on  atoms)  as  in  the  ordinary  process  of 
radiation  ;  and  partly  in  X-rays  : — all  of  which  effects 
are  readily  seen  at  different  stages  of  vacuum  in 
a  Crookes'  tube.  The  momentum  of  the  flying 
particles  shot  off  from  the  cathode  can  also  be 
exhibited  by  putting  into  their  path  some  form  of 
vane  or  little  windmill,  which  will  then  be  driven 
mechanically,  as  the  vanes  of  a  radiometer  are 
driven  by  the  recoil  of  the  molecules  of  the  residual 
air  from  the  warmer  surface, — a  stress  being  thus  set 
up  between  the  vanes  and  their  glass  enclosure.  In 
the  electric  vacuum  tube  experiment,  the  stress  seems 
to  be  between  the  cathode,  or  gun,  and  a  layer  or 
stratum  of  the  residual  gas  not  very  far  from  it — for 
unless  the  exhaustion  is  very  high  the  gradient  of 
potential  close  to  the  cathode  is  very  steep, — so  the 
propelling  force  is  clearly  the  force  of  electrical 
repulsion,  the  particles  travelling  down  the  grade  of 
potential  just  as  they  travel  in  ordinary  electrolysis, 
and  then  proceeding  for  the  rest  of  the  journey  by 
their  acquired  momentum.  But  whereas  in  ordinary 
electrolysis  they  meet  with  constant  encounters  and 
therefore  progress  very  slowly,  in  a  high  vacuum 
they  can  fly  for  several  inches  in  a  free  path  without 
encountering  anything,  and  therefore  without  causing 
any  disturbance, — thus  giving  rise  to  no  appearance 
but  that  of  the  dark  space.  Phenomena  occur  only 
where  they  strike. 

This  was  the  view  of  the  nature  of  cathode  rays  taken 
by  the  whole  world  after  Crookes'  demonstration ; 
it  was  supposed  that  they  were  flying  atoms,  and  that 


32    FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

they  were  flying  with  ordinary  molecular  speed,  but 
with  a  long  free  path — much  longer  than  would  have 
been  expected  from  ordinary  gaseous  theory.  The 
extraordinary  length  of  free  path  was  somewhat 
difficult  to  reconcile  with  the  doctrine  that  they  were 
flying  atoms  obedient  to  the  ordinary  laws  of  gases ; 
'except  that,  being  subject  to  electrical  propulsion  all 
in  the  same  direction,  their  course  was  more  regular, 
and  their  encounters  therefore  fewer,  or  less  effective 
in  causing  deflection,  than  if  they  had  been  moving 
at  random.  This  same  feature  of  regularity  it  is 
which  confers  momentum  upon  them  ;  their  motion 
does  not  constitute  heat,  and  is  not  to  be  considered 
as  corresponding  to  temperature  ;  they  are  moving 
in  orderly  succession  like  an  army  or  like  a  wind, 
rather  than  with  the  irregular  unorganised  motion 
appropriate,  and  solely  appropriate,  to  the  terms 
"  heat "  and  "  temperature,"  and  to  the  ordinary 
kinetic  theory  of  gases.  Crookes  indeed  hazarded  the 
surmise — by  one  of  those  flashes  of  intuition  which 
are  sometimes  vouchsafed  to  a  discoverer  but  are  often 
ridiculed  by  representatives  of  orthodox  science  at  the 
time — that  he  had  obtained  matter  in  "a  fourth 
state  ; "  and  even  that  he  had  got  in  his  tube  some- 
thing equivalent  to  what  was  contemplated  in  the 
"  corpuscular "  theory  of  light.  There  is  some  cor- 
respondence with  fact  even  in  this  last  mode  of 
statement,  when  the  particles  are  moving  quickly 
enough,  for  a  nuclear  wave- front  or  ether-pulse  is 
then  travelling  with  them  ;  but  how  true  the  first 
was — that  the  matter  in  the  dark  space  was  in  a 
fourth  state,  neither  solid  nor  liquid  nor  gaseous — • 
how  true  that  was  we  shall  presently  see. 

Meanwhile  let  us  summarise  the  evidence  for  the 
view  that  the  cathode  rays  are  at  any  rate  charged 


CH.  iv.j  BY   CATHODE   RAYS  33 

particles  of  some  kind,  in  extremely  rapid  motion. 
That  they  are  in  motion  must  be  granted  from  the 
fact  of  their  bombardment — driving  mills,  heating 
platinum,  and  the  like ;  and  in  order  to  show  that 
they  are  charged,  the  most  direct  plan  is  to  catch 
them  in  a  hollow  vessel  connected  with  an  electro- 
scope, as  Perrin  did  ;  but  another  plan  is  to  show 
that  they  have  the  properties  of  an  electric  current. 
If  they  are  charged  while  in  motion  they  constitute  a 
current,  on  Maxwell's  theory,  and  therefore  should 
be  able  either  to  deflect  a  magnet  or  to  be  deflected 
by  it;  and  here  comes  one  of  the  most  simple  and 


Electroscope 


FIG.  2. — Simplest  form  of  Perrin's  apparatus  for  proving  that  cathode 
rays  carry  a  negative  charge.  The  rays  from  a  pass  through  an  earthed 
screen  b  into  a  hollow  or  Faraday  vessel  c. 

important  experiments  in  physics  at  the  present 
time.  A  definite  form  of  some  old  experiments 
foreshadowed  by  Pliicker  (1862),  and  developed  by 
Hittorf,  Goldstein,  and  many  other  vacuum  tube 
observers,  was  arranged  by  Crookes  in  1879,  when 
he  made  the  track  of  the  rays  visibly  luminous  by 
passing  a  pencil  of  them  through  a  slit  and  letting 
them  graze  along  the  surface  of  a  film  of  mica  covered 
with  phosphorescent  powder,  and  when  he  then 
brought  near  them  a  common  horseshoe  magnet. 
When  this  is  done  the  track  of  the  rays  is  at  once 
seen  to  be  curved ;  showing  that  it  is  not  a  beam 
of  light  we  are  looking  at,  but  a  torrent  of  charged 
particles ;  since  they  behave  like  an  electric  current 
and  are  deflected  by  a  magnet.  It  is  ultimately  the 
very  same  phenomenon  as  can  be  observed  with 
difficulty,  owing  to  its  smallness,  when  a  current 


L.E. 


34    FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

flows  through  metals, — an  effect  discovered  by  E.  H. 
Hall  in  America,  and  known  as  the  Hall  effect. 

The  fact  that  the  particles  are  thrown  off  the 
cathode,  being  evidently  vigorously  repelled  by  it,  is 
sufficient  to  suggest  that  they  must  be  negatively 
charged ;  the  direction  of  the  curvature  caused  by  a 
magnetic  field  enables  us  to  verify  at  once  that  the 
flying  particles  are  negatively  charged,  and  no 
comparable  rush  of  positive  particles  in  the  opposite 
direction,  or  in  any  direction,  has  been  observed. 
The  speed  of  transmission  of  the  positive  current  is 
very  great,  and  it  must  be  conveyed  by  a  multitude 
of  positive  particles,  but  individually  their  motion 
is  comparatively  slow  (see  however  chap.  vi.).  In 
that  respect  evidently  the  magnetic  curvature  of 
cathode  rays  in  gases  differs  from  the  magnetic 
curvature  of  a  current  in  metals  ;  viz.,  that  whereas 
in  metals  the  major  action  is  sometimes  upon  the 
negative  and  sometimes  upon  the  positive  stream, 
according  to  the  nature  of  the  metal — the  difference, 
which  is  all  that  is  observable,  being  always  small, — 
in  the  cathode  stream  it  is  the  negative  alone  -that 
is  acted  upon,  and  so  the  action  is  always  large. 

It  seems,  therefore,  that  for  some  reason  or  other 
the  negatively  charged  bodies  in  a  vacuum  tube  are 
much  more  mobile  than  the  positive,  and  that  the 
mobility  of  the  negatively  charged  bodies  is  extreme. 
One  striking  method  by  which  their  mobility  was 
displayed  consisted  in  the  fundamental  observation 
by  Professor  Schuster*  that  all  parts  of  gas  in  a 
closed  vessel  became  conducting  when  an  electric 
discharge  had  taken  place  in  one  corner  of  it;  so 
that  even  though  the  vessel  consisted  of  different 
compartments,  one  compartment  was  made  feebly 

*  Bakerian  lecture  1890,  Proc.  Roy.  Soc.,  vol.  47,  p.  526. 


CH.  iv.]  BY   CATHODE   RAYS  35 

conducting  by  a  discharge  in  the  other,  provided 
that  the  two  had  any  kind  of  gaseous  communi- 
cation ;  a  fact  which  looked  as  if  some  extremely 
mobile  particles,  probably  the  negatively  charged 
particles  of  cathode  rays,  could  wander  about  to 
a  considerable  distance  in  a  very  short  time  and 
take  their  share  in  the  conveyance  of  an  electric 
current.  The  conductivity  of  gases  appeared  to  be, 
indeed,  entirely  due  to  these  loose  or  dissociated  or 
detached  charged  particles,  or  ions,  and  where  they 
were  absent  the  gas  did  not  conduct  at  all ;  it 
could  be  broken  down,  being  a  weak  dielectric,  by  a 
sufficiently  strong  force,  but  it  would  not  leak ; 
whereas,  when  these  loose  charged  particles  were 
about,  it  leaked  readily,  becoming  to  all  intents  and 
purposes  an  electrolyte  amenable  to  the  feeblest 
electric  influence.  The  production  of  this  electrolytic 
condition  is  called  "  ionisation."  The  act  of  breaking 
down  the  air  by  an  electric  discharge  was  thus 
found  to  render  the  surrounding  air  for  a  time 
electrolytic.  Its  electrolytic  quality,  however,  did 
not  last  long.  The  mobility  of  the  particles  which 
enabled  them  to  travel  to  a  considerable  distance 
also  enabled  them  to  get  rid  of  themselves  by 
clinging  to  the  sides  of  the  vessel,  or  perhaps  by 
re-uniting  with  some  opposite  charges,  which  after 
some  time  in  their  rapid  journeys  they  must 
casually  encounter.  Prof.  Townsend,*  however,  found 
that  the  conducting  power  lasted  unexpectedly  long 
if  no  dust  was  present :  the  dust  particles  apparently 
acting  as  intermediate  receivers  and  storers  of 
charge,  promoting  interchanges,  which  did  not  very 

*  J.  S.  Townsend  of  Trinity  College,  Dublin,  then  working  in  the 
Cavendish  Laboratory,  Cambridge,  now  Waynflete  Professor  of  Physics 
in  the  University  of  Oxford. 


36    FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

readily  occur  through  direct  encounters.  And  the 
time  that  thus  elapsed  before  the  whole  of  the 
conductivity  disappeared  from  dust-free  air  suggested 
that  the  moving  particles  must  be  very  small,  so  that 
intimate  collisions  were  comparatively  infrequent. 

The  mobility  or  diffusiveness  of  the  molecules 
of  a  gas  depends  on  their  mean  free  path,  and 
that  depends  on  their  atomic  size ;  the  smaller 
they  are,  the  more  readily  can  they  escape 
collision.  Hence  it  is  that  collisions  are  so  rare  in 
astronomy  :  the  bodies  are  small  compared  with  the 
spaces  between  them.  The  behaviour  of  charged  par- 
ticles seemed  to  indicate  that  they  must  in  some 
cases  be  something  smaller  than  atoms  :  it  seemed 
hardly  likely  that  material  atoms  could  behave  in 
the  way  they  did.  It  was  recollected  that  it  had 
occurred  to  some  philosophers,  among  them  Dr. 
Johnstone  Stoney,  that  electric  charges  really  existed 
on  an  atom  in  concentrated  form,  not  diffused  all 
over  its  surface  but  concentrated  at  one  or  more 
points, — perhaps  acting  as  satellites  to  the  main 
bulk  of  the  atom ;  so  on  that  view  it  was  j  ust 
possible  that  these  flying  particles  might  be  not 
charged  atoms  at  all,  but  charges  without  the  atoms, 
the  concentrated  charges  detached — knocked  off  as 
it  were  in  the  violence  of  the  discharge,  and  after- 
wards going  about  free.  Such  particles  would 
naturally  travel  at  an  immense  pace,  because  they 
would  still  be  exposed  to  the  full  electric  force  that 
they  had  experienced  before,  and  yet  would  have 
shaken  off  the  encumbrance  of  the  material  atom 
with  which  they  had  been  associated.  It  is  true  that 
no  such  disembodied  charges,  or  electric  ghosts,  had 
ever  been  observed.  All  the  experiments  that  had 
been  made  in  electrostatics  had  been  made  on  charged 


CH.  iv.]  BY   CATHODE   RAYS  37 

matter, — the  surface  or  boundary  of  the  matter  acting 
as  the  locality  for  an  electric  charge  ;  and  no  other 
locality  for  a  charge  was  known.  The  facts  of 
electrolysis  had  suggested  or  proved  that  the  atoms 
themselves  could  carry  charges,  and  hence  that  if  a 
liquid  were  electrified,  it  must  be  due  to  some  of  the 
atomic  charges  of  one  sign,  appearing  in  overbalancing 
proportion  at  the  surface ;  though  perhaps  still  in 
association  with  their  respective  atoms. 

Yet  at  the  same  time  the  occurrences  at  an 
electrode,  where  an  ion  plainly  gave  up  its  charge 
and  escaped  without  it,  indicated  the  possibility  that 
perhaps  the  electric  charge  could  exist  alone ;  at  any 
rate  that  it  could  be  handed  from  one  atom  to 
another,  and  thus  might  conceivably  exist  alone  for 
an  instant.  During  this  momentary  isolation  some 
charges  might,  in  the  freedom  of  a  rarefied  gas 
discharge,  possibly  escape,  and  wander  about  free. 

To  such  hypothetical  isolated  charges,  the  unit 
charge  or  charge  of  a  monad  atom,  the  name 
"electron"  had  been  given  ;  and  when  I  speak  of  an 
"electron"  I  mean  to  signify  the,  at  first  purely 
hypothetical,  isolated  electric  charge.  Whereas  by 
the  term  "ion"  I  always  signify  the  atom  and  its  j 
charge  together.  The  ions  consist  of  Faraday's  anions 
and  cations.  Lord  Kelvin  prefers  the  term  electrion 
to  electron. 

Now  if  the  flying  particles  which  constitute  the 
cathode  rays  were  electrons  rather  than  ions, — if  they 
were  detached  charges,  leaving  their  atoms  behind 
them  (necessarily  leaving  those  atoms  positively 
charged), — their  extreme  mobility  and  diffusiveness 
and  high  speed  would  be  perfectly  natural ;  and 
although  they  would  not  be  '  matter '  in  the  ordinary 
sense,  yet  no  difficulty  need  be  felt  at  their  possessing 


38    FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

some  of  the  properties  of  matter,  at  any  rate  such 
properties  as  appertain  to  matter  by  reason  of  its 
having  inertia  ;  because,  as  we  have  seen,  an  electric 
charge  itself  does  possess  a  certain  kind  of  imitation 
inertia.  Hence  these  electrons  in  movement  would 
possess  momentum,  and  might  therefore  propel  wind- 
mills (though  the  actual  motion  of  the  windmills  in 
Crookes  tubes  seems  more  likely  due  to  charge  and 
electric  repulsion  than  to  simple  momentum) ;  they 
would  possess  kinetic  energy,  and  therefore  might 
heat  a  piece  of  platinum  ;  and  if  suddenly  stopped  by 
a  massive  target  when  travelling  at  a  high  speed  they 
might  readily  give  rise  to  phosphorescent  appearances, 
and  even  to  the  sudden  pulse  of  radiation  known  as 
X-rays.  Indeed  the  existence  of  this  last  property  is 
capable  of  clear  deduction  on  electrical  principles 
if  the  matter  is  further  gone  into.  (See  chap,  ix.) 

The  continued  passage  of  a  current  through  a 
vacuum  tube  cannot  be  explained  by  a  torrent  of 
electrons  alone, — there  must  be  some  mechanism 
for  continually  producing  them  fresh  and  fresh, 
near  or  at  the  cathode,  else  they  would  almost  in- 
stantaneously get  exhausted.  The  most  probable 
view  of  the  matter  is  that  suggested  by  J.  J.  Thomson : 
that  the  current  is  conveyed  chiefly  by  positive  ions, 
which  are  produced  in  the  residual  gas  by  ionisation 
due  to  the  first  discharge  of  cathode  rays.  These 
positive  ions  then  pass  along  comparatively  slowly 
toward  the  cathode,  creep  in  towards  it,  as  best  they 
can,  in  face  of  the  bombardment ;  and  then  at  the 
last — experiencing  the  violent  gradient  of  potential 
in  its  immediate  neighbourhood — rush  up  against  it 
and  by  their  shock  produce  a  fresh  supply  of  electrons. 
The  glow  over  the  cathode  is  supposed  to  mark  the 
region  of  this  ionisation.  The  negative  particles,  thus 


CH.  iv.]  BY   CATHODE    RAYS  39 

set  free,  then  fly  off  as  cathode  rays,  setting  up  fresh 
ionisation,  and  producing  a  copious  further  supply  of 
positive  ions ; — on  the  existence  of  which  the  possi- 
bility of  the  cathode  rays  themselves  depend.  The 
positive  and"  the  negative  particles  on  this  view  are 
mutually  dependent :  each  is  the  cause  of  each ;  and 
when  either  fails  to  be  formed  in  a  vacuum  tube  it  is 
impossible  for  it  to  conduct,  even  when  its  terminals 
are  highly  electrified ;  for  if  the  supply  of  either  sign 
of  ion  is  stopped,  that  of  the  other  at  once  fails. 
This  accounts  for  the  action  of '  electric  valves,'  wherein 
the  positive  ions  are  prevented  from  getting  at  the 
cathode  in  one  direction,  by  reason  of  a  special 
arrangement  for  concentrating  an  electron  bombard- 
ment along  the  direct  route,  without  any  back  door 
or  side  entrance  for  the  positive  ions.  The  provision 
of  such  a  back  door,  even  though  the  route  thereto 
be  long,  immensely  eases  the  conveyance  of  current : 
as  was  strikingly  shown  by  Hittorf. 

It  has  been  observed  that  any  obstacle  introduced 
into  the  dark  space  near  the  cathode,  if  it  is  able  to 
check  locally  the  access  of  positive  ions,  will  throw  a 
shadow  both  fore  and  aft, — 1one  towards  the  cathode, 
and  likewise  one  down  the  cathode  rays, — because 
the  generation  of  fresh  electrons  is  thereby  locally 
prevented.*  At  this  stage  we  may  conveniently 
summarise  the  position  thus  : — 

The  magnitudes  which  need  experimental  deter- 
mination in  connexion  with  cathode  rays,  in  order 
to  settle  the  question  and  determine  their  real 
nature,  are  the  speed,  the  electric  charge,  and  if 
possible  the  mass,  bf  the  flying  particles. 

Everything   suggests   that    they    are   flying   with 

*  Schuster,  Proc.  Roy.  Soc.,  xlvii.,  p.  557, 1890 ;  Wehnelt,  Wied.  Ann. 
Ixvii.,  p.  421,  1899. 


40    FORESHADOWING  OF  THE  ELECTRON  [CH.  iv. 

prodigious  speed,  but  it  is  desirable  to  make  a 
measurement  of  that  speed. 

The  force  of  propulsion  exerted  on  them  indicates 
that  they  are  highly  charged ;  and  their  penetrating 
power  suggests  that  they  are  excessively  small,  so 
that  to  them  ordinary  solids,  such  as  metal  sheets, 
appear  porous ;  but  an  experimental  method  is 
necessary  to  determine  what  may  be  called  their 
electrochemical  equivalent, — -that  is  to  say  the  ratio 
of  their  mass  or  inertia  to  their  electric  charge, — 
even  if  it  be  not  possible  to  determine  the  mass 
and  the  charge  separately. 

In  electrolysis  the  electrochemical  equivalent, 
or  the  ratio  m/e,  depends  on  the  nature  of  the 
substance;  and  for  hydrogen  is  of  the  order  10~4 
in  electromagnetic  units,  as  stated  in  Chapter  III. 
It  is  a  matter  of  great  importance  to  determine 
the  value  of  the  same  ratio  for  the  cathode  rays, 
and  to  ascertain  whether  it  varies  with  the  substance 
contained  in  the  vacuum  tube,  or  whether  it  is  the 
same  for  all  substances — being  characteristic  of 
a  single  variety  of  the  flying  particle  and  of  nothing 
else. 


CHAPTER  V. 

DETERMINATION  OF  SPEED  AND  ELECTROCHEMICAL 
EQUIVALENT  OF  CATHODE  RAYS. 

IF  the  cathode  rays  consist  of  flying  electrified 
particles  they  will  be  deflected,  or  their  paths  curved, 
by  the  proximity  of  a  magnet :  and  this  is  a  well 
known  and  prominent  fact  concerning  them.  With 
some  care  the  amount  of  deflexion,  caused  by  a 
magnetic  field  of  known  strength,  may  be  measured. 

The  curvature  of  path  produced  in  cathode  rays 
by  a  transverse  magnetic   field,   or,  the  amount   of 
spirality  produced  by  a  longitudinal  magnetic  field, 
constitutes  an  evident  mode  of  attacking  the  problem 
of  estimating  their  velocity. 

If  the  velocity  is  constant  and  the  magnetic  field 
uniform,  the  curve  into  which  the  stream  is  bent 
round  the  lines  of  force  will  manifestly  be  a 
circle ;  and  its  course  can  be  readily  traced  either 
directly,  after  Crookes'  manner,  by  letting  it  graze 
a  phosphorescent  substance,  or  indirectly  by  inference 
from  the  position  of  a  linear  target  placed  so  as  to 
catch  the  deflected,  rays.  If  the  direction  of  velocity 
is  inclined  to  the  direction  of  the  field,  the  course  of 
a  particle  will  be  compounded  of  a  circular  motion 
round  a  line  of  force,  and  an  unchanged  rectilinear 
motion  along  it :  that  is  to  say,  it  will  be  a  spiral,. 


42  DETERMINATION   OF   SPEED  [CH.  v. 

more  or  less  elongated,  threading  itself  along  the 
negative  field  :  the  direction  of  twist  depending  on 
the  sense  of  the  field. 

There  is  no  difficulty  in  determining  the  radius 
of  curvature  r ;  and  the  theory  of  normal  deflexion 
is  the  simplest  possible, — nothing  more  than  stating 
that  the  magnetic  force  H,  acting  on  the  current 
element  eu,  is  the  necessary  deflecting  or  centripetal 
force,  my?/r,  required  to  overcome  the  mechanical 
inertia  of  the  particles  ;  i.e., 

mu2 

-  =  jmeun., 

whence  —u=  uKr ; 
e 

or  the  ratio  e/m  is  to  the  velocity  of  the  particles  as 
the  curvature  of  their  path  is  to  the  intensity  of 
magnetic  field  which  curves  it.  Prof.  Schuster  of 
Manchester  was  among  the  first  to  make  measure- 
ments of  this  kind. 

The  two  factors  on  the  right  of  this  equation  are 
directly  measurable  (/u.  being  conventionally  ignored 
as  usual,  or — a  better  mode  of  expression — united 
with  H  as  induction-density) ;  but  the  two  factors 
on  the  left  are  both  unknown,  hence  neither  can  be 
determined  by  this  means  alone,-—an  assumption 
must  be  made  about  one  or  other  of  them,  or  else 
another  independent  kind  of  experiment  must  be 
made. 

Assume,  as  many  experimenters  did,  that  u  is  a 
velocity  appropriate  to  atoms  flying  in  a  gas  of 
ordinary  temperature,  then  the  value  of  e/m  comes 
out  not  so  very  far  discrepant  from  the  usual  ionic 
value,  measured  in  liquid  electrolysis,  viz.,  104  c.g.s. 
Or,  conversely,  assume  the  usual  ionic  or  electrolytic 


CH.  V.] 


OF   CATHODE   RAYS 


43 


value  for  this  ratio,  and  the  cathode  ray  velocity 
comes  out  something  quite  appropriate  to  atoms 
of  matter. 

This,  however,  is  a  trap.  These  accidental  coin- 
cidences may  retard  progress  in  a  most  serious 
manner,  for  they  satisfy  the  mind  and  deter  people 
from  investigation.  It  is  almost  impossible  to  be 


FIG.  3.— Modified  Perrin  apparatus  adopted  by  J.  J.  Thomson  for, 
measuring  the  charge,  and  at  the  same  time  the  magnetic  deflexion,  and 
sometimes  the  thermal  energy  also,  of  cathode  rays.  The  rays  from  the 
cathode,  after  passing  through  a  perforated  anode  and  proceeding  in  a 
straight  line,  can  be  deflected  by  a  magnet  a  measured  amount,  so  as 
just  to  enter  a  hole  in  an  earthed  guard-screen  D,  and  then  a  hollow 
cavity  provided  with  an  electrode  E,  whereby  the  aggregate  charge 
conveyed  by  them  is  measured. 

completely  on  guard  against  them,  and  they  are 
usually  accepted  until  a  more  thorough  qualitative 
acquaintance  with  the  subject  leads  to  an  instinctive 
feeling  that  something  is  wrong  somewhere. 

So  it  was  in  this  case  :  the  long  free  path  and  the 
penetrating  power  of  the  cathode  rays  kept  insisting 
that  the  particles  were  not  really  atoms  of  ordinary 
matter, — a  truth  which  both  Lenard  and  Crookes 
had  instinctively  grasped,  in  spite  of  much  criticism 


44  DETERMINATION   OF   SPEED  [CH.  v, 

and  valid  arguments  the  other  way;  so  in  1897 
J.  J.  Thomson  made  a  much  more  serious  attack  on 
the  whole  position. 

He  arranged  that  the  magnet  should  deflect  the 
rays  into  an  insulated  hollow  vessel,  connected  with 
an  electrometer  and  a  known  capacity,  so  that  the 
aggregate  charge  of  the  cathode  ray  particles  collected 
in  a  given  time  could  be  measured  by  the  rise  of 
potential  observed  (cf.  Fig.  3).  He  also  arranged 
that  inside  the  hollow  vessel  they  should  fall  upon 
a  thermal  junction  of  known  heat  capacity,  con- 
nected by  very  thin  wires  to  a  galvanometer  (acting 
therefore  as  a  calorimeter),  so  as  to  measure  their 
aggregate  energy. 

Thus  he  could  make  the  following  simultaneous 
determinations  : 


m 

—u 

In  these  three  equations  there  are  four  unknown 
quantities  ;  but  one  pair  can  be  treated  as  a  ratio, 
and  another,  N,  can  be  eliminated,  and  thus  we  get  — 

2W 


When  these  brilliant  measurements  were  actually 
made  in  the  laboratory,  the  atomic  nature  of  cathode 
rays  was,  if  not  actually  disproved,  at  all  events 
rendered  highly  improbable  ;  for  their  speed  was 
found  to  be  of  the  order  ten  thousand  miles  per 
second,  or  even  as  high  as  ^  that  of  light  in  a 


UNIVERSITY 

<JH.  v.]  B?8OPs^THbDE   RAYS  45 

favourable  case,  being  always  of  the  order  109  c.g.s., 
while  the  electrochemical  equivalent  was  of  the  order 
10~7  c.g.s.,  or  about  T^Vo  that  °f  hydrogen. 

Changing  the  kind  of  residual  gas  in  the  tube,  and 
changing  the  electrodes,  made  no  difference  to  this 
last  value.  The  cathode  rays  were  evidently  inde- 
pendent of  the  nature  of  the  matter  present  :  an 
exceedingly  momentous  fact.  If  they  were  matter  at 
all,  they  appeared  to  be  matter  of  some  fundamental 
kind,  independent  of  the  distinctions  of  ordinary 
•chemistry.  Their  velocity,  however,  depended  on 
the  potential  difference  between  the  electrodes,  in  a 
way  that  suggested  that  they  were  really  projectiles 
urged  by  the  potential  gradient  acting  along  a  given 
length  of  path.  They  were  propelled  by  the  cathode 
through  an  aperture  in  the  anode,  and  the  measure- 
ment of  their  speed  was  made  in  the  tube  beyond  the 
anode,  where  they  are  travelling  by  their  own 
momentum.  The  distance  apart  of  anode  and 
•cathode  did  not,  and  on  .the  projectile  hypothesis 
ought  not  to,  affect  this  speed ;  for  though  the 
potential  gradient  is  steeper  when  anode  and  cathode 
are  put  close  together,  the  length  of  path  during 
which  the  particles  are  subject  to  it  is  diminished 
by  a  compensating  amount, — -so  that  the  velocity  is 
theoretically  independent  of  the  distance  between  the 
electrodes,  as  long  as  the  total  difference  of  potential 
is  maintained ;  it  is  the  absolute  difference  of 
potential  that  determines  the  speed.  (This  is  a 
familiar  result  of  the  conservation  of  energy,  and  is 
illustrated  by  ordinary  falling  bodies.)  But  mani- 
festly if  the  electrodes  are  too  close  together  it  may 
be  difficult  to  secure  a  high  difference  of  potential 
between  anode  and  cathode,  since  they  may  spark 
into  each  other  outside  the  tube;  and  if  there  is 


46  DETERMINATION   OF   SPEED  [CH.  v. 

much  residual  gas  in  the  tube  it  will  likewise  be 
difficult  to  maintain  a  high  potential  difference ; 
because  that  residual  gas,  under  the  influence  of 
the  cathode  rays,  will  conduct.  Consequently  the 
best  speeds  are  obtained  at  high  vacuum  ;  and  if 
the  density  of  the  residual  gas  inside  the  tube  is 
constant,  the  speed  will  be  constant.  The  nature  of 
the  electrodes  makes  no  difference,  unless  they  give 
off  gas  or  otherwise  make  it  difficult  to  maintain  the 
required  potential  difference. 

Although  the  speed  of  the  particles  in  cathode 
rays  was  thus  found  excessively  great,  their  energy 
was  only  moderate,  and  their  aggregate  mass  was 
therefore  proved  to  be  excessively  minute ;  their 
aggregate  electric  charge,  however,  was  considerable. 
They  were  able  to  raise  an  electrical  capacity  of 
•15  microfarad  several  volts,  sometimes  as  much 
as  5  volts,  in  the  course  of  a  second ;  and  in  the 
same  time  they  might  be  able  to  raise  a  calorimeter, 
whose  heat  capacity  was  about  4  milligrammes  of 
water,  by  2°  C.  Nevertheless  their  mass  was  so 
small  that  it  would  have  taken  one  hundred  years 
to  collect  a  weighable  amount :  and  then  only 
about  one-thirtieth  part  of  a  milligramme.  They 
travelled  with  a  velocity  a  hundred  thousand  times 
greater  than  the  speed  of  rifle  bullets,  and  re- 
presented the  greatest  velocity  up  to  that  time 
observed  in  matter, — if  matter  they  were.  And 
the  electrochemical  equivalent,  instead  of  coming 
out  in  accordance  with  that  observed  in  liquids, 
came  out  some  thousand  times  smaller ;  that  is  to 
say,  the  charge  associated  with  each  particle  of  the 
cathode  rays  seemed  a  thousand  times  greater,  in 
proportion  to  the  mass,  than  the  charge  associated 
with  an  electrolytic  ion,  even  of  hydrogen. 


CH.  v.]  OF   CATHODE    RAYS  4T 

If  the  flying  particles  were  really  atoms,  there  was 
no  escape  from  the  certainty  that  they  were 
extraordinarily  highly  charged  atoms ;  but  if,  as 
seemed  more  likely  to  the  instinct  of  most  of  those 
who  worked  at  the  subject,  the  charge  on  the  flying 
particles  was  the  same  as  the  charge  possessed  by  an 
atom  in  electrolysis,  then,  assuming  that  the  experi- 
ments were  correct  and  correctly  interpreted,  there 
would  be  no  escape  from  the  conclusion  that  the 
mass  associated  with  the  ionic  charge  in  cathode  rays 
must  be  a  thousand  times  smaller  than  the  mass  of  a 
hydrogen  atom  ;  in  which  case  the  cathode  projectiles 
might  conceivably  be  the  detached  and  hitherto 
hypothetical  individual  electrons  or  atoms  of  elec- 
tricity themselves.  It  would  be  extremely  rash, 
however,  to  jump  to  such  a  far-reaching  conclusion 
on  such  comparatively  scant  evidence.  The  evidence 
must  be  confirmed  by  other  departments  of  Physics 
or  by  other  determinations  based  on  a  different 
method ;  and  they  must  be  further  scrutinised  in 
the  light  of  other  and  totally  different  phenomena. 
We  will  first  describe  a  determination  made  by 
another  method,  and  then  some  striking  confirmatory 
measurements  applied  to  phenomena  which  belong 
apparently  to  other  departments  of  Physics. 

Further  Measurements  of  Cathode  Ray   Velocity 

and  m/e  Ratio  by  Aid  of  Electrostatic 

Deflection. 

Another  and  perhaps  simpler  method  of  deter- 
mining the  two  quantities  u  and  m/e  was  also 
employed  by  J.  J.  Thomson, — was  indeed  the  first 
used  by  him,  though  it  was  not  safe  to  draw  a  full 
deduction  from  it  alone — viz.,  by  deflecting  the 
same  rays  both  electrostatically  and  magnetically ; 


48  DETERMINATION   OF   SPEED  [CH.  v. 

by  introducing  a  pair  of  supplementary  electrodes,  one 
above  and  one  below  the  course  of  the  rays  inside 
a  vacuum  tube,  and  connecting  them  to  the  poles 
of  a  low-potential  battery, — a  few  storage  cells  for 
instance, — thus  obtaining  a  vertical  electrostatic  field 
at  right  angles  to  the  cathode  rays.  At  the  same 
time  a  magnetic  field,  produced  by  lateral  magnet 
poles  or  by  the  lines  of  force  due  to  an  electric 
current  in  a  circular  ring,  could  be  arranged  at  right 
angles  to  both  the  other  directions ;  and  thus  the 
electrostatic  deflection  could  be  compared  with,  or 
could  be  used  to  neutralise,  the  magnetic  deflection. 
The  electric  field,  being  .fixed  in  direction  and  urging 
the  particles  along — not  across — the  lines  of  force, 
will  act  differently  to  a  magnetic  field  and  will  cause 
the  particles  to  move  in  a  parabola — the  shape  which 
the  earth  gives  to  a  horizontal  jet  of  water. 

Fig.  4  shows  J.  J.  Thomson's  apparatus  for 
measuring  the  deflexion  of  cathode  rays  caused  by 
an  electric  field  at  right  angles  to  them.*  The  rays 
starting  from  the  cathode  C  traverse  a  couple  of 
earth-connected  slits  AB  and  after  having  passed 
between  the  electrified  plates  D  and  E,  impinge  on 
the  glass  at  P,  producing  a  small  but  vivid  phosphor- 
escent spot.  The  position  of  this  spot  is  read  on  a 
scale  pasted  on  the  outside  of  the  glass.  In  ordinary 
vacua  screening  prevents  any  effect  from  being  ob- 
served, by  reason  of  conducting  power  in  the  residual 
air,  developed  by  ionisation  caused  by  the  impact  of 
the  flying  particles ;  consequently  Hertz  failed  to 
obtain  the  deflexion  which  was  otherwise  to  be 
expected;  but  by  pushing  the  vacuum  to  a  higher 
stage  J.  J.  Thomson  overcame  this  difficulty, 
measured  the  deflexion  PP',  and  employed  this 

*  Phil.  Mag.,  vol.  44,  p.  293  (1897). 


CH.  V.] 


OF   CATHODE   RAYS 


49 


method  to  assist  in  measuring  the  velocity  and 
other  constants  of  the  cathode  ray  particles. 

By  noting  the  shift  of  the  luminous  spot,  the 
deflexion  of  the  narrow  beam  which  has  travelled 
through  a  length  I  of  either  an  electric  field  of 
strength  E,  or  a  magnetic  field  of  strength  H,  can 
be  directly  measured. 

If  u  is  the  original  velocity  of  the  ray  particles, 
travelling  at  right  angles  to  one  of  the  deflecting 
fields,  either  of  them  will  have  a  time  l/u  in  which 


FIG.    4. — Thomson's    apparatus    for    observing    and    measuring    the 
electrostatic  deflexion  of  cathode  rajs. 

to  act ;  and  in  that  time  an  extra  velocity  w 
will  be  caused  in  the  direction  of  the  electric  force,  or 
perpendicular  to  the  direction  of  the  magnetic  force, 
such  that  the  rate  of  change  of  momentum  of  each  par- 
ticle will  be  jj-  =  Ee  in  the  one  case,  and  =  juXieu  in 

ijU 

the  other  ;  wherefore  the  deflexion,  if  small,  will  be — 

/»     w     e    EZ  .     ,, 

0  =  —  = s-  in  the  one  case, 

u     m    u 


and  Of  =  —  - —  in  the  other. 


m    u 


L.E. 


50  DETERMINATION   OF   SPEED  [CH.  v 

u=       . 
//xi    c; 


Hence 


m 


0 


This  method,  when  applicable,  appears  to  give  fairly 
accurate  results  ;  and  the  outcome  of  the  measure- 
ments is,  that  when  H  or  C02  or  Air  is  in  the  tube, 

u  —  2  or  3  x  1  09  centimetres  per  second, 
and  —  =  from  1*1  to  1*5  x  10~7  c.g.s.  units. 

e 

The  chief  difficulty  about  this  mode  of  experimenting 
is  caused  by  the  fact  that  the  ionisation  of  residual 
air  in  the  tube  causes  it  to  become  a  temporary 
conductor,  thereby  screening  the  flying  particles  from 
most  of  the  electrical  influence.  There  is  no 
guarantee  that  they  feel  the  full  effect  of  the  electric 
field  which  is  ostensibly  being  applied  ;  indeed  it 
is  not  easy  to  let  them  feel  any  of  the  effect.  It 
used  to  be  thought  that  they  were  not  susceptible 
to  electrostatic  action  at  all,  and  this  was  often 
adduced  as  an  obvious  argument  against  their 
being  electrically  charged  particles  ;  but  fortunately 
Thomson  soon  surmised  the  cause  of  this  masking 
of  the  simple  effect  to  be  expected,  and  succeeded 
in  showing  that  with  high  enough  vacua,  and  other 

Erecautions,  the  screening  ionised  atmosphere  could 
e  removed,  and  the  electrostatic  deflexion  metrically 
observed. 

Measuring   Velocity  by  combined  Electric  and 
Magnetic  Deflexion  Method. 

Now  that  it  is  possible  to  apply  the  electrostatic 
deflexion  method  to  curve  the  path  of  flying  charged 


CH.  v.]  OF   CATHODE   RAYS  51 

particles,  the  simplicity  of  combining  this  with 
magnetic  deflexion,  and  thereby  making  a  couple 
of  measurements  simultaneously,  is  so  great  that 
it  has  practically  replaced  the  more  elaborate  plan 
first  described,  —  namely  the  method  by  observ- 
ing the  aggregate  charge,  the  aggregate  energy, 
and  the  magnetic  deflexion  only,  —  a  method  which, 
first  as  an  original  determination,  and  now  as  a 
check,  has  been  of  high  value. 

The  simple  plan  has  now  been  applied  to  rays  of 
various  kinds,  and  it  may  be  well  to  give  its 
simplest  possible  form,  before  proceeding  to  a  more 
complicated  case.  It  consists,  (1)  in  observing  the 
radius  of  curvature  r  caused  by  a  magnetic  field 
of  measured  strength  H  ;  (2)  in  finding  the  electric 
field  E  which,  applied  at  right  angles  to  the  magnetic 
field,  just  succeeds  in  neutralising  all  deflexion  ;  then 
a  centrifugal  force  equation 


e        u 


applies  to  experiment  No.   1  ;  and  a  balanced  force 
equation      ...  E 


E 
or   u= 


applies  to  experiment  No.  2. 

This  second  experiment  gives  .  the  velocity,  by 
itself;  and  the  first  in  combination  with  it  gives  the 
electro-chemical  equivalent. 

So  the  determination  of  'velocity  for  the  case  of 
particles  'flying  all  with  one  speed  is  remarkably 
easy  :  it  comes  out,  in  centimetres  per  second,  as 


52  DETERMINATION   OF   SPEED          [CH.  v. 

4 

simply  the  ratio  of  the  strengths  of  the  electric  and 
magnetic  fields  (both  expressed  in  EM  units,  that 
is  with  M=!)  which  can  produce  equal  effects 
upon  the  flying  particles,  and  which  therefore,  if 
applied  in  opposition,  are  just  able  to  neutralise 
each  other. 

Note  on  Dimensions. 

To  verify  that  the  "  dimensions  "  of  the  last  given 
equation  are  correct,  we  can  remember  that  an  electric 

F  TT 

field  is  of  dimension  —  =  -= — .,  _.,  where  F  is  force, 

e     I  v  (/of ) 

and   I   is  length ;    and  that  a  magnetic   field  is  of 

TT  T? 

dimension   —  =  ^ — .,  _x  ;   so  the  ratio  of  an  electric 

m     TjfjdF) 

to  a  magnetic  field  is  */(V/K)  ;  wherefore  -th  of  that 

1  M 

ratio  is  —r/ — r  =  a  velocity. 

vV) 

For  practical  purposes  it  may  be  convenient  to 
write  the  equation  as  a  proportion  sum  thus  : 

the  velocity  of  the  particle 
the  velocity  of  light 

the  electric  field  in  electrostatic  units 
the  magnetic  field  in  electromagnetic  units  ' 

it  being  understood  that  the  fields  are  adjusted  till 
their  effects  are  equal. 

Effect  on  Lenard  Rays. 

Another  mode  of  demonstration  was  employed  by 
Professor  Lenard,  and  served  to  identify  his  rays  with 
escaped  cathode  rays. 


CH.  v.]  OF   LENARD   RAYS  53 

Fig.  5  shows  Lenard's  apparatus  for  showing  that 
his  rays  are  accelerated  or  retarded  by  passing  along 
the  lines  in  an  electric  field  between  two  disks  ab. 
Here  C  is  the  cathode  of  a  Lenard  tube  similar  to 
that  shown  in  fig.  1,  and  the  rays  enter  an 
aluminium  window  at  A,  thence  passing  on  through 
an  earthed  tube  n  leading  to  one  of  the  charged 
disks.  The  disks  are  perforated  to  allow  the  rays  to 
pass  through  them ;  they  go  on  through  another  tube 


TO    EARTH 


FIG.  5. — Lenard's  apparatus  for  exhibiting  the  effect  of  a  longitudinal 
electric  field  in  affecting  the  velocity  of  cathode  or  Lenard  rays. 

m,  which,  with  the  disks,  is  kept  at  high  potential,  and 
thence  between  the  plates  de,  which  represent  either 
an  electric  or  a  magnetic  field ;  after  which  they 
encounter  a  phosphorescent  screen  S,  and  depict  upon 
it  a  luminous  spot.  The  observation  consists  in 
observing  the  change  of  position  of  this  spot  when 
the  sign  of  the  electrification  of  the  plates  ab  is 
changed ;  for  if  the  longitudinal  field  alters  the 
velocity,  the  deflexion  caused  by  the  field  de  will 
also  be  modified,  and  thereby  the  change  in  velocity 
is  demonstrated. 


54 


DETERMINATION   OF   SPEED 


[CH.  V. 


Direct  Determination  of  the  Speed  of  Cathode 

Rays. 

Figs.  6  and  7  illustrate  sufficiently  the  ingenious 
device  applied  by  Wiechert,  in  accordance  with  a 
method  of  Des  Coudres,  for  directly  measuring  the 
velocity  of  cathode  rays  during  the  time  of  their 


J3/ 


FIG.  6. — Connexions  of  the  circuits  in  Wiechert's  experiment   for 
measuring  directly  the  speed  of  cathode  rays  as  they  travel  down  a  tube. 

transit  down  the  axis  of  an  exhausted  glass  tube  of 
moderate  length. 

Keferring  to  either  of  the  figures,  the  tube  has  a 
curved  cathode  C  at  one  end,  whereby  the  rays  are 
focussed  through  an  aperture  in  a  screen  B ;  they 
then  travel  down  the  tube  to  another  perforated 
screen  B',  whence  the  central  portion  of  them  reaches 
a  phosphorescent  screen  at  S. 

The  tube  is  excited  by  a  kind  of  Tesla  induction 


CH.  v.]  DIRECT   PROCESS  55 

coil    T,   whose    terminals    lead    respectively   to   the 
cathode  C  and  to  a  ring-anode  A. 

Ley  den  jars  I  and  J  can  be  excited  by  a  Ruhm- 
korff  coil,  or  in  any  ordinary  manner,  and  they 
discharge  across  the  spark-gap  G.  Thereby  a  sub- 
sidiary oscillating  circuit,  of  very  high  frequency, 
characterised  by  the  condensers  H  and  K,  and 
limited  t6  the  region  above  the  spark-gap  G,  is 
set  in  action ;  and  an  oscillatory  discharge  is  con- 
veyed to  the  symmetrical  terminals  PQ,  whence  it 
can  pass  round  a  pair  of  wire  loops  in  parallel,  MN 


S 


FIG.  7. — Enlarged  portion  of  fig.  6,  showing  the  vibration  of  the 
cathode  rays  by  an  alternating  circuit  and  the  adjustment  of  their  range 
of  excursion  by  a  fixed  magnet. 

and  M'N'.  The  effect  of  the  alternating  field,  thus 
generated  in  the  loop  MN  (fig.  7)  is  to  wave  the 
cathode  rays  rapidly  to  and  fro,  so  that  only  in  the 
middle  of  their  path  will  they  pass  through  the 
aperture  in  the  disk  B — the  effect  on  the  distant 
phosphorescent  screen  being  then  quite  faint.  But 
if  a  permanent  magnet  D  is  applied  to  them,  the 
oscillation  is  deflected,  and  can  be  limited  to  the 
region  between  the  centre  and  the  circumference  of 
the  disk — as  illustrated  by  the  figure;  thereby  a 
greater  number  of  rays  get  through,  and  the  screen 
becomes  more  luminous  than  when  the  magnet  is  not 
applied,  because  the  aperture  will  now  be  at  the 
-extremity  of  the  swing  of  the  oscillating  rays.  If 


56  DETERMINATION   OF   SPEED  [CH.  v. 

the  magnet  is  too  strong  the  screen  S  will  become 
dark,  because  the  oscillating  rays  will  be  too  much 
deflected,  so  it  is  possible  to  tell  pretty  sharply  the 
phase  of  the  oscillating  rays  in  the  right-hand  portion 
of  the  tube  by  watching  the  screen  S  and  adjusting 
the  strength  of  the  magnet. 

So  much  for  the  right-hand  end  of  the  tube.  Now 
proceed  to  the  left-hand  end,  or  rather  to  the 
movable  portions  depicted  to  the  left  of  figs.  6  and  7. 
We  have  there  also  an  oscillating  current,  M'N',  in 
precisely  the  same  phase  of  standing  oscillation  as 
its  other  branch  MN ;  consequently,  if  the  rays  take 
no  time  to  travel  down  the  tube,  those  which  get 
through  the  disk  B'  will  be  deflected  as  before ; 
but  if  the  time  taken  to  travel  down  the  tube 
corresponds  with  a  quarter  of  the  extremely  rapid 
oscillation-period  of  the  condensers  HK,  then  the 
rays  deflected  a  maximum  amount  by  the  first  branch 
of  the  circuit  will  not  be  deflected  at  all  by  the 
second,  and  therefore  will  reach  the  middle  of  the 
screen. 

By  either  altering  the  frequency  of  oscillation,  or 
adjusting  the  distance  apart  of  the  parts  represented 
by  BB',  it  is  possible  to  cause  the  deflexion  on  the 
left-hand  side  to  be  either  in  the  same  phase,  or  in 
opposite  phase,  with  the  first  half;  or  to  be  a  zero,  of 
the  first,  second,  or  third  order. 

In  this  way,  though  obviously  the  experiment  is  a 
difficult  one,  Wiechert  was  able  to  make  measure- 
ments of  the  speed  of  the  cathode  rays  produced 
under  given  circumstances. 

Unfortunately  this  speed  is  not  a  fixed  and  definite 
constant,  like  the  velocity  of  light :  it  does  not  indeed 
depend  upon  the  nature  of  the  gas  in  the  tube,  nor 
on  the  substance  of  the  electrodes,  but  it  does  vary 


CH.  v.]  DIRECT  PROCESS  57 

with  the  density  of  the  residual  gas  and  with  the 
intensity  of  the  electric  field. 

In  order  to  prevent  the  diffusion  and  spreading  out 
of  the  rays,  on  their  passage  down  the  tube,  a  longi- 
tudinal magnetising  helix  was  applied  to  it,  so  as  to 
concentrate  the  rays  along  the  axis. 

If  u  is  the  velocity  to  be  measured,  and  I  the 
distance  they  travel  to  give  the  first  zero,  then 
u  —  knl,  where  n  is  the  frequency  of  the  electric 
oscillation  in  the  circuit  MN. 

In  one  experiment  I  was  39  centimetres,  and  n 
was  32  million  per  second;  wherefore  u  comes  out 
4*5  x  109  cm.  per  sec. 

As  soon  as  the  velocity  is  known,  the  ratio  e/m  can 
be  determined  by  measuring  the  magnetic  deflexion 
of  the  rays.  The  range  of  uncertainty  for  this 
determination,  as  made  by  Wiechert,  lies  between 
1*55  and  1*01  times  10r.  It  can  hardly  be  con- 
sidered the  most  accurate  method  of  measurement, 
but  its  directness  and  ingenuity  entitle  it  to  atten- 
tion. 


CHAPTER  VI. 

DETERMINATION  OF  ELECTROCHEMICAL  EQUIVA- 
LENT IN  THE  CASE  OF  ELECTRIC  LEAKAGE 
IN  ULTRA-VIOLET  LIGHT. 

THE  same  ratio  of  m  to  e,  or  a  ratio  of  quite  com- 
parable magnitude,  is  obtained  from  phenomena 
which  at  first  sight  appear  to  be  distinct. 

One  of  these  phenomena  is  the  effect  of  ultra- 
violet light  in  discharging  negative  electricity  from 
a  clean  metal  or  other  surface  ;  a  phenomenon  dis- 
covered by  Hertz,  and  the  investigation  of  which 
was  continued  especially  by  Righi  and  by  Elster  and 
Geitel.  (See  one  of  the  appendices  to  my  "  Signalling 
without  Wires,"  published  by  the  Electrician  Co.) 
If  ultra-violet  light,  whether  from  a  spark  or  from 
a  flame,  fall  upon  a  negatively  electrified  surface, 
then  in  general  there  will  be  a  leak  of  electricity 
from  that  surface  :  which  electricity  can  be  received 
by  any  body  placed  opposite  the  illuminated  one, 
and  can  be  used  to  charge  an  electrometer  of 
known  capacity,  and  so  be  measured.  The  writer, 
assisted  by  Mr.  Benjamin  Davies,  has  made  very 
many  experiments  in  this  subject,  which,  how- 
ever, have  not  yet  been  published.  Now  Elster 
and  Geitel  made  the  notable  discovery  that  the 
application  of  a  magnet  affected  the  rate  of  leak, 


CH.  VL]  DISCHARGE   BY   LIGHT  59 

according  to  the  direction  of  its  lines  of  force.  This 
phenomenon  suggested  a  magnetic  deflexion  of  the 
lines  of  leak,  which  were  shown  by  Kighi  to  be 
singularly  definite  trajectories,  and  indicated  that 
the  leakage  was  due  to  the  bodily  propulsion  of 
negatively  electrified  particles  analogous  to  the 
cathode  rays.  A  vacuum  is  not  necessary  to  observe 
the  effect,  but  in  a  vacuum  the  effect  is  more  pro- 
minent and  more  accurately  measurable.  The 
difference  between  this  case  and  an  ordinary  vacuum- 
tube  case,  is  that  there  is  no  great  E.M.F.  or  gradient 
of  potential  applied,  so  there  is  nothing  of  the 
nature  of  a  disruptive  discharge  ;  in  fact  there  is  no 
leak  at  all  until — by  the  stimulus  of  the  presumably 
synchronous  vibrations  of  ultra-violet  light — the 
molecules  are  thrown  into  a  state  of  agitation,  and 
the  attachment  of  the  negative  charge,  or  of  some 
negatively  charged  corpuscles,  thereby  loosened. 

Two  things  are  necessary  to  get  the  particles  away 
from  the  plate  ;  they  must  be  loosened  by  the  impact 
of  ultra-violet  light — the  direction  of  polarisation  of 
this  light  having  a  very  decided  influence  when 
the  surface  is  smooth, — and  the  surface  on  which 
they  exist  must  likewise  be  negatively  charged, 
so  as  to  repel  them.  Neither  light  alone  nor 
electrification  alone  will  produce  any  considerable 
effect ;  co-operation  is  necessary.  Light  alone  is 
able  to  cause  a  slight  positive  electrification,*  by 
the  diffusion  away  of  negative  corpuscles — a  process 
which  is  assisted  by  a  blast  of  air.  Whether 
electrification  alone  can  produce  a  perceptible  effect 
depends  on  the  temperature  of  the  metal :  when 
that  is  high,  it  can — as  was  discovered  by  Guthrie. 

*This  effect  was  discovered  simultaneously  by  Righi  and  by 
Hallwachs.  See  Phil.  Mag.,  1888,  April,  p.  314,  and  July,  p.  78. 


60      LEAKAGE  IN  ULTRA-VIOLET  LIGHT     [CH.  vi. 

J.  J.  Thomson  devised  a  most  ingenious  method 
of  carrying  out  this  experiment — that  of  discharge 
by  means  of  ultra-violet  light — in  a  metrical 
manner,  and  of  deducing  from  it  the  electrochemical 
equivalent  of  the  charged  particles,  that  is  to  say 
the  amount  of  matter  which  each  contains  com- 
pared with  the  electric  charge  which  each  carries. 


FIG.  8. — J.  J.  Thomson's  apparatus  for  measuring  the  magnetic 
deflexion  of  the  electric  charge  thrown  off  clean  negative  metal  by 
ultra-violet  light  in  a  vacuum.  The  negative  electrode  is  a  clean  zinc 
plate  AB  which  can  be  raised  or  lowered,  the  other  is  wire  gauze  CD 
connected  to  an  electroscope.  Ultra-violet  light  enters  through  the 
quartz  plate  EF,  and  then  a  magnetic  field  is  applied. 

To  this  end  he  employed  the  usual  arrangement 
of  a  small  negatively  charged  zinc  plate  on  which 
ultra-violet  light  from  a  distant  arc-lamp  could 
shine ;  the  light  passing  through  a  plate  of  quartz, 
and  also  through  a  parallel  piece  of  wire  gauze 
connected  with  an  electrometer.  The  distance  be- 
tween the  zinc  plate  and  the  metallic  gauze  was 
variable,  and  the  experiment  consisted  in  observing 
how  much  electricity  reached  the  gauze  from  the 


CH.  VI.] 


DISCHARGE   BY   LIGHT 


61 


negatively  charged  plate,  under  the  influence  of 
light ;  first  without,  and  then  with,  a  magnetic 
field  of  measured  strength  applied  across  the  region 
between  them. 

A  little  calculation  of  extreme  beauty  showed  him 
that  the  paths  of  the  flying  particles  under  magnetic 

Ga.uze 


Zinc 


FIG.  9. — Diagram  showing  the  theoretical  paths  of  the  electrons 
emitted  from  clean  negatively-charged  zinc  in  ultra-violet  light,  under  the 
influence  of  a  strong  perpendicular  magnetic  field ;  the  zinc  and  gauze 
being  a  magnified  representation  of  the  AB  and  CD  in  fig.  8.  The  rays 
would  naturally  reach  the  gauze  and  convey  a  current  to  the  electrometer, 
but  under  the  influence  of  the  magnetic  field  their  paths  become  cycloids 
and  they  fail  to  reach  the  gauze  unless  it  is  brought  nearer.  The  critical 
distance  between  the  zinc  and  the  gauze — when  they  are  just  able  to 
reach  it — is  what  is  measured. 


influence  would  be  cycloids,  whose  generating  circles 
contained  the  ratio  m/e  as  well  as  the  ratio  E/H2 ; 
that  is  to  say  their  trajectory,  if  it  could  be  observed, 
would  involve  the  electrochemical  equivalent  required, 
and  likewise  the  ratio  of  the  electric  to  the  magnetic 


62      LEAKAGE  IN  ULTRA-VIOLET  LIGHT     [CH.  vi. 

field  applied,  as  well  as  the  absolute  strength  of  the 
magnetic  field. 

The  calculation  is  so  simple  that  it  may  be  given 
here  : 

Let  figure  9  show  the  zinc  and  the  gauze  facing 
each  other,  close  together,  with  a  gradient  of 
potential  (V  -  V)/d  =  E  between  them  ;  and  let  a 
magnetic  field  of  density  H  (which  letter  is,  in  this 
case,  to  represent  M  times  the  intensity,  for  brevity 
of  writing)  be  applied  normal  to  the  paper. 

Then  the  motion  of  a  charged  particle  detached 
and  propelled  from  the  origin  into  the  region  between 
the  plates,  provided  that  the  plates  are  in  vacuum 
so  that  there  is  no  resisting  medium  to  interfere, 
will  be — taking  the  axis  of  x  as  a  perpendicular  to 

the  plate —  ..     ^      TT  . 

mx  =  &e  —  iiey 

my  =  Hex 

the  initial  values  of  x,  y,  x,  and  y,  being  all  zero. 
The  solution  of  these  equations,  under  these  initial 

conditions,  is  /,  7  ,x 

x  =  a(l  -cos ot) 

y  —  a(bt  —  sin  bt) 

Era       ,  7     TT     e 
where  a  =  TT9    and  b  =  H  .  —  ; 
He  ra 

and  from  these  we  see  that  x  is  oscillatory  in  accord- 
ance with  a  versine,  ranging  from  0  to  2a  and  back  ; 
while  y  is  both  oscillatory  and  progressive,  com- 
pleting its  period  in  a  time  -=--,  and  increasing  in 

every  such  period  by  the  amount  2-n-a.  In  other 
words,  the  equations  represent  a  cycloid  traced  by 
the  rim  of  a  circle  of  radius  a  rolling  on  the  zinc 
plate. 


CH.  vi.]  DISCHARGE   BY   LIGHT  63 

There  is  no  known  way  of  actually  observing  this 
quite  invisible  and  purely  theoretical  trajectory  ;  but 
when  it  is  perceived  that  in  accordance  with  this 
theory  all  the  particles  moving  between  the  plates 
will  have  similar  paths — so  far  as  they  do  not  come 
near  the  edge  of  either  plate,  in  which  case  they 
would  not  be  propelled  so  far — it  becomes  plain  that 
there  should  be  a  critical  distance,  within  which  the 
gauze  would  receive  and  intercept  all  the  particles, 
and  beyond  which  not  a  single  one  would  be  able  to 
reach  it.  In  the  figure  the  gauze  is  depicted  as  set 
just  beyond  the  critical  distance,  so  that  it  would 
receive  no  electricity,  even  though  the  ultra-violet 
light  were  fully  shining ;  but  so  that  if  either  its 
distance  from  the  zinc  were  diminished,  or  the  electric 
field  strengthened,  or  the  magnetic  field  weakened, 
the  gauze  would  at  once  come  within  range  and 
receive  a  plentiful  supply  of  charge  from  the  hypo- 
thetical cycloidally-flying  particles.  And  the  critical 
distance  at  which  this  would  happen — a  thing  easily 
experimentally  observed — would  be  independent  of 
the  brightness  of  the  ultra-violet  light,  and  would 
merely  equal  the  diameter  of  the  generating  circle.  In 
other  words, — the  critical  distance  between  the  plates, 
when  effective  transfer  of  charge  occurred,  should  be 

2a,  or  ;   a    quantity   which   by    this    ingenious 

6-Ll 

means  is  therefore  measurable.  Wherefore  the  ratio 
m/e  for  this  case  can  be  experimentally  determined, 
if  E  and  H  are  both  known.  The  apparatus 
employed  was  shown  in  Fig.  8. 

The  sharpness  of  actual  experimental  observation 
of  the  critical  distance  was  not  found  quite  so  great 
as  this  simple  theory  would  indicate,  because  of 
disturbing  causes ;  one  of  which  was  the  presence  of 


64      LEAKAGE  IN  ULTRA-VIOLET  LIGHT     [CH.  vi. 

some  residual  air,  interfering  with  the  perfectly  free 
path  of  the  moving  bodies.  Nevertheless  it  was  sharp 
enough  for  fair  determination  ;  and  the  result  was 
again,  in  this  case  also,  that  the  ratio  e/m  came  out 
107  c.g.s.,  or  more  exactly  7xl06;  corresponding 
closely  with  the  values  found  by  J.  J.  Thomson, 
confirmed  subsequently  by  both  Lenard  and  Kauf- 
mann,  for  the  cathode  ray  particles. 

Another  phenomenon  on  which  measurements  were 
made  wras  the  discharge  of  negative  electricity  from 
an  incandescent  carbon  filament  in  an  atmosphere  of 
rarified  hydrogen.  This  also  is  subject  to  disturb- 
ance by  a  magnetic  field,  as  was  shown  by  Elster  and 
Geitel ;  and  a  series  of  measurements,  on  lines  similar 
to  the  preceding,  resulted  in  a  value 

-  =87x  106  c.g.s., 
m 

a  value  of  the  same  order  of  magnitude  as  before :  one 
thousand  times  greater  than  the  electrochemical  or 
electrolytic  value  for  hydrogen,  and  many  thousand 
times  greater  than  for  other  substances,  but  always 
constant  and  independent  of  the  nature  of  the  sub- 
stance present. 

Another  method  for  measuring  these  quantities,  in 
what  may  seem  a  more  direct  manner,  was  devised 
by  Professor  Lenard  and  is  depicted  in  fig.  10.  It 
will  be  realised  that  the  remarkable  character  of 
these  experiments  is  the  fact  that  nothing  is  visible  : 
there  are  no  cathode  rays  to  be  seen,  nor  any 
phosphorescent  spot  produced ;  all  that  can  be 
observed  is  either  a  maximum  deflexion  of  the 
electrometer,  as  by  Lenard's  plan,  or  a  zero  deflexion 
suddenly  changed  to  a  finite  deflexion,  in  J.  J. 
Thomson's  plan. 


GH.  VI.] 


DISCHARGE   BY   LIGHT 


65 


:  Lenard's  method  may  be  described  as  follows:— *-•; • 
Light  from  the  source  L,  which  is  a  spark  between 
zinc  electrodes,  passes  through  a  quartz  plajbe  Q, 
where  it  enters  the  vacuum  and  falls  upon  a 
negatively  electrified  aluminium  plate  C.  B  is  a 
perforated  earthed  screen  through  which  the  particles 
are  shot  till  they  fall  upon  the  plate  E,  which  is 
connected  to  an  electrometer ;  or  if  deflected  by  a 
magnet  they  will  fall  upon  the  plate  F.  The  amount 


FIG.    10.— Lenard's    apparatus    for    measuring    the    electrochemical 
equivalent   of  the   discharge   of   negative   electricity   from  a   cathode 
»  illuminated  by  ultra-violet  light  in  vacuo. 


IS 


of"  charge  received  by  these  two  terminals 
separately  measured  and  plotted,  with  magnetic 
field  as  abscissa.  The  charge  received  by  E  tgill 
decrease,  and  that  received  by  F  will  increase;  as 
the  magnetic  field  is  increased,  until  a  maximum 
is  received  by  F ;  which  will  happen  when  the  centre 
of  the  plate  is  the  middle  of  the  stream  of  rays,. 
A  further  increase  in  the  magnetic  force  will  cause 
the  charge  received  to  fall  off.  The  field  required 
to  give  this  maximum  is  measured — being  determined 
by  metrical  examination  of  the  plotted  curve.  The 
paths  of  the  particles  between  B  and  F  must ;  be 


L.E. 


66      LEAKAGE  IN  ULTRA-VIOLET  LIGHT     [CH.  VL 

circles, — since  they  are  not  subjected  to  any  but  a 
deflecting  force  when  they  have  passed  through  the 
screen.  When  the  maximum  is  received  by  the  plate 
F,  the  tangent  to  the  mean  circle  will  be  horizontal 
at  the  position  of  the  hole  B ;  and  this  fact,  together 
with  the  passing  of  this  circular  trajectory  through 
the  centre  of  the  plate  F,  is  sufficient  to  determine  it, 
and  so  to  give  its  radius  of  curvature, — which  will 
be  equal  to 


The  velocity  u  is  separately  estimated  by  assuming 
that  it  is  acquired  under  electrical  influence  between 
C  and  B,  the  equation  being 


the   latter   factor  being  the   difference   of  potential 
between  C  and   B. 

Thus  the  two  quantities  u  and  e/m  are  determined. 

Positive  and  Negative  Carriers. 

In  connexion  with  the  above  experiments  it  is 
important  to  notice  that  the  above  value  of  e/m  for 
the  negative  carriers  is  only  obtained  at  low  pressures. 
If  the  pressure  is  high  the  ordinary  electrolytic  value 
of  e/m,  or  something  still  smaller,  can  be  obtained;  and 
this  suggests  that  at  ordinary  pressures  the  electron 
becomes  loaded  up  by  attaching  itself  to  an  atom,  or 
even  by  collecting  round  itself  a  group  of  atoms. 
Further  evidence  of  this  is  afforded  by  the  fact  that 
there  is  but  little  difference  between  the  velocities  of 
the  positive  and  negative  ions,  when  urged  by  an 
electric  field,  in  a  gas  at  atmospheric  pressure.  It 
will  be  seen,  further  on,  that  in  the  case  of  the 


CH.VI.]  POSITIVE   CARRIERS  67 

electrons  discharged  from  Radium,  their  velocity  is 
so  great  that  this  loading  effect  is  imperceptible. 

Nothing  larger  than  the  ordinary  electrolytic  value 
for  the  e/m  ratio  is  ever  given  by  the  positive  carriers. 
These  are  not  so  easy  to  observe,  but  WIEN*  has 
examined  them  by  detecting  and  measuring  the 
slight  magnetic  deflexion  exhibited  by  certain 
rays  behind  a  perforated  cathode  in  a  vacuum  tube, 
which  Goldstein  discovered  and  called  Kanal-strahlen, 
and  which  Wien  and  Ewers  proved  were  carriers  of 
positive  electricity.  Wien  has  shown  that  they  move 
fairly  quickly — that  is  to  say  about  360  kilometres 
per  second — in  spite  of  the  fact  that  in  hydrogen  their 
ratio  e/m  is  of  the  order  104,  that  is  to  say  the 
proper  value  for  a  hydrogen  atom  or  ion.  With 
other  substances  the  ratio  has  been  found  to  vary 
with  the  substance  and  approximately  to  equal  the 
electrolytic  value,  for  these  positively  charged 
atoms.  J.  J.  Thomson  has  likewise  made  measure- 
ments on  the  positive  carriers,  by  means  of  the 
discharge  from  incandescent  filaments  and  other 
positively  charged  hot  bodies,  and  has  confirmed 
Wien's  results — obtaining  an  electrolytic  value  for 
their  electrochemical  equivalent. 

Thus  it  is  forcibly  suggested  that  whereas  the 
positive  carriers  of  electricity  are  always  ions,  con- 
sisting of  a  unit  +  charge  associated  with  an  atom, 
the  negative  carriers  are  sometimes  dissociated  from 
the  main  bulk  of  the  atom,  as  if  they  were  only 
fractions  or  fragments  or  constituents  or  appendages 
of  an  atom.  These,  detached  and  flying  loose,  are 
able  to  attain  to  prodigious  speed.  For  any  acceler- 
ation to  which  they  are  subjected  is  a  thousand-fold 

*Wied.  Ann.  Ixv.  p.  440.  See  also  Ewers  in  Wied.  Ann.  Ixfx. 
p.  187. 


68      LEAKAGE  IN  ULTRA-VIOLET  LIGHT     [CH.  vi. 

greater  than  it  is  even  for  an  atom  of  hydrogen,— 
weighed  down  and  burdened  as  that  is  with  a  mass 
of  inert  material,  and  subject  only  to  the  very  same 
propulsive  force.  ,  •  i  . 

Think  of  the  mobility  of  a  particle  which  experienced 
the  usual  gravitation  pull  and  had  only  10100  of  the 
corresponding  mass  to  carry.  Such  a  mobile  particle 
as  that  would  drop  under  the  influence  of  gravity,  not 
16  feet  in  the  first  second,  as  everything  we  know 
does  near  the  surface  of  the  earth,  but  16,000  feet, 
or  about  three  miles ;  and  would  in  one  second 
acquire  under  gravity  a  velocity  of  six  miles  per 
second ;  enough  almost  to  carry  it  out  of  the  range 
of  the  earth's  attraction  altogether,  and  more  than 
enough  to  carry  it  round  the  world,  if  fired  horizon- 
tally with  such  a  speed. 

The  acceleration  to  which  particles  are  subject  in  a 
vacuum  tube  is  far  greater  even  than  this,  because 
there  the  forces  are  so  prodigious  ;  gravitation  force 
on  ions  is  almost  infinitesimal  compared  with  common 
electrical  force  on  their  charges.  Suppose,  for  in- 
stance, that  they  are  in  a  field  such  as  may  easily  occur 
in  a  vacuum  tube,  of  3,000  volts  per  centimetre,  one- 
tenth  of  what  ordinary  air  will  stand,  or  ten  electro- 
static units.  The  force  urging  one  of  these  carriers 
to  move  is  then  10  x  10~10=  10~9  dyne;  the  mass 
being  moved,  if  it  is  a  whole  atom  of  hydrogen,  e.g. 
if  it  were  a  positive  carrier  in  a  hydrogen  atmosphere, 
is  only  10~24  gramme;  and  accordingly  the  acceleration 
it  experiences  is  1015  centimetres  per  second  per  second, 
or  a  billion  times  g.  Whereas  if  it  were  the  smallest 
kind  of  negative  carrier,  its  acceleration  would  be  a 
thousand  times  greater  still. 

.  The  velocity  acquired  in  passing  over  a  distance  of 
five  centimetres  under  this  force  is  obtained  by  finding 


CH.  vi.]  NEGATIVE   CARRIERS  69 

the  square  root  of  2fh ;  that  is  to  say,  it  is  108  centi- 
metres per  second  for  a  positive  carrier,  and  3  x  109 
centimetres  per  second  for  a  negative  carrier ;  and 
these  are  approximately  the  orders  of  magnitude 
actually  observed. 

Thus  the  hypothesis  becomes  more  and  more  j  ustified 
that  units  of  positive  charge  are  always  associated 
with  atoms,  in  operations  which  we  can  control, 
and  are  consequently  always  complete  ions;  while 
the  units  of  negative  charge  appear  in  some  cases 
with  a  separate  existence, — perhaps  carrying  with 
them  part  of  the  atom,  in  which  case  they  might  be 
called  corpuscles,  having  a  material  nucleus  ;  perhaps 
pure  disembodied  electricity,  whatever  that  may 
be — an  electrical  charge  detached  from  matter,— a 
mere  complexity  in  the  ether,  in  which  case  they 
would  correspond  with  those  hypothetical  entities 
familiar  in  theoretical  and  mathematical  treatment  as 
"electrons." 


CHAPTER  VII. 
IONISATION  OF  GASES. 

IT  is  constantly  necessary  to  speak  of  the  air  or  other 
medium  being  '  ionised '  by  the  passage  of  rays,  and 
by  many  other  processes.  The  term  means  that  the 
molecules  are  split  up,  or  dissociated,  into  their 
constituent  atoms ;  which,  being  oppositely  charged, 
form  anions  and  cations  respectively.  It  appears  to 
be  an  effect  due  to  the  violent  encounter  of  an  ener- 
getically flying  particle  with  a  comparatively  stationary 
molecule  :  a  sudden  electric  wave  or  pulse,  if  thin  and 
forcible  enough,  may  do  the  same ;  the  effect  in  any 
case  is  to  break  the  molecule  asunder  into  constituent 
ions,  some  positively,  some  negatively,  charged, 
thereby  converting  the  medium  into  a  true  gaseous 
electrolyte,  until  the  dissociated  atoms  have  had  time 
to  recombine — a  time  which  may  be  measured  in 
minutes.  It  is  owing  to  this  effect  that  X-rays  are 
able  so  readily  to  discharge  an  electroscope  or  other 
charged  body,  whatever  the  sign  of  its  charge  may 
be ;  for  it  is  manifest  that  any  ions  in  the  atmosphere 
of  opposite  sign  will  be  attracted  to  it  and  will 
neutralise  any  charge  it  may  possess.  Ionised  air 
can  always  be  detected  by  its  making  electroscopes 
leak,  irrespective  of  any  defect  of  insulation  in  solid 
supports. 


CH.  vii.]  HOT  METALS  71 

The  ionising  power  of  X-rays  was  observed  by 
Righi  soon  after  their  discovery,  and  almost  simul- 
taneously by  other  physicists. 

The  terrestrial  atmosphere  out  of  doors  is  usually 
more  or  less  ionised,  and  in  underground  air  the 
ionisation  is  still  more  marked,  probably  owing  to 
radio-activity  in  the  soil.  Elster  and  Geitel  have 


TO    CXECrV3OMCT£-/«? 


FIG.  11. 

•examined  this  matter  thoroughly,  and  Lenard  found 
that  even  the  splashing  of  water  introduced  ions  into 
air,  so  that  the  atmosphere  at  base  of  a  waterfall  was 
usually  in  some  degree  ionised. 

Behaviour  of  Hot  Metals  in  Gases. 

Fig.  11  must  stand  as  representative  and  typical 
of  a  mass  of  important  work  on  the  ionisation  and 
disintegration  of  material  effected  by  high  tempera- 
ture ;  it  represents  the  simple  apparatus  of  Elster 


*2  IONISATION  OE   GASES  [CH.  vn. 

(ind  Geitel  by  which  they  examined  in  great  detail 
•a  number  of  incandescent  metals  in  the  form  of  a 
wire  or  strip  heated  by  an  electric  current  in  different 
gases.  In  J.  J.  Thomson's  variety  of  experiment 
this  current  was  produced  in  the  secondary  of  a 
transformer,  so  as  to  be  conveniently  insulated.  The 
details  are  long  and  complicated,  and  must  be  referred 
to  in  J.  J.  Thomson's  book  on  The  Conduction  of 
Electricity  through  Gases  \  but  briefly  it  may  be 
said  that  when  the  gas  in  the  vessel  is  air,  the  metal 
plate  A  receives  a  positive  charge  when  the  wire  is 
heated  to  a  dull  red  glow ;  as  it  becomes  hotter  the 
charge  increases  until  the  wire  is  at  a  yellow  heat ; 
if  it  is  made  hotter  than  that,  the  charge  diminishes, 
and,  at  the  highest  temperature,  is  very  small.  In 
hydrogen  the  plate  is  found  to  receive  negative  elec- 
tricity when  the  wire  is  hot  enough,  though  at  a  lower 
temperature  it  receives  positive.  To  get  rid  of 
occluded  gases,  J.  J.  Thomson  often  kept  it  red  hot  for 
a  week  or  more.  McClelland,  Branly,  H.  A.  Wilson, 
and  others  have  investigated  this  phenomenon,  which 
has  also  been  studied  in  a  different  form  by  Preece 
and  Fleming — following  up  a  curious  observation 
made  by  Edison  in  connexion  with  incandescent 
lamps.  Kecent  measurements  by  0.  W.  Eichardson 
have  done  much  to  reduce  it  to  a  definite  physical 
specification.  The  evidence  that  an  incandescent 
platinum  wire  disintegrates,  or  at  any  rate  gives  off 
material,  is  the  fact  discovered  by  Aitken,  that  a 
cloud  becomes  visible  in  a  luminous  beam,  if  the 
moist  gas  surrounding  the  wire  be  suddenly  cooled. 
This  indeed  can  occur  at  a  much  lower  temperature 
than  incandescence.  Mr.  Owen  (Phil.  Mag.,  Sept., 
1903),  found  that  when  a  platinum  wire  was  in  air 
there  was  always  a  cloud  when  the  temperature  of 


CH.VIL]  CONDUCTION   IN   AIR  73 

the  wire  was  raised  to  about  300°  C.,  even  after 
long-continued  previous  incandescence  of  the  wire  ; 
whereas  in  pure  hydrogen  the  wire  had  to  be  raised 
to  red  heat  before  a  cloud  formed. 

Measurements  of  lonisation  Current. 

The  whole  subject  of  the  dissociation  or  breaking  up 
of  molecules  which  is  effected  in  gases  by  Rontgen  rays, 
by  radium  radiation,  and  by  a  great  number  of  other 
influences — a  process  which  is  known  as  ionisation, 
because  the  broken  constituents  of  the  molecule  are 
oppositely  charged — is  too  large  to  be  conveniently 
entered  upon  here.  It  has  been  worked  at  by  a 
multitude  of  experimenters,  and  for  an  account  of 
their  results  the  work  of  J.  J.  Thomson  on  The 
Discharge  of  Electricity  through  Gases,  must  be 
referred  to.  It  may  suffice  to  say  that  the  products 
of  decomposition,  though  in  the  first  instance  no 
doubt  simple  ions,  seem  to  be  speedily  complicated 
by  the  aggregation  of  other  molecules  round  them ; 
and  accordingly  the  diffusion  or  progress  of  these  ions 
is  liable  to  be  retarded,  and,  when  measured,  is  found 
slower  than  might  otherwise  have  been  expected. 
On  the  whole,  the  negative  ions  tend  to  move  faster 
than  the  positive  ones,  but  the  difference  is  not 
necessarily  greater  than  can  be  observed  in  liquid 
electrolysis.  Eecent  work  by  H.  A.  Wilson  and 
E.  Gold,  on  conduction  in  flames,  has  however  shown 
that  the  negative  carriers  in  that  case  are  free 
electrons. 

One  of  the  easiest  tilings  to  measure  is  the  con- 
ductivity of  air  in  this  ionised  condition,  that  is  to 
say,  the  total  current  transmitted  .by  it  between  two 
electrodes  immersed  in  it  and  connected  to  some 
sufficiently  sensitive  current-measuring  device — a 


74  IONISATION   OF  GASES  [CH.  vn. 

galvanometer  in  some  cases,  or  an  electrometer 
arranged  so  as  to  show  a  measured  leak  in 
others. 

A  saturation  value  of  the  current  can  thus  be 
found,  when  all  the  ions  present  are  taking  part  in 
the  action  to  the  full  extent ;  the  current  then 
reaches  a  maximum,  which  cannot  be  exceeded ;  and 
its  amount  would  furnish  an  estimate  of  the  number 
of  ions  present,  if  the  speed  and  the  charge  of  each 
were  known.  Measurements  of  the  total  current  Neu, 
the  quantity  of  electricity  conveyed  per  second,  have 
been  made  by  Lenard1  and  Bighi2  and  Thomson,3 
and  in  various  gases  by  Rutherford,4  now  Professor 
at  Montreal ;  by  Beattie6  and  de  Smolan  at  Glasgow, 
by  Zeleny6  of  Minnesota,  by  McClelland7  on  hot 
gases  from  flames,  by  McLennan8  of  Toronto,  by 
Richardson,9  H.  A.  Wilson,10  and  Owen11  on  in- 
candescent filaments.  Townsend  also  has  made 
many  experiments  on  the  diffusion  speed  of  ions. 

Professor  Zeleny  measured  the  velocity  by  a  safe 
and  direct  method  of  making  the  particles  fly  down  a 
tube  against  a  wind,  and  observing  the  rate  of  the 
current  of  air  which  was  just  able  to  withstand  their 
progress  :  these  measurements  constituting  a  satis- 
factory confirmation  of  Thomson's  and  Rutherford's 
more  indirectly  inferred  results. 

1  Wied.  Ann.,  vol.  63,  p.  253. 
zRend.  della  R.  Accad.  dei  Linc&i,  May,  1896. 
3  Phil.  Mag.,  November,  1896. 
*Ibid.t  November,  1896,  and  April,  1897. 

6  Ibid.,  June,  1897.  6  Ibid.,  July,  1898.          7  Ibid.,  July,  1898. 

*Phil.  Trans.,  vol.  195,  p.  49,  1899. 
9  Ibid.,  vol.  201,  1903.  ™  Ibid.,  vol.  202,  1903. 

11  Phil.  Mag.,  August,  1904. 


CH.  vii.]  BY   RONTGEN   RAYS  T5 

Condensation  of  Moisture  Experiments. 

C.  T.  R  Wilson  investigated  the  amount  of  expan- 
sion required  by  both  positive  and  negative  ions  to 
act  effectively  as  nuclei  in  condensing  moisture.  The 
ions  were  produced  by  Kontgen  rays,  and  electrolytic 
terminals  were  inserted  to  effect  a  separation  of 
the  ions.  He  found  that  with  an  expansion  such 
that  the  ratio  of  the  final  to  the  initial  volume  was 
1*25,  there  was  a  fog  in  the  half  of  the  vessel  which 
contained  negative  ions,  and  hardly  any  condensation 
in  the  half  containing  positive  ones,  but  that  when 
the  expansion-ratio  was  as  much  as  1*31  there  was 
little  or  no  difference  to  be  seen  between  the  two 
halves.  Thus  proving  that  the  negative  ions  are 
more  efficient,  as  centres  of  condensation  for  water- 
vapour,  than  the  positive  ions. 

It  may  be  doubted  whether  electrons  themselves 
are  able  to  act  as  nuclei  and  condense  vapour  round 
them,  and  it  appears  unlikely  that  they  can  do  that 
without  the  aid  of  one  or  more  atoms  of  matter. 
On  this  subject  Mr.  C.  T.  K.  Wilson  has  favoured  me 
with  the  following  opinion  : — 

"  I  certainly  think  that  in  practically  all  cases  the 
electron  has  already  been  loaded  to  form  a  negative 
ion,  before  the  expansion  by  which  the  necessary 
supersaturation  is  brought  about  has  been  effected. 
In  air  which  contains  less  moisture  than  corresponds 
to  a  four- fold  supersaturation,  equilibrium  is  probably 
reached  when  the  electron  has  collected  around  itself 
a  group  of  molecules  not  much  larger  than  the  ion 
in  dry  air.  If  however  a  four-fold  supersaturation 
is  exceeded,  the  conditions  become  unstable  and  the 
cluster  of  molecules  increases  to  a  visible  drop.  If 
electrons  enter  the  expansion  chamber  immediately 


76  IONISATION   OF  GASES  [OH  vn. 

after  an  expansion,  while  the  four- fold  supersaturation 
is  still  exceeded,  no  doubt  they  will  form  nuclei  for 
the  condensation  of  drops  without  any  pause  at  the 
ion  stage.  But  in  the  ultraviolet-light  experiments 
I  have  no  doubt  that  the  electrons,  or  all  but  an 
insignificant  proportion  of  them,  had  been  loaded  up 
and  had  existed  as  ions  before  the  expansion  was 
made." 

The  next  chapter  contains  an  account  of  what  are 
probably  the  most  important  experiments  yet  made 
in  the  Cavendish  Laboratory. 


CHAPTER  VIII. 
DETERMINATION  OF  THE  MASS  OF  AN  ELECTRON. 

So  far,  all  the  measurements  quoted  have  resulted  in 
a  consensus  of  certainty  respecting  our  knowledge  of 
e/m.  for  gaseous  conduction  and  radiation ;  and  the 
measurements  made  on  the  cathode  rays  in  a  Crookes's 
tube,  or  near  a  plate  leaking  in  ultra-violet  light, 
have  likewise  given  us  a  knowledge  of  their  velocity, 
and  shown  that  it  is  about  one- thirtieth  of  the  velocity 
of  light :  more  or  less  according  to  circumstances. 
But  so  far  no  direct  estimate  has  been  made  of  either 
e  or  m  separately.  The  difficulty  of  making  these 
measurements  is  great,  because  we  are  dealing  with  an 
aggregate  of  an  enormous  and  unknown  number  of 
these  bodies.  It  would  not  be  difficult  to  make  a 
determination  of  the  aggregate  mass  of  a  set  of  pro- 
jectiles, say  Nra,  where  N  is  the  number  falling  on  a 
target  in  a  given  time,  by  means  of  the  heat  which 
the  blow  generates ;  or  better,  perhaps,  by  the 
momentum  which  they  would  impart  to  a  moving 
arm  after  the  fashion  of  a  ballistic  pendulum ; 
provided  their  velocity  u  were  known,  as  in  this 
case  it  is.  The  aggregate  energy  ^  Nmu2,  or  the 
aggregate  momentum  Nmtt,  could  thus  be  found ;  but 
howls  m  to  be  separated  from  N  ? 

Again,  if  the  particles  are  collected  in,  a  hollow 


78  DETERMINATION  OF  THE  MASS    [CH.  vm. 

vessel  attached  to  an  electrometer  of  known  capacity, 
it  is  not  difficult  to  estimate  the  total  quantity  of 
electricity  which  enters  the  vessel  in  a  given  time, 
that  is  to  say,  to  determine  Ne ;  but,  again,  how  are 
we  to  discriminate  e,  from  N  ? 

Another  thing  that  is  comparatively  easy  to  deter- 
mine, especially  in  such  cases  as  leak  from  a  negative 
surface  under  the  action  of  ultra-violet  light,  or  the 
conductivity  of  air  induced  by  the  influence  of  Rontgen 
rays,  is  the  total  current  transmitted ;  viz.  the  quantity 
New,  the  quantity  of  electricity  conveyed  per  second 
between  electrodes  immersed  in  the  air,  and  main- 
tained at  a  sufficiently  high  difference  of  potential 
to  cause  all  the  corpuscles  or  the  ions  present  to 
take  part  in  conducting  the  current. 

We  may  consider  the  following  quantities  experi- 
mentally determined,  by  researches  carried  on  at 
the  Cavendish  laboratory  and  elsewhere,  and  so  far 
already  described  or  indicated  in  the  preceding  three 
chapters:-  gfm 

u 

Ne 
Nw 

New 

But  still  we  have  not  described  a  method  of 
measuring  separately  either  e  ox  m:  only  methods 
of  measuring  their  ratio. 

If  only  it  were  now  possible  to  count  the  corpuscles 
or  electrons, — to  determine  the  number  N  which  are 
started  into  existence,  or  which  enter  the  hollow 
vessel  or  which  take  part  in  conveying  the  current  in 
the  case  of  a  leak  by  ultra-violet  light, — we  should  no 
longer  have  to  guess  at  the  actual  value  of  e  and  of  m 
separately,  but  should  have  really  determined  them. 


CH.  viii.]  OF   AN   ELECTRON  79 

This  brilliant  research  has  actually  been  carried  out 
by  Professor  J,  J.  Thomson,  by  means  of  a  method 
partly  due  to  Mr.  C.  T.  K.  Wilson,  supplementing  a 
fact  discovered  by  Mr.  Aitken,  and  interpreted  in  the 
light  of  hydrodynamic  principles  laid  down  long  ago 
by  Sir  George  Stokes. 

I  must  be  excused  for  waxing  somewhat  enthusiastic 
over  this  matter :  it  seems  to  me  one  of  the  most 
brilliant  things  that  has  recently  been  done  in  experi- 
mental physics.  Indeed  I  should  not  need  much 
urging  to  cancel  the  "  recently  "  from  this  sentence ; 
save  that  it  is  never  safe  for  a  contemporary  to  usurp 
the  function  of  a  future  historian  of  science,  who  can 
regard  matters  from  a  proper  perspective. 

The  matter  is  rather  long  to  explain  from  the 
beginning,  and  I  must  take  it  in  sections. 

Aitken  and  Cloud  Nuclei. 

First  of  all,  Mr.  John  Aitken,*  of  Edinburgh,  dis- 
covered in  1880  that  cloud  or  mist  globules  could 
not  form  without  solid  nuclei,  so  that  in  perfectly 
clear  and  dust-free  air  aqueous  vapour  did  not 
condense,  and  mist  did  not  form.  (See,  for  instance, 
my  lecture  to  the  British  Association  at  Montreal,  in 
1884,  on  "Dust"— Nature,  vol.  31,  p.  268.) 

Without  solid  surfaces,  in  clear  space,  vapours 
could  become  supersaturated ;  but  the  introduction 
of  a  nucleus  would  immediately  start  condensation, 
and  according  to  the  number  of  nuclei,  or  conden- 
sation centres,  so  will  be  the  number  of  cloud 
globules  formed. 

Every  cloud  or  mist  globule  is  essentially  a 
minute  falling  raindrop,  not  floating  in  the  least,  but 
falling  through  a  resisting  medium — falling  slowly 

*  Trans.  R.S.  Edin.,  vol.  30,  pp.  337-368  (1883). 


80  DETERMINATION  OF  THE  MASS    [CH.  vjii. 

because  it  is  of  such  insignificant  weight  compared 
with  its  surface — but  falling  always  relatively  to  the 
air.  A  cloud  may  readily  be  carried  up  by  a  current 
of  air,  but  that  is  only  because  the  air  is  moving  up 
foster  than  the  drops  are  trickling  down  through  it. 
No  motion  of  the  air  disturbs  the  relative  falling 
motion  :  the  absolute  motion  with  reference  to  the 
earth's  surface  is  the  resultant  of  the  two. 

The  fact  that  nuclei  are  required  for  mist  precipi- 
tation can  be  .  proved  by  filtering  them  out  with 
cotton  wool,  and  finding  that  as  the  nuclei  get  fewer 
the  mist  condensation  differs  in  character,  becoming 
ultimately  what  is  called  a  Scotch  mist,  such  as  forms 
in  fairly  clean  air ;  where  since  the  dust  particles  are 
comparatively  few,  the  centres  of  condensation  are 
few  also,  and  accordingly  have  each  to  condense  a 
considerable  amount  of  vapour ;  so  that  the  drops  are 
not  nearly  so  close  together  and  are  bigger ;  wherefore 
they  fall  quicker,  like  very  fine  rain.  In  perfectly 
clean  elaborately-filtered  air  the  dew  point  may  be  far 
passed  without  any  vapour  condensing,  and  the  space 
will  remain  quite  transparent  in  spite  of  its  being 
supersaturated  with  vapour. 

The  reason  for  this  effect  of,  and  necessity  for, 
nuclei,  is. thrown  into  strong  relief  by  Lord  Kelvin's 
theory  concerning  the  effect  of  curvature  on  vapour 
tension,*  because  the  more  a  liquid  surface  is  curved 
the  more  it  tends  to  evaporate,  and  an  infinitely 
convex  surface  would  immediately  flash  off  into 
vapour.  Consequently  an  infinitesimal  globule  of 
liquid  cannot  exist;  vapour  can  only,  condense  on  a 
surface  of  finite  curvature,  such  as  is  afforded  by  a 
dust  particle  or  other  body  consisting  of  a  large 
aggregate  of  atoms.  For  it  must  be  remembered 

*  See,  for  instance,  Maxwell's  Theory  of  Heat,  1891  edition,  p.  290. 


CH.  VIIL]  OF   AN   ELECTRON  81 

that  a  single  grain  of  lycopodium  powder  contains 
about  a  trillion  atoms,  and  a  dust  particle  big  enough 
to  condense  vapour  need  not  consist  of  more  than  a 
billion,  or  perhaps  not  more  than  a  million,  atoms, 
and  need  by  no  means  be  big  enough  to  be  visible 
even  in  a  microscope.  It  is,  however,  material  enough 
to  be  stopped  by  a  properly  packed  cotton-wool  filter. 

J.  J.   Thomson  and  Electrical  Nuclei. 

In  1888  it  was  shown  by  J.  J.  Thomson,  in  his 
book  Applications  of  Dynamics  to  Physics  and 
Chemistry,  p.  164,  that  electrification  of  a  body 
would  partially  neutralise  the  effect  of  curvature,  and 
so  assist  the  condensation  of  vapour  on  a  convex 
surface. 

Consider  a  drop  of  liquid,  or  a  soap  bubble ;  the 
effect  of  the  curvature  of  the  surface  is  to  give  a 
radial  component  of  surface  tension  inwards,  causing 
an  increased  pressure  internally.  The  effect  of 
electrification  is  just  the  opposite :  it  causes  a  direct 
pressure  outwards,  which  goes  by  the  name  of  electric 
tension. 

The  way  these  depend  on  size  is  as  follows : 

The  radial-pressure  component  of  the  surface- 
tension  T  is 

inwards. 


r 

The  electric  tension  is 


outwards. 


They  are  differently  affected,  therefore,  by  the  size 
of  the  globule  ;  hence  at  some  size  or  other  they  must 
balance,  and  such  an  electrified  convex  surface  will 

L.E.  F 


82  DETERMINATION  OF  THE  MASS    [CH.  vni. 

behave  as  if  it  were  unelectrified  but  flat.  Accord- 
ingly vapour  which  would  refuse  to  condense  on  an 
unelectrified  convex  surface,  until  far  below  the  dew 
point,  will  begin  to  condense  on  it,  if  sufficiently 
electrified,  the  instant  the  dew  point  is  reached. 

The  critical  size  at  which  the  ionic  charge  enables 
a  sphere  of  water  to  act  as  regards  condensation  as  if 
it  were  flat,  can  be  reckoned  by  equating  the  pressure 
to  the  tension,  thus  : 


r      Sir  KT* 
e2  10-21       1 


whence  r=10~8  approximately,  or  is  of  atomic 
magnitude. 

Hence  ions  may  be  expected  to  condense  vapour 
at  the  ordinary  dew-point  ;  and  anything  bigger 
which  possesses  the  same  charge  can  condense  it 
still  more  easily. 

Accordingly  an  electric  charge  assists  vapour  to 
condense  ;  and  a  sufficient  electric  charge  might 
cause  it  to  condense  on  quite  a  small  body  —  as 
small  even  as  an  atom.  Hence  in  the  presence  of 
ions,  dust  particles  are  not  necessary  for  conden- 
sation. -  Vapour  may  condense  on  these  electrical 
nuclei  without  the  need  for  solids  of  finite  curva- 
ture. The  electrical  nuclei  cannot  be  completely 
filtered  out  by  cotton  wool  :  they  will  exist  or 
can  be  produced  in  dust-free  air.  No  doubt  if 
they  are  passed  through  a  great  amount  of  metal 
gauze  they  may  be  diminished  in  number,  but 
they  are  not  easily  got  rid  of  except  by  their 
own  diffusion,  which  does  ultimately  enable  them 
to  pair  off  or  to  migrate  to  the  sides  of  the  vessel. 


CH.  VIIL]  OF  AN  ELECTRON  83 

They  can  be  got  rid  of  most  quickly,  however,  by  intro- 
ducing an  electric  field,  that  is  to  say  by  supplying 
electrodes  maintained  at  a  few  volts  difference  of 
potential.  They  will  then  immediately  make  a 
procession,  as  in  electrolysis,  only  with  much  greater 
speed,  because  their  motion  is  much  less  resisted  or 
interfered  with  by  chance  collisions ;  so  they  will 
soon  reach  and  cling  to  their  respective  electrodes, 
and  in  that  case  again  no  true  mist  can  form.  But 
it  must  be  remembered  that  any  of  the  numerous 
causes  of  ionisation  can  produce  some  of  them 
again. 

While  ions  are  present  in  considerable  numbers 
a  thick  mist  will  form  whenever  the  space  is 
saturated  with  vapour,  but  it  will  be  a  mist 
of  different  appearance  from  the  slight  rain-like 
condensation  which  may  be  seen  forming  round  the 
few  residual  dust  particles.  The  mist  globules  will 
usually  be  of  uniform  size,  and  some  estimate  of  that 
size  can  be  roughly  attempted  by  the  diffraction 
colours  which  can  be  seen  if  a  point  of  light  is  looked 
at  through  the  mist :  not,  however,  a  very  easy  plan 
for  making  a  trustworthy  estimate.* 

Electrical  nuclei  can  be  produced  in  various 
ways — by  anything,  in  fact,  which  dissociates  the  air 
or  which  fills  it  with  ions.  Some  are  produced  by 
the  splashing  and  spray  of  water ;  some  are  given  off 
from  flames,  and  from  red-hot  bodies ;  they  are 
produced  in  considerable  numbers  when  Kontgen 
and  when  Becquerel  rays  travel  through  air ;  they 
can  be  given  off  by  radio-active  substances  like 
uranium;  and  they  are  easily  emitted  by  a  nega- 
tively charged  metallic  surface  exposed  to  ultra-violet 
light. 

*See  C.  T.  K.  Wilson,  Phil.  Trans.,  1897,  A,  vol.  189,  p.  283. 


84  DETERMINATION  OF  THE  MASS    [CH.  vm. 

Wilson  and  Metrical   Cloud  Condensation. 

Mr.  C.  T.  K.  Wilson,*  in  his  study  at  the  Cavendish 
Laboratory  of  cloud  formation  under  the  influence 
of  Rontgen  rays  and  other  agents,  devised  a  plan 
for  precipitating  a  definite  and  known  quantity  of 
aqueous  vapour  in  a  visible  form.  This  was  done  by 
an  arrangement  for  making  a  sudden  or  adiabatic 
expansion  of  saturated  air,  and  making  it  to  a 
carefully  measured  amount.  The  apparatus  employed 
is  shown  in  Fig.  12. 

One  test-tube  moving  inside  another  is  employed 
as  a  piston,  and  by  a  certain  arrangement  the  piston 
was  enabled  to  drop  with  great  suddenness  and  thus  to 
produce  a  measured  small  exhaustion  and  consequent 
cooling  in  the  reservoir  containing  the  gas  under 
experiment  ;  saturated  as  it  is  with  vapour,  and 
supplied  with  electric  nuclei.  The  mist  at  once 
formed,  and  the  drops  began  to  fall  slowly,  as 
usual.  Mr.  Wilson  tried  to  get  an  estimate  of 
their  size  from  the  colours,  but  it  was  difficult  and 
unsatisfactory.  If  the  size  had  been  known,  their 
number  would  have  been  known  too,  because  the 
measured  amount  of  expansion  had  produced  a 
known  fall  of  temperature  below  the  dew  point, 
and  so  had  condensed  a  known  amount  of  aqueous 
vapour,  which  would  be  distributed  equally  among 
all  the  equal  globules. 

It  occurred  to  J.  J.  Thomson  that  a  better  estimate 
of  size  could  be  made  by  observing  their  rate  of 
falling,  which  is  a  thing  not  difficult  to  observe  since 
they  all  fall  together,  being  all  of  the  same  size.  In 
any  mist  formed  in  a  bell-jar  it  is  easy  to  watch  it 
settling  down,  by  watching  its  fairly  definite  upper 

*Phil  Trans.,  A,  1897,  vol.  189,  p.  265. 


CH.  VIII.] 


OF   AN   ELECTRON 


85 


To  Earth. 


To 
Eiectrometer. 


FIG.  12. — A  represents  one  of  the  vessels  in  which  the  fog  is  formed 
whose  rate  of  fall  is  to  be  measured  by  Mr.  Wilson's  method :  it  is 
arranged  for  the  ionisation  produced  by  X-rays.  The  vessel  A,  con- 
taining some  water,  and  covered  by  an  earthed  aluminium  plate,  is 
in  communication  with  a  vessel  C  through  the  tube  B.  Inside  C  is  a  thin- 
walled  test-tube  P,  which  serves  as  a  piston  or  bell-jar  (shown  rather 
too  stumpy)  and  with  its  lip  always  dipping  under  water  like  a  gasometer. 
D  is  an  indiarubber  stopper  closing  the  end  of  tube  C :  the  lower  part 
of  the  tube  C  ought  to  be  shown  filled  with  water  to  such  a  height  that 
the  mouth  of  the  piston  is  always  below  the  surface.  A  glass  tube  con- 
nects the  inside  of  the  test-tube  P  with  a  space  E.  The  space  E  may 
be  put  in  connection  with  an  exhausted  s^ace  F  through  the  tube  H. 
The  end  of  the  tube  H,  inside  the  space  E,  is  ground  flat,  and  is  closed 
by  an  indiarubber  stopper  I,  which  is  kept  pressed  against  the  tube  H 
by  means  of  a  spiral  spring.  The  stopper  I  is  fixed  to  a  rod  K ;  by 
pulling  the  rod  down  smartly  the  pressure  inside  the  test-tube  is 
lowered,  and  the  piston  P  falls  rapidly  until  it  strikes  against  the 
indiarubber  stopper  D.  The  falling  of  the  piston  causes  the  gas  in 
A  to  expand  :  the  tubes  R  and  S  are  for  the  purpose  of  varying  the 
amount  of  the  expansion.  Before  an  expansion  the  piston  P  is  raised 
by  admitting  air  through  T,  which  is  then  closed.  Then,  when  every- 
thing is  ready,  K  is  pulled,  and  the  cloud  forms  in  A. 


86  DETERMINATION  OF  THE  MASS    [CH.  vm. 

surface,  a  clear  space  being  left  above  it  which 
gradually  increases  in  thickness  as  the  cloud  falls. 
The  rate  of  movement  of  the  top  of  the  cloud  will 
give  the  rate  of  falling  of  the  individual  globules  of 
which  it  is  composed.  And  this  brings  us  to  the 
next  section. 

Prof.  Stokes  and  Falling  Spheres. 

Many  years  ago,  in  1849,  Sir  George  G.  Stokes* 
discussed  the  motion  of  solids  through  fluids,  and 
among  others  of  a  sphere  moving  through  a  viscous 
fluid  urged  by  its  own  weight.  It  is  a  familiar  fact 
that  large  bodies  fall  through  air  or  water  or  any 
resisting  medium  more  quickly  than  small  ones  of 
the  same  shape.  Thus  coarse  sand  settles  down 
through  water  quicker  than  fine  sand,  and  the  finest 
powder  takes  a  very  long  time  to  settle ;  in  fact 
this  difference  of  the  rate  of  falling  is  used  as  a 
practical  process  of  separating  granular  materials  into 
sizes,  and  is  called  levigation. 

So  it  is  in  air  :  large  raindrops  fall  violently,  small 
raindrops  fall  gently,  and  mist  globules  hardly  fall 
at  all — fall  so  slowly  that  their  motion  is  difficult 
to  observe, — but  the  same  law  governs  all,  so  long 
as  the  motion  is  not  too  violent,  or  so  long  as  the 
falling  body  has  no  edges  such  as  will  cause  eddies 
during  the  fall.  A  sphere  falling  slowly,  controlled 
by  viscosity  alone  without  waves  or  eddies,  is  the 
simplest  case.  It  soon  reaches  what  is  called  a 
terminal  velocity — the  speed  at  which  the  viscous 
resistance  exactly  balances  its  weight.  At  this 
speed  it  is  subject  to  zero  resultant  force,  so  it 
simply  obeys  the  first  law  of  motion  and  moves  at 
a  constant  speed,  t  This  constant  speed  or  terminal 

*  Camb.  Trans.  Phil.  Soc.,  ix.  48.         t  Of.  Nature,  vol.  31,  p.  266. 


CH.  VIIL]  OF  AN  ELECTRON  87 

velocity   was   calculated  by   Sir   George    Stokes   for 
the  case  of  a  falling  raindrop  of  radius  r  as  follows  : 


9  viscosity  of  air' 

where  p  is  the  excess  density  of  the  sphere  over  the 
medium  it  moves  in ;  provided  there  is  no  finite 
slip  at  the  surface.  The  maximum  possible  effect 
of  surface  slip — which  will  occur  to  some  extent 
when  the  falling  globules  are  very  minute — is  to 
make  the  possible  terminal  velocity  half  as  great 
again :  in  other  words  to  convert  the  numerical 

2  1 

coefficient  -  into  -. 

This  simple  formula  gives  the  connexion  between 
the  rate  of  fall  of  any  small  rain  or  fogdrop  and  its 
size ;  and  by  observation  of  this  speed,  therefore, 
knowing  the  viscosity  of  air,  it  is  possible  to  calculate 
the  dimensions  of  the  falling  drops. 

J.  J.   Thomsons  Experiment  of  Counting. 

We  have  now  all  the  materials  ready  for  under- 
;  standing  the  experiment  to  be  performed,*  so  as  to 
count  the  ions  which  are  produced  in  air  under  the 
influence  of  Rontgen  rays,  or  which  have  been  produced 
from  a  negatively  electrified  surface  illuminated  with 
ultra-violet  light.  The  apparatus  for  the  former  is 
depicted  in  Fig.  12.  The  ionising  beam  of  X-rays 
enters  the  chamber  A  from  above,  through  an  earthed 
aluminium  lid  which  keeps  it  airtight. 

The  rate  of  leak,  which  must  be  observed  in  order 
to  calculate  N<m,  is  determined  by  connecting  the 
water  and  the  aluminium  plate  to  the  terminals  of 

*  Phil.  Mag.,  December,  1898,  and  December,  1899. 


88  DETERMINATION  OF  THE  MASS    [CH.  vm. 

an  electrometer  ;  a  sufficient  difference  of  potential 
being  maintained  between  them. 

And  now,  metrical  condensation  having  been  pro- 
duced by  the  expansion  appliance,  and  a  mist  formed, 
the  rate  of  its  fall  or  gradual  subsidence  can  be 
observed  by  looking  through  the  vessel  at  an  illumi- 
nated surface  ;  whence  by  Stokes's  theorem  the  size 
of  each  globule  is  known.  The  quantity  of  water 
which  had  gone  to  form  globules  is  known  from  the 
measured  amount  of  expansion,  by  a  process  the 
details  of  which  I  will  not  give  here  ;  and  so 
the  number  of  such  globules,  and  therefore  the 
number  of  their  condensation-centres  or  nuclei  or 
ions,  can  be  determined. 

If  c  is  the  observed  rate  of  fall  in  stagnant  air, 
the  linear  dimensions  of  the  falling  drops  will  be 

//9//c\         7/4  '5  x  '000  18 
r  =  V  WJ  =  Vi        981 


In  a  given  case  c  was  observed  to  be  0*14  centimetres 
per  second  ;  hence  the  volume  of  each  drop  was  in 
that  case  . 

-7rr3=l-6xlO-10c.c.  ; 
o 

and  so,  if  the  aggregate  amount  of  water  in  all  the 
drops  in  a  given  space  is  reckoned  from  the  measured 
amount  of  adiabatic  expansion  which  caused  the  chill 
and  the  precipitation,  the  drops  can  be  counted. 

Professor  Thomson,  a  few  months  later,  repeated 
this  experiment,  the  ions  being  now  produced  by 
illuminating  a  negatively  electrified  zinc  plate  with 
ultra-violet  light.  The  apparatus  used  is  shown  in 
fig.  13.  A  clean  zinc  surface  in  vacuo,  faced  by  a 
transparent  conductor  through  which  the  light  could 
shine  on  it,  and  by  a  window  of  quartz  which  makes 


CH.  VIII.] 


OF  AN  ELECTRON 


89 


the  vessel  airtight  so  that  it  might  be  exhausted  and 
yet  allow  the  ultra-violet  light  to  pass,  was  employed, 
and  connected  to  the  expansion  apparatus,  fig.  12, 
instead  of  the  vessel  A.  The  current  ~Neu  was 
measured  just  as  in  the  original  experiment. 


FIG.  13. — J.  J.  Thomson's  auxiliary  apparatus  for  the  counting  experi- 
ment. Ultra-violet  light  passes  through  the  quartz  plate  CD  and 
through  a  layer  of  liquid,  which  keeps  the  air  saturated,  and  which 
constitutes  one  electrode,  to  a  clean  zinc  plate  K,  which  constitutes  the 
other,  and  which  is  kept  negatively  electrified.  Connexion  through 
the  tube  L  is  made  with  the  expansion  apparatus  shown  in  fig.  12,  this 
being  employed  instead  of  the  vessel  A  in  that  figure.  Then  when 
the  sudden  measured  expansion  is  caused,  a  fog  is  condensed  round  the 
negative  ions  which  have  sprung  into  being  in  consequence  of  the 
electrons  thrown  off  by  the  ultra-violet  light;  and  the  rate  of  settling 
down  of  this  cloud  is  then  measured. 

A  great  many  precautions  must  be  taken,  because 
there  will  be  some  residual  cloud  found  even  when 
electrons  or  intended  nuclei  are  not  present.  Positive 
ions  and  other  stray  or  undesired  nuclei — if  present — 
can  be  eliminated  by  aid  of  their  different  behaviour. 
A  differential  observation  is  generally  necessary ; 


90  DETERMINATION  OF  THE  MASS    [CH.  vm. 

moreover  care  must  be  taken  to  ensure  that  all  the 
desired  nuclei  are  utilised,  and  not  only  a  portion. 

The  number  of  drops  found  in  a  certain  experiment, 
by  this  means,  was  about  30,000  to  the  cubic  centi- 
metre ;  the  total  quantity  of  water  which  went  to 
form  them  being  about  the  two-hundredth  part  of  a 
milligramme.  The  number  of  drops  is  of  course 
equal  to  the  number  of  nuclei.  Wherefore  the  nuclei 
are  counted. 

Result. 

The  result  of  the  execution  of  this  ingenious 
counting  process  is  that  the  absolute  charge  and  the 
absolute  mass  of  an  electron  are  at  length  directly 
determined.  Hitherto  we  have  determined  by  many 
and  various  ways  the  ratio  e/m  and  the  speed  u.  We 
have  likewise  been  able  to  determine  Neu  and  Ne 
and  Nm^2,  as  already  explained.  Now  at  length  we 
have  determined  N  ;  and  at  once  the  terms  in  the 
ratio  e/m  are  disentangled. 

e  comes  out,  as  suspected,  in  all  cases,  the  regular 
ionic  charge,  of  the  order  of  magnitude  3  x  10~10 
electrostatic,  or  10~20  electromagnetic  units.  Hence, 
while  m  comes  out  for  positive  carriers  and  for  all  ions 
the  appropriate  mass  of  the  atoms  present, — or  in 
some  cases  greater  than  this,  by  reason  of  the  forma- 
tion of  molecular  aggregates, — for  the  negative 
carriers  set  free  by  ultra-violet  light,  and  for  the  other 
cases  where  e/m=  107,  the  masses  come  out  definitely 
of  the  order  10~27  grammes;  or  about  -7-^0 th  part  of 
the  smallest  and  lightest  previously  known  quantity 
of  matter,  viz.,  an  atom  of  hydrogen. 

The  existence  of  masses  smaller  than  atoms  is 
thus  experimentally  demonstrated,  and  a  discovery 
clinched  of  epoch-making  importance. 


CHAPTER  IX. 

FURTHER   DETAILS    CONCERNING   ELECTRONS   AND 

IONS. 

Confirmatory  Measurements  of  Charge. 

A  CONFIRMATORY  measure  of  the  charge  e,  can  be 
made  by  first  observing  the  rate  of  fall  of  a  cloud 
condensed  round  the  ions  acting  as  nuclei — a 
measurement  which  gives  the  weight  w  of  each 
drop, — and,  then  applying  to  the  cloud  a  vertical 
electric  field  and  adjusting  its  strength  until  it  is  just 
able  to  check  the  fall  and  hang  the  drops  in  air  like 
Mahomet's  coffin.  For  under  these  conditions  of 
course  w  =  Ee,  and  since  everything  except  e  has  been 
measured,  e  is  at  once  known.  This  ingenious  pro- 
cess was  devised  by  Mr.  H.  A.  Wilson,  and  is 
described  by  him  in  the  Philosophical  Magazine  for 
April,  1903.  In  practice  the  above  would  be  slightly 
modified  and  a  simple  differential  method  employed. 
The  numerical  result  at  which  he  arrived  was  that 
the  value  of  e  =  3'I  x  10  ~10.  The  result  also  had  the 
effect  of  confirming  the  applicability  of  Stokes'  law, 
in  the  cases  where  fall  had  been  permitted. 

This  seems  to  be  the  value  obtained  for  the  electric 
charge  associated  with  every  kind  of  monad  ion,  both 
positive  and  negative,  as  well  as  for  the  separate 


92  ELECTRONS   AND   IONS  [CH.  ix 

electrons.  The  same  value  characterises  even  the 
molecular  aggregates  which  are  often  found  in 
conducting  air  or  other  gas. 

Fig.  14  shows  H.  A.  Wilson's  apparatus  for  sus- 
pending a  condensed  cloud  against  gravity  by  means 
of  a  known  electric  field.  The  magnet  M,  attracting 
its  keeper,  opens  connexion  with  an  injector  pump 
through  a  valve  V,  and  thereby,  through  the  action 
of  the  test  tube  T,  produces  a  measured  amount  of 
expansion — in  C.  T.  E.  Wilson's  manner — as  exhibited 
in  fig.  12.  The  expansion  could  subsequently  be 
measured  by  the  gauge  H. 

A  cloud  is  formed  in  the  bell-jar  B,  and  the  electric 
field  is  applied  between  the  plates  attached  to  the 
terminals  C  D,  kept  electrified  by  a  battery  of  a  great 
number  of  cells.  The  battery,  however,  was  only 
applied  after  the  cloud  had  formed,  otherwise  all  the 
ions  would  be  removed  from  the  vessel  by  electrolytic 
action.  Rontgen  rays  were  used  to  produce  the  ions, 
but  the  coil  exciting  the  rays  was  switched  off  and 
stopped,  by  means  of  an  automatically  working  switch 
S,  the  instant  before  the  valve  was  pulled  by  the 
magnet. 

J.  J.  Thomson  has  recently  repeated  his  original 
experiments,  and  by  combining  a  determination  of 
New  with  an  independent  velocity  measurement,  he 
has  made  what  is  now  regarded  as  a  standard  estimate 
of  e,  namely,  3'4  x  10~10  electrostatic  units. 

H.  A.  Wilson's  confirmation  of  this  by  a  totally 
different  method — the  Mahomet's  coffin  method — by 
which  he  finds  3'1  x  10~10,  has  already  been  mentioned. 

The  importance  of  obtaining  accuracy  in  these 
measurements  is  that  thereby  lies  our  chance  of 
determining  ra  with  accuracy — the  mass  either  of 
an  electron,  or  of  an  atom  of  matter. 


CH.  IX.] 


A   CHORD   EXPERIMENT 


93 


One  of  the  first  direct  determinations  of  the  aver- 
age charge  on  a  gaseous  ion  was  made  by  Professor 


H 


FIG.  14. 


Townsend  (Philosophical  Magazine,  February,  1898), 
his  method  consisting  in  bubbling  newly-prepared 
gas  through  water  and  measuring  the  charge  on  each 
droplet.  The  deduction  must  be  regarded  as  rather 


94  ELECTRONS   AND  IONS  [CH.  ix. 

hypothetical,  because  it  was  an  assumption  that  each 
droplet  contained  only  one  ion.  Nevertheless,  that 
appears  to  be  the  truth,  since  the  charge  found  on 
each  was  3  x  10~10  electrostatic  units. 

A  further  method  applied  by  Professor  J.  J.  Thom- 
son, and  described  in  the  Philosophical  Magazine  for 
March,  1903,  was  used  in  a  determination  of  the 
maximum  current  passing  between  electrodes  in 
ionised  air. 

It  may  possibly  be  of  assistance  to  some  if  we 
quote  here  an  explanatory  remark  drafted  by  Mr. 
G.  Owen  : 

Thomson's  Deductions. 

"  What  Professor  Thomson  succeeded  in  doing  was 
to  measure  the  charge  on  the  negative  ion  produced 
in  air  by  the  influence  of  Rontgen  rays.  The  ques- 
tion might  naturally  be  asked  :  What  grounds  had 
Professor  Thomson  for  drawing  a  general  conclusion 
concerning  the  mass  of  an  electron  from  a  deter- 
mination of  the  charge  on  an  ion  produced  in  air  by 
one  particular  agency? 

"  The  answer  is  as  follows :  The  negative  ions 
produced  in  a  gas  were  known  to  have  the  same 
properties  irrespective  of  the  source  of  their  pro- 
ductionf  For  instance,  the  negative  ions  produced 
by  X-rays,  radium  rays,  and  ultra-violet  light,  travel 
with  the  same  velocity  under  a  given  electric  force ; 
and  further,  behave  identically  with  regard  to  their 
power  of  acting  as  nuclei  of  condensation  for  super- 
saturated water-vapour.  It  was  therefore  justifiable 
to  assume,  in  the  first  place,  that  the  charge  on  an 
ion  produced  by  X-rays  was  equal  to  the  charge  on 
an  ion  produced  by  the  impact  of  ultra-violet  light 
on  a  metal  surface.  (This  conclusion  Prof.  Thomson 


CH.  ix.J  SIZE   OF  ELECTRON  95 

verified  later  on  by  direct  experiment.)     Again,  the 
& 

ratio  —  had  been  determined  for  the   cathode   ray 
m 

particles,  and  for  the  carriers  of  negative  electricity 
from  incandescent  filaments  and  from  metal  plates 
illuminated  by  ultra-violet  light  at  low  pressures, 
and  it  will  be  remembered  that  in  all  these  cases  the 

p 

same  value   of  —  was  obtained,  thereby  justifying 

the  surmise  that  the  charge  on  an  electron  was  the 
same  as  that  on  an  ion  produced  by  ultra-violet 
light,  and  therefore  the  same  as  on  a  negative  ion 
produced  by  X-rays." 

Estimate  of  Size. 

On  the  hypothesis  that  the  flying  or  vibrating 
fragment  is  a  material  corpuscle  charged  with 
electricity,  so  that  it  has  a  duplex  constitution  and 
a  compound  kind  of  inertia,  part  material  and  part 
electrical,  no  further  progress  can  be  made.  But  on 
the  hypothesis  that  the  flying  or  vibrating  particle  is 
an  electron — a  charge  of  electricity  and  nothing 
else — a  constituent  of  an  atom  but  with  no  material 
nucleus — so  that  the  whole  of  atomic  properties 
might  possibly  turn  out  to  be  due  to  an  aggregate 
of  electrons  of  opposite  sign,  of  which  one  or  two 
are  comparatively  free  and  detachable — on  this 
hypothesis  a  determination  of  the  mass  of  a 
corpuscle  carries  with  it,  as  a  consequence,  a  de- 
termination of  its  size  also. 

Because,  as  has  already  been  pointed  out,  any 
required  amount  of  self-induction  can  be  conferred  on 
a  wire  by  making  it  fine  enough,  and  any  required 
amount  of  energy  can  be  conferred  upon  an  electric 


96  ELECTRONS   AND   IONS  [CH.  ix. 

charge  by  making  it  concentrated  enough.  The 
energy  at  a  given  speed  of  motion  will  be  proportional 
both  to  the  quantity  and  the  potential,  and  the  latter 
can  be  made  as  great  as  we  please  by  making  the  size 
of  the  body  possessing  the  charge  extremely  small. 

It  is  the  intense  region  of  force  close  to  the  wire  or 
close  to  the  charged  particle  which  is  the  effective 
region  ;  and  so,  as  stated,  a  knowledge  of  the  mass  or 
kinetic  energy  at  a  given  speed  suffices,  on  a  purely 
electric  theory  of  matter,  to  determine  the  size  of  the 
electron  constituents  of  which  it  is  hypothetically 
composed.  For  whether  there  be  any  intrinsically 
material  inertia  or  not,  there  certainly  is  an  electrical 
inertia.  The  cause  of  it  in  the  electrical  case  is 
known  :  it  is  due  to  the  reaction  of  the  electric  and 
magnetic  fields  during  acceleration  periods,  and  is 
denominated  self-induction. 

Quite  possibly  there  is  no  other  kind.  Quite 
possibly  that  which  we  observe  as  the  inertia  of 
ordinary  matter  is  simply  the  electric  inertia,  or  self- 
induction,  of  an  immense  number  of  ionic  charges,  or 
electric  atoms,  or  electrons. 

This  is  by  far  the  most  interesting  hypothesis, 
because  it  enables  us  to  progress,  and  is  definite. 
The  admixture  of  properties — partly  explained,  viz. 
the  electrical,  partly  unexplained,  viz.  the  material — 
lands  us  nowhere ;  unless,  by  some  only  partially 
imagined  means,  we  were  able  to  estimate  how  much 
of  the  total  appertains  to  each  ingredient. 

The  mass  of  a  corpuscle  has  been  measured  as 
something  akin  to  j^Vo  °f  an  atom  of  hydrogen,  and 
its  charge  asJ'lO"10  electrostatic  unit.  Now  this 
amount  of  electricity  will  have  that  amount  of  inertia 
if  it  exists  on  a  sphere  of  radius  10~13  centimetre, 
but  not  otherwise.  Consequently  we  may  assume 


CH.  ix.]  SIZE   OF  ELECTRON  97 

the  size  of  the  supposed  pure  electron  to  be  of  the 
order  10~13  centimetre  in  diameter;  or  100*000  of 
the  linear  dimension  known  as  molecular  magnitude, 
viz.  10~8  centimetre. 

The   calculation  of  order   of  magnitude   is   quite 
simple,  for  all  ordinary  speeds  ;  because,  for  them 


,->i   a  =  —  .  pe  =  107  x  10~20  =  10~13  centimetre, 
m 

though  it  might  with  some  data  be  estimated  as  small 
as  10  ~14.*  Minuteness  like  that  easily  explains  the 
penetrating  power  of  cathode  rays.  Especially  if  the 
atoms  of  matter  are  themselves  composed  of  such 
minute  particles.  For  the  interspaces  will  be 
enormous  compared  with  the  filled-up  space,  and  a 
point  can  penetrate  far  into  such  an  assemblage 
without  striking  anything. 

Penetrability  of  Matter  by  Electrons. 

The  mean  free  path  of  a  particle  is  a  question  of 
probability.  In  a  space  containing  n^  obstacles  to  the 
unit  volume,  a  space  Ax  will  contain  n  =  Axnl  of 
them  ;  and  the  chances  of  a  collision,  while  one  of 
them  travels  a  length  x,  will  be  approximately  their 
combined  areas,  as  targets,  compared  with  the  total 
area  available  for  both  hit  or  miss  —  that  is  to  say, 

mra2       1.1  .,     o         x 

-  ;  which  we  may  write  px  or  -, 
A  x 

where  x  is  the  "  mean  free  path,"  or  average  distance 
travelled  by  any  one  particle  without  a  collision  with 
another,  and  ft  the  number  of  encounters  while 

*See  Lodge  in  the  Electrician  for  March  12,  1897,  vol.  38,  page  644, 
where  the  size  is  deduced  from  the  then  just  discovered  Zeeman  effect. 
L.E.  G 


98  ELECTRONS   AND   IONS  [CH.  ix. 

travelling  unit  distance.  But  in  saying  this  we  are 
ignoring  the  forces  between  the  particles,  as  well  as 
their  motion,  and  are  not  considering  a  swing  round 
as  a  collision. 

Nevertheless,  as  regards  order  of  magnitude — 

Ax         1         d* 

/yi  — .  _  

mra?     n^a"     tra2' 

where  d?  is  the  cubic  space  allotted  to  each  particle, 
while  £ iraz  is  the  actual  bulk  of  each. 
Therefore  approximately 

a; total  space  occupied 

a  ~~  a  few  times  the  aggregate  volume  of  the  particles* 

a  statement  roughly  analogous  to  Clausius'  or 
Loschmidt's  theorem  in  the  kinetic  theory  of  gases. 

Hence  the  mean  free  path  can  be  estimated  by 
considering  how  much  space  the  substance  of  all  the 
electrons  in  an  atom  occupies,  as  compared  with  all 
the  space  which  the  atom  occupies  itself.  In  other 
words,  we  have  to  consider  what  the  size  10~13  for  an 
electron's  diameter  means,  as  compared  with  the  size 
10"8  for  an  atom's  diameter.  In  the  solar  system  the 
diameter  of  the  earth  is  24^00th  part  of  the  diameter 
of  its  orbit  round  the  sun.  Consequently  if  the  earth 
represented  an  electron,  an  atom  would  occupy  a 
sphere  with  the  sun  as  centre  and  four  times  the 
distance  of  the  earth  as  radius. 

In  other  words,  if  an  average  atom  is  composed  of 
electrons,  they  are  about  as  far  apart  in  that  atom  in 
proportion  to  their  size  as  the  planets  in  the  solar 
system  are  in  proportion  to  their  size. 

In  an  atom  of  hydrogen  there  would  have  to  be 
roughly  1,000,  or  say  more  exactly  700,  electrons  in 
order  to  make  up  the  proper  mass. 


CH.  ix.]  SIZE    OF  ELECTRON  99 

In  an  atom  of  sodium,  which  is  twenty-three  times 
as  heavy,  there  must  be  about  15,000  electrons. 

And  in  an  atom  of  mercury  there  must  be  over 
100,000  electrons,  if  atomic  mass  be  wholly  due  to  them. 

Consider  then  an  atom  of  mercury  containing 
100,000  of  these  bodies  packed  in  a  sphere  10"8 
centimetre  in  diameter.  One  would  think  at  first 
they  must  be  crowded ;  but  there  is  plenty  of  room. 
Each  electron  is  only  10~13  centimetre  across,  and 
there  are  only  about  fifty  of  them  in  a  row  along  any 
diameter  of  the  atom,  whereas  there  might  be  a 
hundred  thousand  in  the  same  length ;  hence  the 
empty  space  inside  the  atom  is  enormously  greater 
than  the  filled  spaces.  At  least  a  thousand  times 
greater  in  linear  dimension,  or  a  thousand  million 
times  greater  in  bulk. 

The  whole  volume  of  the  atom  is  10~24  c.c.  ;  the 
aggregate  volume  of  all  the  electrons  composing  the 
atom  is  105  x  10~39  =  10~84  c.c. ;  consequently  the  space 
left  empty  is  1010  or  ten  thousand  million  times  the 
filled  space. 

Even  inside  an  atom  of  mercury,  therefore,  the 
amount  of  crowding  is  fairly  analogous  to  that  of  the 
planets  in  the  solar  system.  For  though  the  outer 
planets  are  spaced  further  apart  than  the  inner  ones, 
they  are  also  bigger,  to  practically  a  compensating 
extent. 

Now,  going  back  to  what  is  sometimes  called 
Loschmidt's  theorem  in  the  kinetic  theory  of  gases, 
obtained  roughly  above — 

mean  free  path 
^  diameter  of  particle 

volume  of  space  available  to  particles 
~  combined  volume  of  all  their  substance 


100  ELECTRONS   AND   IONS  [CH.  ix. 

—  we  have  reckoned  the  latter  fraction,  in  the  inside 
of  an  atom  of  mercury,  as  — 


=10 
" 


10 


100,000  x  |7r(lO-13)3     105  x  10'3 

Hence  the  mean  free  path  of  an  electron  inside 
an  atom  of  mercury  will  be  comparable  to  109  times 
the  size  of  an  electron,  i.e.,  it  will  be  10~4  centi- 
metre ;  that  is,  it  may  get  through,  on  the  average, 
the  substance  of  some  10,000  mercury  atoms  in  a 
row,  before  collision  with  anything. 

In  any  other  less  dense  substance  it  will  go 
further.  In  ordinary  air,  on  an  average  free  journey, 
it  would  escape  collision  with  a  hundred  million 
molecules  in  a  room,  which  would  be  equivalent  to 
a  distance  of  about  four  inches.  In  the  case  of 
corpuscles  plunging  into  a  dense  metal,  the  actual 
distance  achieved  by  them  is  very  small,  only  the 
thousandth  part  of  a  millimetre  on  the  average,  and 
it  need  by  no  means  necessarily  be  a  straight  line; 
so  a  target  of  platinum  succeeds  in  stopping  them 
very  near  its  surface,  and  enables  the  X-rays 
generated  by  the  shock  fairly  to  emerge.  Some 
corpuscles  will  be  stopped  more  suddenly  than  this, 
and  some  will  travel  further,  but  10~4  centimetre, 
or  the  thousandth  of  a  millimetre,  should  be  com- 
parable with  the  average  distance  travelled  in  a 
solid  as  dense  as  platinum. 

Effects  of  an  Encounter. 

This  distance,  however,  gives  no  notion  of  the 
value  of  the  negative  acceleration  during  a  collision, 
because  the  greater  part  of  that  thousandth  of  a 
millimetre  is  free  flight;  the  stoppage  occurs  only 
as  the  last  episode  of  that  flight,  viz.  at  the  instant 


CH.  ix.]  COLLISION  101 

of  collision.  The  colliding  masses  are  100,000  to  1, 
so  the  change  of  velocity  at  impact  could  be  esti- 
mated ;  but  the  impact  will  really  be  more  of  an 
astronomical  or  cometary  character,  and  the  effect 
is  analogous  to  the  entrapping  of  comets  when  they 
pass  near  a  planet,  thereby  rendering  them  per- 
manent members  of  the  solar  system. 

The  ordinary  behaviour  of  a  foreign  comet,  which 
comes  and  goes,  may  be  called  a  collision  with,  and 
rebound  from,  the  sun;  for  although  there  is  no  real  en- 
counter of  main  substance,  that  is  what  it  would  appear 
like  if  it  could  be  seen  from  the  depths  of  space  ;  and 
the  two  branches  of  the  comet's  hyperbolic  orbit  would 
look  like  straight  lines  of  approach  and  recession. 

Comets  which  happen  to  pass  very  near  a  planet, 
however,  are  deflected,  swirled  round,  and  often 
virtually  caught  by  that  planet,  receding  only  with 
an  insignificant  differential  velocity  which  is  unable 
to  carry  them  away  from  the  attraction  of  the  sun  : 
towards  which  they  then  drop.  If  they  do  not 
actually  drop  into  it,  they  will  continue  to  revolve 
round  it  in  an  elliptic  orbit,  becoming  a  member  of 
the  solar  system,  and  liable  ultimately  to  be  degraded 
into  a  swarm  of  meteors. 

This  is  the  sort  of  process  known  to  occur  in 
astronomy  ;  and  circumstances  not  unlike  that  may 
attend  the  encounter,  or  apparent  collision,  of  a 
furiously-flying  comet-like  electron  with  part  of 
the  massive  system  of  an  atom. 

The  stoppage,  therefore,  will  occur  well  within  the 
limits  of  atomic  magnitude,  10~8  centimetre;  and  so 

u2 
the  acceleration  will  be  of  the  order  —r  =  1026  c.g.s., 

and  the  force  needed  thus  to  stop  even  a  single 
electron  will  be  the  tenth  of  a  dyne. 


V 
102  ELECTRONS   AND  IONS  [CH.  ix. 

No  wonder  that  violent  radiation  -effects  are  pro- 
duced. The  "power"  required  to  stop  an  electron, 
flying  with  one-thirtieth  of  the  speed  of  light,  inside 
a  molecular  thickness,  can  be  estimated  thus — 

1  u 

energy  -f  time  =  -  DMT  .  ^7 

*— '  ff  *^ 

=  10-27(109)3108=  108  ergs  per  second  ; 
or  thus — 


=  10°  again, 
tt 

which  is  equivalent  to  ten  watts.     (Though  the  time 
it  lasts  is  only  the  10~17  part  of  a  second.) 

But  only  a  small  fraction  of  this  goes  into 
radiation.  The  radiating  power  can  be  estimated 
thus,  from  Larmor's  expression  for  it,  as  deduced  in 
Appendix  G, 

/xe2  10~40 

— -(u)2=      10  x  1062=  100  ergs  per  second. 

The  rest  therefore,  it  would  appear,  must  take  the 
form  of  heat. 

It  is  worth  considering  what  circumstances  would 
give  radiation  an  advantage  over  heat,  and  vice  versd. 
Because  sometimes  conspicuously  the  target  gets 
heated,  and  sometimes  X-rays  are  emitted.  Let  u 
be  the  speed  and  I  the  distance  of  stoppage,  then 


uz 


so  the  force  required  to  stop  it  is 


CH.  ix.]  COLLISION  103 

The  "  power  "  of  the  blow  is 


whereas  the  radiation  power  is— 

2    fu*V_pe*u*. 
'  \2l)  ~~=  6vP  ' 


,i       f       radiating  power     a   u     2a 

therefore  6F =  T  .  -  =  — , 

total  power         I    v     vt 

where  t  is  the  time  of  stoppage,  and  v  is  the  velocity 
of  light. 

Hence  effective  radiating  power  depends  chiefly  on 
very  sudden  stoppage,  and  on  the  speed  being 
near  that  of  light.  If  the  velocity  is  a  tenth  that 
of  light,  and  if  an  electron  can  be  stopped  in  some- 
thing like  its  own  diameter,  about  10  per  cent,  of 
the  energy  will  go  in  radiation,  and  the  rest  will 
take  other  forms,  presumably  heat.  But  it  would 
take  immense  "  power "  to  effect  such  a  stoppage  as 
that :  not  less  than  two  or  three  thousand  kilowatts 
for  each  electron.  So  probably  a  stoppage  within 
atomic  dimension  is  all  that  can  be  expected,  and 
that  could  be  managed  by  something  like  50  watts. 
But  then  an  exceedingly  small  fraction  of  the  whole — 
only  about  one  millionth — would  in  that  case  take 
the  form  of  X-rays ;  their  wave-shell  then  having  a 
thickness  comparable  with  molecular  magnitude : 
whereas  in  the  previous  case  it  was  incomparably 
thinner,  and  therefore  far  more  penetrating.  Both 
thicknesses  however  are  very  small  compared  with 
the  wave-lengths  of  ordinary  light. 

As  the  velocity  diminishes,  more  and  more  of  the 
energy  takes  the  form  of  heat ;    which  agrees  with 


104  ELECTRONS   AND   IONS  [CH.  ix. 

the   fact   that   at   moderate   vacua   the    target   gets 
red-hot. 

The  ratio  of  the  radiation  power  to  the  total  power, 
is  as  the  dimensions  of  an  electron  to  the  distance 
light  would  travel  during  the  period  of  the  stoppage  : 
taking  the  acceleration  as  uniform.  So  to  get  all 
the  energy  radiated  it  is  necessary  to  stop  a  pellet 
moving  with  a  tenth  the  speed  of  light  in  something 
like  a  tenth  of  its  own  diameter. 


CHAPTER  X. 

THE  ELECTRON  THEORY  OF  CONDUCTION 
AND  OF  RADIATION. 

MEANWHILE  the  probability  of  the  existence  of  elec- 
trons and  the  possibility  of  regarding  them  as  the 
basis  of  all  electric  and  of  most  other  material 
phenomena,  had  seized  hold  of  the  imagination  of 
several  mathematical  physicists,  notably  of  Professor 
H.  A.  Lorentz  and  of  Dr.  J.  Larmor.  The  former, 
who  was  first  in  the  field  (1892  and  1895),  was 
driven  in  this  direction  by  the  problem  of  the 
astronomical  aberration  of  light  and  the  optics  of 
moving  media  treated  from  the  electric  standpoint. 
The  latter  reached  the  same  goal  independently,  from 
the  dynamics  of  the  free  ether,  on  the  basis  of 
MacCullagh  and  Kelvin,  which  required  discrete 
mobile  sources  of  disturbance  (electrons)  as  a  basis  for 
development.  Both  these  philosophers  endeavoured 
to  trace  all  electric  properties  to  the  behaviour  of 
electrons,  usually  of  course  in  association  with 
material  atoms ;  while  Larmor's  procedure  also  im- 
pelled him  to  make  intelligible  by  conceptual  ' models' 
the  dynamical  possibility  of  a  structure  in  the  ether 
which  should  have  the  properties  of  an  electron, 
whether  positive  or  negative, — the  two  being  treated 
as  mirror  images  of  each  other — and  so  to  reduce  a 


106  CONDUCTION    AND   RADIATION        [CH.  x. 

great  part  of  Physics  to  its  simplest  terms.  This 
fine  attempt,  made  in  1894,  involved  definite  illus- 
trative conceptions — of  the  structure  of  an  electron, 
of  its  size  on  the  theory  that  inertia  is  entirely 
electric,  of  the  velocities  with  which  electrons  revolve 
in  the  molecule,  and  generally  of  an  electronic 
theory  of  matter :  but  in  absence  of  knowledge  the 
mass  of  an  electron  was  then  naturally  assumed 
comparable  with  that  of  a  hydrogen  atom.  A  great 
amount  of  suggestive  material  is  to  be  found  in 
Dr.  Larmor's  contributions  to  the  Transactions  of  the 
Koyal  Society  for  1894,  5,  7 ;  some  of  them  were 
summarised  in  the  book  called  Ether  and  Matter 
published  by  the  Cambridge  University  Press  in 
1900. 

Suffice  it  here  to  say  that  the  electron  constitutes 
the  basis  of  the  whole  treatment,  and  that  there  is 
supposed  to  be  no  true  electric  current  except  electrons 
in  motion.  They  may  move  with  the  atoms,  as  in 
the  electrolysis  of  liquids ;  they  may  fly  alone,  as  in 
rarefied  gases ;  or  they  may  be  handed  on  from  one 
fixed  atom  to  the  next,  as  in  the  process  of  conduction 
in  solids. 

Conduction. 

The  possible  modes  of  conduction  or  transmission 
of  electricity  are  in  fact  three,  which  I  may  call 
respectively  the  bird-seed  method,  the  bullet  method, 
and  the  fire-bucket  method. 

The  bird-seed  method  is  adopted  in  liquids  and 
usually  in  gases  of  ordinary  density ;  it  is  exempli- 
fied in  electrolysis ;  the  bird  carries  the  seed  with 
it,  and  only  drops  it  when  it  reaches  an  electrode. 

The  bullet  method  is  the  method  in  rarefied  gases, 
as  has  been  clearly  realised  by  aid  of  the  cathode 


CH.  x.]  CONDUCTION  107 

rays :  the  space  near  the  cathode  represents  the  length 
between  the  breech  and  the  muzzle  of  the  gun,  and 
the  rest  of  the  path  is  analogous  to  the  trajectory 
of  a  bullet.  When  the  projectile  strikes  an  atom  the 
shock  may  cause  it  to  pass  another  on,  and  so 
continue  the  convection. 

The  fire-bucket  method  must  be  the  method  of 
conduction  in  solids,  where  the  atoms  are  not  sus- 
ceptible of  locomotion  and  can  only  pass  electrons 
on  from  hand  to  hand ;  oscillating  a  little  in  one 
direction  to  receive  them,  and  in  another  direction 
to  deliver  them  up,  and  so  getting  thrown  gradually 
into  the  state  of  vibration  which  we  call  heat. 
But  it  may  be  observed  that  this  need  for  motion, 
in  order  to  pass  electrons  on,  becomes  less  and  less 
according  as  the  body  is  less  subject  to  the  irregular 
molecular  disturbance  we  call  heat.  It  may  be  the 
expansion  and  molecular  separation,  or  it  may  be 
the  irregular  jostling  and  disturbance,  that  impede 
easy  conduction ;  but  certainly  conduction  improves 
as  temperature  falls,  and  transmission  becomes  quite 
easy  at  very  low  temperatures.  The  conduction  of 
heterogeneous  alloys  is  a  less  simple  matter,  being 
probably  mixed  up  with  back  E.M.F.  developed  at 
innumerable  junctions, — otherwise  it  would  be  in- 
structive to  examine  the  effect  of  low  temperature 
on  the  conductivity  of  a  metal  which  did  not 
contract  with  cold. 

The  extra  conductivity  of  hot  electrolytes  is  a 
totally  different  phenomenon  :  it  is  not  true  conduc- 
tion, but  convective  locomotion  of  ions,  in  their 
case.  The  same  effect  of  temperature  which  lessens 
their  viscosity  increases  their  conductivity. 

Insulators  are  bodies  where  conduction  can  only  be 
accomplished  with  violence.  Metals  are  bodies  in 


108  CONDUCTION   AND   RADIATION       [CH.  x. 

which  the  transfer  of  an  electron  from  one  atom  to 
another  is  easy,  demanding  no  force  as  long  as  the 
process  is  not  hurried — a  process  of  the  nature  of  a 
diffusion.  The  transmission  of  vibrations  along  a 
chain  of  connected  molecules  may  well  occur  through 
a  not  dissimilar  kind  of  connection ;  and  hence  the 
conduction  of  electricity  and  the  conduction  of  heat, 
though  really  different  processes,  may  have  many 
points  in  common. 

A  fair  approximation  to  the  phenomena  of  con- 
duction in  metals  has  been  worked  out  in  detail  by 
Riecke,  Drude,  Thomson,  Lorentz,  and  many  others ; 
in  which  the  electrons  are  supposed  to  remain  free 
for  periods  so  long  that  their  mean  energy  of  motion 
is  a  function  of  the  temperature,  as  in  gas-theory. 

Most  is  known  about  electrolytic  and  gaseous 
conduction.  In  gaseous  conduction  the  negative 
electrons,  when  free,  fly  fast ;  whereas  the  ions 
generally,  and  all  the  positive  charges,  travel  more 
slowly  by  reason  of  their  association  with  matter. 

In  liquid  conduction  charges  of  either  sign  are 
always  associated  with  atoms,  and  travel  only  as 
ions,  at  a  slow  diffusion  rate  which  was  calculated 
by  Kohlrausch,  has  been  observed  directly  by  myself,* 
Mr.  Whetham  and  others,  and  is  well  known. 

The  rate  of  transmission  in  solids  can  only  be 
inferred,  and  it  would  appear  from  the  Hall  effect  (see 
Larmor,  Phil.  Trans.,  Aug.  1894,  p.  815),  as  if  in 
one  class  of  solids  the  positive  were  able  to  travel 
fastest,  whereas  in  another  class  negative  travelled 
fastest :  a  difference  which  is  familiar  in  liquids.  In 
acids,  for  instance,  the  positive  charges  travel  much 
the  quickest,  because  they  are  associated  with  light 

*  Lodge,   British  Association   Report,   Birmingham   Meeting,    1886, 
pp.  389-413. 


CH.  x.]  RADIATION  109 


and  presumably  small  hydrogen  atoms ;  and  it  is 
owing  to  the  comparatively  easy  migration  of  the 
light  or  small  hydrogen  atom  that  acids  are  in 
general  such  good  conductors. 

The  Hall  magnetic  bend,  like  Faraday's  magnetic 
rotation,  is  a  differential  effect,  and  would  be  zero 
if  positive  and  negative  were  equally  acted  upon.  In 
gases  it  is  differential  too,  but  there  the  negative 
charges  are  liable  to  be  so  free  as  compared  with 
the  positive,  and  to  be  so  conspicuous,  that  the  Hall 
effect  in  gases,  especially  in  rarefied  gases,  is  very 
great  in  comparison  with  the  small  residual  effects 
found  in  liquids  and  solids.  Consequently  the 
effect  of  a  magnet  in  curving  the  path  of  cathode 
rays  in  a  Crookes  tube  is  readily  demonstrated. 

Radiation. 

But  it  is  not  only  the  progressive  motion  or  loco- 
motion of  the  electric  atomic  appendages  that  we 
have  to  consider ;  we  must  assume  also  that  they 
are  susceptible  of  motion  in  the  atom  itself,  either 
vibrating  like  the  bead  of  a  kaleidophone,  or  re- 
volving in  a  minute  orbit  like  an  atomic  satellite. 
Indeed  it  is  to  the  concerted  vibrations  or  revolu- 
tions of  the  system  of  electrons,  in,  or  on,  or  round, 
an  atom,  that  its  radiating  power  is  due.  Matter 
alone  has  no  perceptible  connection  with  the  ether, 
a  fact  which  is  proved  in  my  paper  in  the  Philo- 
sophical Transactions  for  1893  and  1897;*  it  is 
electric  charge  which  gives  it  any  connection,  and 
even  then  it  has  no  viscous  connection — there  is  no 
connection  that  depends  upon  odd  powers  of  velocity, 
so  as  to  be  of  the  nature  of  friction, t — it  is  purely 

*  Lodge,  Phil.  Trans.,  vol.  184,  pp.  727-804,  and  vol.  189,  pp.  149-166. 
t  See  especially  Phil.  Trans.,  vol.  189,  p.  164. 


110  CONDUCTION  AND  RADIATION        [CH.  x. 

accelerative  connection ;  it  is  only  when  the  charge 
vibrates,  and  during  its  accelerative  periods,  that  it  is 
able  to  influence  the  ether  at  a  distance  by  emission  of 
waves.*  These  waves  consist  probably  of  alternations 
of  shear,  with  no  motion  of  the  ether  as  a  whole, 
but  only  a  to-and-fro  quiver  of  its  equal  opposite 
constituents  over  some  excessively  small  amplitude  : 
a  kind  of  motion  which  constitutes  what  we  know  as 
radiation.  It  is  not  the  atom  pulsating  as  a  whole 
which  disturbs  the  ether,  but  the  pulsations  or 
vibrations,  or  the  startings  and  stoppings  and 
revolutions,  of  its  electric  charge.  Acceleration  of 
electric  charge  is  the  only  known  mode  of  originat- 
ing ether  disturbance.  But  normal  or  centripetal 
acceleration,  involving  nothing  more  than  change  of 
direction,  is  just  as  effective  as  actual  change  of 
speed.  If  an  electric  charge  is  able  to  describe  a 
small  orbit  four-hundred-billion  times  a  second,  it 
will  emit  the  lowest  kind  of  visible  red  light. 
This  number  of  revolutions  is  equal  to  the  number 
of  seconds  in  about  fourteen  million  years,  or  in 
the  time  since  some  early  geologic  period.  If 
it  revolves  faster  it  will  emit  light  of  higher  re- 
frangibility ;  and  the  particular  kind  of  radiation 
emitted  by  the  atom  of  any  substance,  when  in  a 
fairly  free  state,  will  depend  on  the  orbital  period 
of  its  electrons,  if  they  could  be  considered  as  inde- 
pendent. But  if  that  were  so,  every  atom  would  soon 
radiate  itself  to  destruction.  The  condition  that  an 
atom  must  fulfil  in  order  to  have  a  chance  of  survival 
by  retaining  its  energy,  was  given  by  Larmor  (Phil. 
Mag.,  Dec.  1897)  in  the  form  that  the  vector  sum  of 
the  accelerations  of  all  its  electrons,  with  due  regard 
to  their  signs,  should  be  permanently  null.  This 

*  See  Chaps.  I.  and  IX.,  also  Appendix  G. 


CH.  x.]  MAGNETISED   RADIATION  111 

further  condition  is  quite  consistent  with  those 
imposed  by  dynamics. 

Every  frequency  of  rotation  will  correspond  to  a 
definite  line  in  the  spectrum.  But  if  this  be  its  real 
cause,  radiation  must  be  susceptible  to  magnetic 
influence,  for  a  revolving  electric  charge  consti- 
tutes a  circular  current ;  and  if  a  magnetic  field  be 
started  into  existence  with  its  lines  threading  that 
circuit,  it  must,  while  it  is  changing  in  intensity,  cause 
the  speed  either  to  increase  or  to  decrease,  and  so 
will  either  raise  or  lower  the  refrangibility.  If 
electrons  are  revolving  in  every  direction,  and  if  a 
magnetic  field  is  applied  to  them,  then  during  the  rise 
of  the  field  the  pace  of  some  will  be  increased  and  of 
some  decreased ;  and  this  increase  or  decrease  will  not 
stop  until  the  magnetic  field  is  destroyed  again. 

Hence  it  would  appear  that  if  a  source  of  radiation 
is  put  into  a  magnetic  field,  and  its  lines  examined 
with  a  spectroscope,  they  should  be  affected,  either 
by  way  of  shift  or  broadening,  or  in  some  other  way. 
It  happened,  however,  that  when  Dr.  Larmor  theo- 
retically perceived  this,  and  estimated  the  order  of 
magnitude  of  the  effect  to  be  expected,  he  made  the 
assumption  natural  in  1895  that  an  electron  was 
comparable  in  mass  with  a  hydrogen  atom.  On  this 
assumption,  knowing  what  he  did  about  the  massive- 
ness  of  an  atom,  he  calculated  that  the  effect  would 
be  too  small  to  see ;  indeed,  Faraday  had,  with 
imperfect  appliances  many  years  ago,  looked  for  some 
such  effect — not  then  guided  by  theory,  but  simply 
with  the  object  of  trying  all  manner  of  experiments — 
and  had  failed  to  see  anything ;  Prof.  Tait  also  had 
been  moved  by  theory  in  the  same  direction,  but  no 
fresh  experimental  attempt  to  examine  the  question 
was  initiated.  Nor  was  the  matter  publicly  referred 


112  CONDUCTION    AND   RADIATION        [CH.  x. 

to  until,  as  hinted  above,  Zeeman  of  Amsterdam,  in 
1897,  with  a  good  grating  and  a  strong  electromagnet, 
skilfully  observed  a  minute  effect,  consisting  in  a 
broadening  of  the  lines  emitted  by  a  sodium  flame 
placed  between  its  poles.  On  seeing  a  two-line 
notice  of  this  in  Nature  in  December,  1896,  Dr. 
Larmor  wrote  to  me,  saying  that  this  must  be  the 
effect  which  he  had  thought  of,  but  concluded  must 
be  too  small  to  see.  On  receiving  this  intimation 
I  immediately,  with  a  little  trouble,  repeated  and 
verified  the  experiment,*  and  exhibited  it  at  the 
Royal  Society  soire'e  in  May  that  same  year. 

From  this  simple  but  important  beginning  the 
large  subject  of  the  influence  of  a  magnetic  field  on 
the  radiation  from  different  substances  has  been 
laboriously  worked  at ;  not  only  by  the  original 
discoverer,  but  by  Preston  in  Dublin,  Michelson  in 
America,  Runge,  and  others ;  and  a  whole  series  of 
important  facts  have  been  made  out.  Every  line  has 
been  studied  separately ;  some  lines  are  tripled,  some 
quadrupled,  some  sextupled,  and  so  on — as  said  above. 
One  mercury  line  is  resolved  into  nine  or  perhaps  eleven 
components.  The  effect  is  therefore  not  too  small  to 
see,  though  it  needs  excessively  high  power  and  per- 
fect appliances  to  display  it ;  and  so  it  became  evident 

*  See  Proc.  Roy.  Soc.t  vol.  60,  pp.  466,  513,  and  vol.  61,  p.  413,  or  Nature, 
vol.  56,  p.  237  ;  also  several  articles  by  Lodge  in  The  Electrician,  for  1897, 
vol.  38.  The  whole  matter  is  elucidated  by  Zeeman,  aided  by  Lorentz, 
on  the  basis  of  theory  illustrated  by  a  picture  or  model  of  an  orbitally 
revolving  electron,  which,  though  crude,  was  adequate  as  a  guide  :  the 
small  mass  of  the  revolving  particle  being  thereby  deduced,  and  being 
in  general  conformity  with  J.  J.  Thomson's  direct  determinations  of 
the  mass  of  an  electron  some  months  previously.  With  higher  ex- 
perimental power  greater  precision  was  reached,  and  an  unexpected 
development  appeared  in  the  tripling  of  each  line,  a  result  which  was 
suggested  by  the  model,  but  could  not  have  been  predicted  from  it 
alone.  Other  lines  were  found  to  divide  into  more  than  three  com- 
ponents, in  a  very  suggestive  but  still  imperfectly  understood  manner, 


CH.  x.]  ZEEMAN   EFFECT  113 

that  if  radiation  were  due  to  moving  electrons,  their 
motion  could  not  be  handicapped  by  having  very 
much  matter  associated  and  moving  with  them.  It 
became  possible,  indeed,  by  making  a  measurement 
of  the  amount  of  doubling  undergone  by  the  lines  in 
a  given  field,  to  ascertain  how  much  matter  was 
associated  with  the  revolving  electric  charge  in  any 
given  case ;  in  other  words,  to  make  a  determination 
of  the  electrochemical  equivalent  effective  in  radi- 
ation— i.e.,  of  the  ratio  m/e.  Indeed,  Professor 
Zeeman,  with  considerable  skill,  had  made  a  rough 
determination  of  this  kind  at  a  very  early  stage,  when 
he  only  saw  the  effect  as  a  slight  broadening  of  the 
sodium  lines ;  and  had  come  to  the  conclusion  that  the 
electrochemical  equivalent  was  quite  different  from 
that  appropriate  to  electrolysis,  being  some  thousand 
times  smaller.  He  found,  in  fact,  that  the  ratio  e/m 
had  in  this  case  also  the  notable  value  already 
suspected  in  connection  with  cathode  rays,  viz.,  the 
value  107  c.g.s. 

More  recent  measurements  have  confirmed  this 
estimate,  and  shown  that  the  ratio  of  charge  to 
matter  in  the  Zeeman  case  is  practically  identical 
with  the  ratio  of  charge  to  matter  in  the  cathode  ray 
case ;  in  other  words,  that  whatever  is  flying  in  the 
cathode  rays  is  vibrating  in  a  source  of  radiation ;  and 
that  if  the  cathode  rays  consist  of  moving  electrons, 
radiation  is  due  to  vibrating  or  revolving  electrons. 
The  more  the  details  of  the  Zeeman  effect  are 
studied,  the  clearer  it  becomes  that  the  electron 
theory  attributed  to  it  from  the  first  by  Zeeman  and 
H.  A.  Lorentz,  as  well  as  by  FitzGerald  and  Larmor 
in  England,  is  satisfactory,  though  not  as  yet 
fully  and  completely  worked  out. 

One  of  the  earliest  publications  in  England,  both 

L.E.  H 


114  CONDUCTION   AND   RADIATION         [CH.  x. 

of  the  fact  and  of  its  elementary  theory,  is  that  given 
by  the  present  writer  in  two  articles  in  the 
Electrician  for  February  and  March,  1897,*  which 
are  worth  referring  to  as  representing  incipient  ideas 
on  the  subject  before  the  full  significance  was  grasped. 
The  high  value  of  the  e/m  ratio,  viz.,  ^x  107  c.g.s., 
or  fifty  million  coulombs  per  gramme,  instead  of  the 
moderate  electrolytic  value,  is  spoken  of  on  page  643 
as  a  difficulty  ;  and  a  FitzGerald  suggestion  amounting 
virtually  to  the  beginnings  of  an  electron  theory  of  the 
Zeeman  effect  is  hinted  at.  Likewise  an  extremely 
short  way  of  expressing  the  theory  of  the  motion  is 
given  by  the  writer,  in  the  following  form  : 

Consider  the  resolved  part  of  any  orbital  motion 
projected  on  to  a  plane  normal  to  the  applied  magnetic 
field  H  ;  and  let  the  angular  velocity  be  o>,  at  any 
point  of  an  orbit  where  the  radius  of  curvature  is 
r  ;  then  the  field  will  exert  a  radial  component  — 


which  will  represent  an  increment  or  decrement  of 

centripetal  force  -,  /        2\ 

a  (mrur)  ; 

whence  it  follows,  to  a  first  approximation  of  order  of 
magnitude,  that  —  TT 

doo=  ±  —  -  —  , 

2m  ' 

and  the  change  of  frequency  caused  by  the  magnet- 
isation in  the  transverse  components  of  the  radiation 
will  therefore  be  — 


4-Trm' 


The  other  or  longitudinal  component  of  the  original 
orbit  will  manifestly  be  unchanged.     This  is  far  from 

*  See  Lodge,  Electrician,  vol.  38,  pp.  568  and  643. 


CH.  x.]  ZEEMAN   EFFECT  115 

being  a  complete  and  satisfactory  theory,  unless  the 
projected  motion  happen  to  be  circular ;  but  it  was  a 
brief  and  early  attempt. 

An  instructive  and  interesting  method  of  demon- 
strating the  Zeeman  effect  was  devised  by  W.  Konig 
and  described  in  the  Jubilee  volume  of  Wiedemann's 
Annalen,  1897,  of  which  a  brief  abstract  is  given  in 
Nature,  vol.  57,  p.  402.  An  emission  flame  con- 
taining the  salt  under  examination  is  placed  in  a 
strong  magnetic  field,  and  viewed  through  an  absorp- 
tion flame,  containing  the  same  salt,  by  means  of  a 
doubly-refracting  prism,  or  other  double  image  instru- 
ment, so  as  to  get  two  images  of  the  emission-flame 
side  by  side.  On  exciting  the  magnet,  the  emission 
frequency,  of  vibrations  perpendicular  to  the  lines  of 
force,  is  put  out  of  tune  with  the  absorption  frequency, 
and  accordingly  the  amount  of  absorption  is  much 
diminished.  The  result  is  that  one  of  the  images 
brightens  up  every  time  the  magnet  is  excited ;  the 
other  image,  which  corresponds  to  vibrations  along 
the  lines  of  force,  remaining  unchanged  and  constitut- 
ing a  convenient  standard  of  brightness. 


CHAPTER  XL 

FURTHER  DISCUSSION  OF  THE  ELECTRON  THEORY 
OF  THE  MAGNETISATION  OF  LIGHT  AND  DE- 
TERMINATION OF  THE  m/e  RATIO  IN  RADIATION. 

AMONG  the  early  contributions  that  have  been  made 
to  the  theory  of  moving  charges,  few  are  more 
remarkable  than  those  of  Dr.  Johnstone  Stoney  in 
connection  with  the  process  of  radiation,  long  before 
there  had  been  any  experimental  verification  of  the 
separate  existence  of  these  electrons,  or  of  the  fact 
that  the  emission  of  light  from  a  substance  is  due 
to  their  motion.  Dr.  Stoney  had  treated  them  in 
an  astronomical  manner,  in  1891,  dealing  with  an 
electron  moving  round  an  atom  as  if  it  were  a 
satellite  moving  round  a  planet,  and  had  discussed 
the  various  perturbations  to  which  they  might  be 
subject,  and  the  effect  of  those  perturbations  on  the 
spectrum  of  the  light  emitted.* 

One  of  the  simplest  kinds  of  perturbation,  fully 
analysed  by  Newton  for  the  motion  of  the  moon, 
is  what  is  called  a  progression  or  recession  of  the 
apses,  being  a  slow  revolution  of  the  orbit  in  its  own 
plane.  Such  a  motion  was  shown  to  be  able  to 

*  "  On  the  Cause  of  Double  Lines  and  of  Equidistant  Satellites  in 
the  Spectra  of  Gases."  G.  Johnstone  Stoney,  Transactions  of  the  Royal 
Dublin  Society,  iv.,  1888-92,  pp.  563-608. 


CH.  XL]          MAGNETISATION   OF   LIGHT  117 

originate  a  doublet  in  the  spectrum ;  for  of  the  two  com- 
ponent circular  vibrations  into  which  the  motion  can  be 
analysed,  one  has  been  made  more  rapid  and  therefore 
its  light  raised  in  refrangibility,  the  other  has  been 
made  slower  and  therefore  lowered  in  refrangibility. 

Another  closely  allied  kind  of  perturbation, 
analogous  to  precession  of  the  equinoxes  in  the  case 
of  the  earth,  would  result  in  a  triplet  in  the  spectrum. 
This  precessional  motion  occurs  in  an  orbit  subject  to 
any  oblique  pull  or  deflecting  force.  Instead  of 
yielding  directly  to  that  pull,  its  effect  is  to  make  the 
axis  describe  a  kind  of  cone,  the  kind  of  motion 
that  one  sees  in  an  inclined  spinning-top  :  the  pull  of 
gravity  on  a  spinning- top  does  not  make  it  topple 
over,  but  makes  it  precess.  So  also  with  a  hoop  or 
bicycle  when  not  vertical :  instead  of  tumbling,  it 
turns  round  and  round  in  a  circuit,  as  long  as  its 
motion  continues ;  only  falling  when  the  motion 
ceases,  or  falls  below  a  certain  critical  value.  Hence 
if  the  orbit  of  an  electron  were  subjected  to  an 
oblique  or  deflecting  force,  the  effect  would  be,  not 
to  place  it  directly  in  the  desired  position  per- 
pendicular to  a  line  of  force,  but  to  cause  it  to 
precess.  And  this  motion  might  be  analysed  into 
three  components, — the  accelerated  and  retarded 
circular  orbits  above-mentioned,  which  would  result 
in  a  doubling  of  the  line,  and  a  third  component, 
viz.  the  one  parallel  to  the  axis,  which  would  be 
unchanged  and  would  therefore  represent  a  spectral 
line  in  its  old  position,  the  centre  of  a  group  of 
three.  All  this  was  clearly  perceived  in  connection 
with  Dr.  Zeeman's  discovery,  with  the  assistance  of 
his  great  compatriot  the  eminent  physicist,  H.  A. 
Lorentz ;  whose  theory  was  in  several  respects 
anticipatory  of  the  experimental  results. 


118  MAGNETISATION   OF  LIGHT          [CH.  XL 

It  must  be  observed  that  the  light  emitted  by  the 
oscillation-components,  above  spoken  of,  will  be  all 
of  one  definite  kind,  due  to  vibrations  in  one  definite 
direction,  and  will  therefore  be  polarised.  The  kind 
of  polarisation  must  depend  on  the  aspect  from  which 
the  light  is  seen.  If  seen  at  right  angles  to  the  axis 
of  precession,  all  three  lines  should  be  plane  polar- 
ised— the  middle  line  at  right  angles  to  the  other 
two.  If,  however,  it  be  looked  at  along  the  axis  of 
precession,  then  there  should  be  no  middle  line ; 
because  the  axial  vibration  would  then  be  end- on,  in 
which  direction  it  produces  no  optical  effect ;  and  the 
two  side  lines  would  be  circularly  polarised. 

Fig.  15  consists  of  diagrams  illustrative  of  the 
changes  caused  in  a  spectrum  line  by  application  of  a 
powerful  magnetic  field  to  the  source  of  radiation. 

/  represents  a  specially  simple  case.  The  cad- 
mium line  A,  seen  by  rays  travelling  along  the 
lines  of  force,  resolves  itself  into  two  lines  B  and  C 
which  are  circularly  polarised  in  opposite  directions. 
This  is  due  to  the  acceleration  of  one  circular 
component  of  the  rectilinear  or  elliptical  vibration 
and  the  equal  retardation  of  the  other  component. 

//  represents  the  same  simple  line  seen  by 
light  travelling  across  the  lines  of  force.  In  that 
case  the  line  becomes  triple  ;  and  if  A  had  been 
plane  polarised,  B  and  C  are  polarised  in  a  plane 
at  right  angles  to  that  of  A'.  This  is  due  to  a 
precessional  movement  of  the  plane  of  the  orbital 
motion,  the  axial  vibration  continuing  unchanged, 
and  the  two  at  right  angles  being  one  accelerated 
and  the  other  retarded. 

///  and  III1  represent  the  effect  of  a  magnetic 
field,  applied  to  a  sodium  source,  on  the  con- 
stituents of  the  yellow  sodium  double-line.  Dx  is 


CH.  XL]          MAGNETISATION   OF   LIGHT 


119 


resolved  into  a  quartet,  and  D2  into  a  sextet,  when 
the  light  travels  across  the  magnetic  field. 

Directly  Zeeman  had  demonstrated  the  fact  that  a 
magnetic  field  applied  to  a  source  of  light  was  able 
to  act  as  a  perceptible  perturbing  cause,  Professor 
Lorentz  was  at  once  able  to  predict  the  main  part  of 
that  which  has  been  here  stated, — about  the  tripling 
of  the  line  seen  sideways  to  the  lines  of  force,  and 
the  doubling  of  the  line  seen  endways, — with  all  the 
polarisations  as  just  stated ;  because  the  lines  of 


n 


tt 


FIG.  15. 

magnetic  force  constitute  the  precessional  axis.  And 
all  these  effects  were  shortly  afterwards  seen  by 
Zeeman  and  others,  and  are  characteristic  of  the 
simplest  circular  orbit. 

As  already  stated,  the  full  meaning  of  these  very 
exquisite  phenomena  is  still  very  far  from  being 
unravelled.  The  most  general  theoretical  result  is 
that  of  Larmor  (Phil.  Mag.,  Dec.  1897)  that  for  any 
atomic  system,  however  complex,  if  the  effectively 
moving  electrons  are  all  negative,  while  the  attraction 
of  the  positive  on  them  is  centrical,  each  line  will  be 
divided  into  three,  exactly  as  in  the  provisional  theory 
of  Zeeman  and  Lorentz. 


120  MAGNETISATION   OF  LIGHT          [CH.  XL 

At  first  sight  one  might  be  inclined  to  suppose 
that  the  orbits  would  all  face  round  and  set 
themselves  normal  to  the  lines  of  force,  like  so 
many  circular  currents ;  but  that  is  to  forget  the 
inerbia  of  the  travelling  electron.  It  is  manifest  that 
since  a  revolving  electron  constitutes  a  circular 
current,  its  tendency  will  be  to  set  itself  with  its 
plane  normal  to  the  lines  of  force ;  but  since  by 
hypothesis  the  revolving  electron  has  inertia,  the 
current  will  not  so  set  itself,  but  will  yield  to 
the  deflecting  force  in  an  indirect  manner,  as  a  top 
does ;  or  as  the  oblate  spinning  earth  does — as 
explained  by  Newton  in  the  Principia, — the  axis  of 
rotation  having  a  conical  motion  round  the  lines 
of  force:  a  motion  which  is  called  "the  precession 
of  the  equinoxes"  in  the  case  of  the  earth,  and 
"  the  Zeeman  effect "  in  the  case  of  a  radiating  atom. 

This  is  an  account  of  the  chief  part  of  the  Zeeman 
effect,  and  may  be  regarded  as  the  most  fundamental 
kind  of  disturbance  caused  by  a  magnetic  field  on  a 
source  of  radiation.  But  there  may  be  other  minor 
disturbances,  just  as  in  the  case  of  the  earth,  whose 
axis  is  not  only  subject  to  precession,  but  also  to 
nutation — a  nodding  movement  superposed  upon  the 
main  motion.  It  is  also  quite  possible  for  the  middle 
line,  or  for  the  two  outer  lines,  or  indeed  for  all  three 
lines,  to  be  doubled ;  thus  giving  rise  not  to  the 
standard  triplet,  but  to  a  quartet  or  a  quintet  or 
even  a  nonet, — appearances  seen  and  photographed 
by  Zeeman,  Preston  and  others.  The  remarkable 
*  echelon '  spectroscope  of  Michelson  has  been  in- 
vented just  in  time  for  application  to  phenomena 
of  this  kind — its  special  function  being  the  close 
examination  in  detail  of  a  minute  portion  of  a 
spectrum  otherwise  produced. 


CH.  XT.]          MAGNETISATION   OF   LIGHT  121 

Even  the  two  constituents  of  the  double  sodium 
line  behave  differently,  when  the  source  is  magnet- 
ised and  the  light  thus  examined — as  illustrated  in 
fig.  15  :  one  of  the  sodium  lines,  D2,  which  had 
appeared  only  broadened  to  Zeeman  at  first,  really 
becomes  a  sextet.  The  other  sodium  or  Dx  line 
becomes  a  quartet ;  and  a  complete  study  of  the 
behaviour,  under  magnetism,  of  all  the  lines  and 
groups  of  lines  given  by  different  substances  must 
result  in  a  great  extension  of  our  knowledge  in  many 
directions  ;  in  fact  it  is  hardly  too  much  to  say  that 
the  discovery  of  Zeeman,  in  the  light  of  the  theory  of 
Lorentz,  has  doubled  the  power  of  spectrum  analysis 
to  throw  light  upon  the  processes  of  radiation  and  the 
properties  of  atoms,  and  has  opened  up  a  new  branch 
of  physics — a  new  department,  as  it  were,  of  atomic 
astronomy,  with  atoms  and  electrons  instead  of 
planets  and  satellites. 


CHAPTER  XII. 
INCREASE  OF  INERTIA  DUE  TO  VERY  RAPID  MOTION. 

THE  hypothesis  to  which  we  have  been  led  is  that 
the  inertia  of  an  electron  is  wholly  of  an  electrical 
character,  and  is  explained  by  the  known  magnetic 
effect  of  an  electric  charge  in  motion,  and  the  con- 
sequent reaction  to  any  change  in  that  motion. 

Usually  inertia  is  treated  as  constant  and  quite 
independent  of  speed ;  but  now  arises  the  question 
whether  the  distribution  of  charge  on  a  charged  body, 
together  with  its  lines  of  force,  will  remain  constant 
and  unaltered  while  the  body  is  rapidly  moving ; 
because  if  the  distribution  of  lines  of  force  is  altered, 
then  the  inertia  due  to  their  lateral  motion  will 
probably  be  altered  too.  This  can  be  made  plain 
after  referring  back  to  Chap.  II. 

Thus,  for  instance,  imagine  that  the  lines  of  electric 
force  of  a  body  in  motion  became  more  concentrated 
towards  the  axis  or  line  of  motion ;  the  effect  would 
be  at  once  to  diminish  the  lateral  component  of  their 
motion,  therefore  to  diminish  the  magnetic  force  which 
that  lateral  component  causes,  and  thus  to  diminish 
the  apparent  or  electromagnetic  inertia  of  the  moving 
charge. 

On  the  other  hand,  if  the  lines  opened  out  and 
became  concentrated  towards  the  equator,  or  plane 


€H.  XIL]         EFFECT   OF   RAPID   MOTION  123 

normal  to  the  line  of  movement,  then  a  greater 
component  of  their  motion  would  be  of  a  kind 
suitable  to  excite  a  magnetic  field ;  moreover,  both 
the  fields  would  by  this  concentration  increase  in 
intensity,  and  the  inertia  would  increase. 

Thus,  then,  it  may  be  possible  that  electric  inertia 
may  depend  in  some  fashion  on  speed,  a  thing 
unknown  in  ordinary  mechanics.  I  do  not  say 
that  such  dependence  must  be  untrue  in  ordinary 

!  mechanics ;  on  the  contrary,  I  feel  reasonably  san- 
guine that  it  will  be  found  true  for  matter  also, 
when  moving  sufficiently  fast — say  over  a  thousand 
miles  a  second, — though  it  is  unlikely  that  it  can 
have  a  practical  influence  in  any  actual  known  case 
of  rapid  movement  in  astronomy.  But  however  this 

l  may  be,  there  is  no  doubt  that  theory  points  to  an 
increase  of  electro- magnetic  inertia  at  excessively 
high  speeds,  and  Mr.  Heaviside  long  ago  calculated 
its  amount. 

It  will  be  observed  that  when  a  charge  moves, 
it  generates  circular  magnetic  lines  of  force.  Now 
these  magnetic  lines  are  not  stationary,  but  are  them- 
selves moving  at  the  same  rate  as  the  body ;  hence 
they  generate  fresh  electrostatic  lines,  i.e.,  cause  an 

j  electric  displacement  away  from  the  axis,  which  dis- 
placement is  superposed  upon  the  original  radial 
displacement  (away  from  or  toward  the  centre)  due 
to  the  charge. 

At  ordinary,  at  even  violent  speeds,  this  second- 
order  electric  effect  is  insignificant,  but  it  is  there  all 
the  time,  and  must  not  be  ignored  when  the  speed 
becomes  extravagantly  high.  It  rapidly  rises  into 
prominence  when  the  speed  approaches  the  velocity  of 
light,  but  at  any  speed  much  smaller  than  this  such  a 
second-order  effect  is  negligibly  small. 


124  INCREASE   OF   INERTIA  [CH.  XIL 

Its  effect  will  be,  as  the  annexed  figure  shows,  to 
alter  the  arrangement  of  the  lines  of  force,  making 
them  move  away  from  the  poles  and  concentrate 
towards  the  equator  of  the  charged  sphere,  when 
the  speed  is  very  great ;  ultimately  becoming  wholly 
concentrated  upon,  or  parallel  to,  the  equatorial 
plane,  in  the  limit ;  if  the  speed  could  attain  that  of 
light.  And  the  electric  lines  of  force  would  then 
be  opened  out  into  a  fan  or  equatorial  brush,  like 
the  spokes  of  a  wheel  which  is  rushing  furiously 
along  an  elongated  axle,  the  circumference  of  the 


FIG.  16. — A  is  the  charge,  AB  its  line  of  motion,  and  AE  its  electric  force 
in  a  certain  direction  when  stationary ;  EF  is  the  magnetically  induced 
electric  component  due  to  the  motion  and  AF  is  the  resultant  electric 
force  which  replaces  the  original  force  AE.  The  magnetic  force,  to  the 
motion  of  which  EF  is  due,  is  perpendicular  to  the  paper,  and  is  itself 
caused  by  the  motion  ;  hence  EF  is  a  quantity  of  the  second  order  and 
is  small  for  speeds  distinctly  less  than  that  of  light. 

wheel  representing  the  direction  of  the  magnetic 
field ;  but  this  very  condensation  so  intensifies  the 
field  as  to  make  the  inertia  ultimately  infinite. 

It  might  be  supposed  that  rearrangement  of  the 
lines  means  that  the  distribution  of  the  charge  itself 
is  altered  by  the  motion,  so  that  all  the  charge  is 
concentrated  upon  the  equator,  whence  the  lines 
of  force  would  start  normal  to  the  surface  as  usual. 
There  are  many  difficulties  about  such  a  conception 
however  (see  Appendix  K),  and  it  is  easier  to 
suppose  that  the  charge  retains  its  distribution  un- 
altered, on  the  surface  of  the  sphere,  and  that  each 
line  of  force  starts  from  its  original  point ;  but  that 


€H.  xii.]  DUE   TO    RAPID   MOTION  125 

it  starts  no  longer  in  a  direction  perpendicular  to 
the  surface,  when  it  is  in  rapid  motion,  but  sets 
out  obliquely,  with  a  deflexion  towards  the  equator, 
so  as  to  give  the  arrangement  above  described ; — like 
trunks  of  trees  on  a  cliff  or  landslide  which  preserve 
their  roots  in  situ  and  gradually  adjust  their  growth 
to  the  vertical  direction  without  being  any  longer 
perpendicular  to  the  soil. 

As  a  matter  of  fact  the  question  all  depends  on 
what  hypothesis  we  make  as  to  the  intrinsic  struc- 
ture of  the  electron.  If  we  liken  it  to  a  perfectly 
conducting  body  with  an  electric  charge,  the  charge 
must  be  confined  to  its  surface ;  and  it  may  be 
proved,  as  Heaviside  did.  that  the  distribution  will 
remain  uniform  (cf.  Larmor,  dEther  and  Matter, 
p.  154).  Or  it  might  be  likened  to  a  solid  globe 
of  uniform  electrification.  It  may  be  something  of 
which  we  have  as  yet  no  conception :  but  the 
experiments  of  Kaufmann  probably  suffice  to  prove 
that,  whatever  the  structure  is,  it  is  symmetrical 
around  a  centre,  after  the  general  manner  of  a 
stratified  spherical  distribution. 

On  the  other  hand  these  considerations  can  be 
avoided  by  treating  the  charge  merely  as  a 
geometrical  point  from  which  the  lines  of  force 
emanate,  and  ignoring  its  size  or  possible  conducting 
power.  This  is  the  keynote  of  I/armor's  treatment 
throughout  his  book  ^Ether  and  Matter,  and  also 
in  his  earlier  papers  :  in  dealing  with  atomic  structure 
it  implies  that  the  electrons  in  the  atom  are  at 
distances  apart  which  are  great  compared  with  their 
radii.  Cf.  the  fundamental  investigation  of  Chapter 
XL  to  be  referred  to  below.  We  could  hardly  tell 
a  priori  which  treatment  would  best  correspond 
with  fact,  but  it  will  turn  out  (see  Chap.  XIII.)  that 


126  INCREASE   OF  INERTIA  [CH.  XIL 

this  second  method  of  treatment  is  not  only  simpler 
but  that  it  is  adequate  to  existing  knowledge,  enabling 
numerical  results  to  be  obtained  which  are  singularly 
concordant  with  experimentally  measured  results. 

In  any  case  an  indication  of  the  mode  of  attack 
can  be  suggested  thus  : 

The  magnetic  force  due  to  motion  is  proportional 
to  the  speed  of  the  motion.  The  secondary  electro- 
static force  due  to  the  motion  of  this  magnetic  field 
is  likewise  proportional  to  the  same  speed.*  Hence 
the  disturbance  of  the  original  uniform  electrostatic 
field  will  be  of  the  second  order,  u2/v2  ;  and  when- 

*The  value  of  the  magnetic  force  at  any   point  P,   with  polar 
coordinates  rf6,  due  to  a  charge  e  flying  with  speed  U,  is 

TI_ 


and  is  in  rings  round  the  line  of  motion  u.     It  is  not  shown  in  the 
diagram  because  it  is  perpendicular  to  the  paper,  through  P. 

Q 


FIG.  17. 


The  electric  force  generated  or  induced  by  motion  across  this 
magnetic  field  —  which  is  necessarily  at  right  angles  to  the  direction  of 
motion  —  is  fiRu  ;  and  in  this  case  is  therefore  equal  to 


This  is  the  secondary  or  induced  E.M.F.,  to  be  superposed  at  every 
point  on  the  primary  or  direct  electric  force  of  the  charge  itself  along 
the  line  eP,  namely  e/Kr2  ;  and  it  is  in  the  direction  PQ,  being  perpen- 
dicular both  to  the  magnetic  field  and  to  the  motion.  So  the  ratio  of 
the  induced  to  the  original  E.M.F.,  at  every  point  in  a  direction  0, 
reckoned  from  the  charge  and  axis  of  motion,  is 


sin  0,    which  equals  —  sin  0. 


In   consequence   of  this  the  original  direction  of  the  stationary 
electric  field,  eP,  is  displaced  or  tilted  into  a  position  such  as  eQ. 


CH.  xu.]  DUE   TO   RAPID   MOTION  127 

ever  we  can  afford  to  neglect  quantities  of  this  order,, 
the  field  and  therefore  the  inertia  of  the  moving 
charge  will  continue  practically  constant. 

But  when  its  speed  of  motion  begins  to  approach 
the  velocity  of  light,  say  even  no  more  than  TVth 
of  that  speed,  then  a  perceptible  disturbance  is 
to  be  expected,  and  something  like  a  1  per  cent, 
increase  of  inertia  must  occur. 

The  complete  investigation  makes  the  inertia 
infinite  when  the  speed  reaches  that  of  light  (see 
Appendix  K),  but  there  is  probably  no  need  to 
press  this  to  extremes,  unless  the  charge  were  an 
absolute  point ;  clearly,  however,  the  inertia  will 
!  then  be  very  great,  and  possibly  therefore  it  may 
always  be  impossible  to  make  matter,  or  at  least 
charged  matter,  move  with  a  speed  greater  than 
that  of  light.  There  may  be  ways  out  of  this, 
j  however,  just  as  it  is  possible  for  a  bullet  to  move 
through  air  with  a  velocity  greater  than  that  of 
sound.  This  is  managed  by  the  violent  adiabatic 
condensation  of  the  air  in  front  of  such  a  bullet, 
the  effect  being  to  raise  the  appropriate  velocity  of 
sound  to  the  required  value ;  and  by  the  ridge  behind 
it  where  discontinuity  makes  its  appearance.  It  seems 
unlikely  that  the  ether  can  adjust  itself  to  excessive 
speed  beyond  the  speed  of  light  without  a  change  of 
structure  akin  to  what  would  be  rupture  in  the  case 
of  a  material  medium. 

It  has  been  shown  both  by  Mr.  Heaviside  and 
by  Prof.  J.  J.  Thomson  that  if  the  speed  of  motion 
is  ever  greater  than  that  of  light,  the  fan  or  radial 
plane  of  lines  of  force  bends  backwards  and  becomes 
a  conical  surface,  gradually  closing  up  as  the  speed 
further  increases  :  in  accordance  with  the  analogy  of 
the  conical  surface  of  discontinuity  aforesaid,  which 


128  INCREASE   OF   INERTIA  [CH.  xn. 

travels  with  a  sufficiently  rapid  bullet,  and  is  demon- 
strated in  Mr.  Boys'  bullet  photographs. 

No  known  speed  which  exists  in  ordinary  matter 
is  sufficient  to  bring  any  variation  of  inertia  into 
prominence.  The  quickest  available  carriage  is  the 
earth  in  its  journey  round  the  sun,  19  miles  a  second, 
or  60  times  faster  than  a  cannon  ball ;  but  the 
earth's  velocity  is  only  the  10000  of  the  speed  of 
light,  and  consequently  any  spurious  inertia  due 
to  its  orbital  motion  is  only  1  part  in  a  hundred 
million  ;  and  even  the  accuracy  of  astronomy  could 
not  display  an  effect  of  that  order  of  magnitude. 

There  are  a  very  few  stars  which  move  200  miles 
a  second,  but  even  these  have  only  one-tenth  per 
cent,  of  the  speed  of  light,  and  the  excess  inertia 
will  be  only  1  part  in  a  million.  The  only  known 
place  where  charges  or  charged  atoms  were  known, 
prior  to  1903,  to  move  at  speeds  greater  than  this, 
was  in  a  vacuum  tube.  There  the  cathode-propelled 
particles  are  flying  20,000  miles  a  second  or  T]^n 
the  speed  of  light,  and  they  may  have  1  per  cent, 
excess  inertia ;  or  more  if  they  can  be  persuaded  to 
go  still  faster. 

But  higher  speeds  are  now  known,  being  obtained 
in  the  spontaneous  emission  of  electrons  and  atoms 
by  radio-active  materials ;  so  it  becomes  of  the 
greatest  interest  to  determine  the  constants,  and 
especially  the  inertia,  for  rays  of  this  kind. 


CHAPTER  XIII. 
JUSTIFICATION  FOE  ELECTRIC  THEOEY  OF  INERTIA, 

BUT  first  we  must  ask,  what  justification  is  there 
for  the  view  that  each  of  the  isolated  corpuscles,  on 
which  measurements  have  been  made,  is  a  purely 
electrical  corpuscle  or  electron  without  material 
nucleus,  all  of  whose  properties  are  to  be  explained 
in  accordance  with  purely  electric  and  magnetic 
laws  ?  Then  we  may  proceed  to  discuss  the  further 
extraordinarily  far-reaching  hypothesis — first  tenta- 
tively put  forward  by  Larmor  in  1894,  Phil.  Trans., 
vol.  185A,  p.  813,  with  mechanical  illustration  of  a 
purely  ethereal  structure  for  such  an  electron — that 
the  electrons  constitute  matter,  that  atoms  of  matter 
are  composed  of  electric  charges,  that  the  funda- 
mental inertia-property  of  matter  is  identical  with 
self-induction. 

There  is  the  reasonable  philosophical  objection  to 
postulating  two  methods  of  explaining  one  thing.  If 
inertia  can  be  explained  electrically,  from  the  pheno- 
mena of  charges  in  motion,  it  seems  needless  to 
require  another  distinct  cause  for  it  also.  But  this 
is  not  all  that  can  be  said ;  it  is  quite  possible  that 
direct  experimental  proof  will  be  forthcoming  before 
long.  One  method  suggested  by  Professor  J.  J. 
Thomson,  for  examining  the  nature  of  the  corpuscles, 


L.E. 


130  ELECTRIC  THEORY  OF  INERTIA    [CH.  xm. 

had  reference  to  the  proportion  of  radiation  to  thermal 
energy  developed  when  corpuscles  encounter  a  target 
which  suddenly  stops  them.  In  so  far  as  they  consist 
of  non- electric  matter  they  would  produce  only  heat 
by  their  dead  collision,  without  any  direct  generation 
of  ethereal  waves ;  in  so  far  as  they  consist  of  elec- 
tric charges  they  would  disperse  a  certain  amount  of 
radiation  energy ;  and  so  the  proportion  of  radiation 
to  heat  might  afford  a  criterion.*  Hitherto,  however, 
no  adequate  measurements  have  been  made  in  this 
direction. 

But  there  is  another  more  likely  avenue  to  a  con- 
clusive result.  We  have  seen  that  when  an  electric 
charge  moves  with  a  speed  approaching  that  of  light, 
its  inertia  is  theoretically  no  longer  constant,  but 
rapidly  increases  and  becomes  infinite  when  the 
light- velocity  itself  is  reached ;  and  rather  complicated 
and  different  expressions  for  this  high-speed  inertia 
have  been  calculated  by  several  mathematical  physi- 
cists, on  different  views  of  the  constitution  of  the 
electron.  See  Appendix  K  for  a  discussion  of  this 
difficult  subject.  It  is  possible  that  this  fact  will 
give  us  the  necessary  clue. 

For  in  certain  cases  of  the  production  of  cathode 
rays,  or  at  any  rate  of  beta  rays,  a  speed  not  far 
short  of  that  of  light  is  reached,  and  in  such  cases 
the  effects  of  the  increased  inertia  can  be  observed. 
Such  an  experimental  determination  has  been  quite 
recently  undertaken  and  executed  with  great  skill 
by  Dr.  Kaufmann,t  who  employed  the  method  indi- 
cated above  (Chap.  V.)  of  comparing  simultaneously 
the  electric  and  the  magnetic  deflexion  of  the  same 
set  of  rays  from  a  speck  of  radium  submitted 

*See  J.  J.  Thomson,  Phil.  Mag.,  April,  1899,  p.  416. 
tSee  Comptes  Rendus  for  October  13,  1902. 


CH.  XIIL]          VARIATION   OF   INERTIA  131 

simultaneously  to  an  electric  and  a  magnetic  field 
coincident  in  direction.  As  a  matter  of  fact  the 
speck  gives  off  rays  of  various  speeds,  which  are 
differently  deflected  into  a  thin  streak  like  a 
comet's  tail  (see  fig.  18) :  and  it  is  the  faint 
impression  they  make  on  a  photographic  plate  in 
high  vacuum  that  is  measured  and  gives  the  data. 
Thus  the  velocity  and  the  e/m  ratio  are  both 
known,  and — to  summarise  briefly  the  result — 
Kaufman n  concluded  that  when  the  speeds  ap- 
proached perceptibly  near  the  velocity  of  light,  the 
electrochemical  equivalent  m/e  increased  by  just 
the  amount  required  in  accordance  with  pure  electric 
theory — the  theory  which  attributes  the  whole  of 
inertia  to  electric  influence.  There  appeared  to  be 
no  quantitative  room  for  any  extra  inertia,  such 
as  that  of  an  inert  particle  of  non-electric  matter 
travelling  with  each  projectile,  retaining  its  inertia 
constant  at  all  speeds,  and  so  contributing  nothing  to 
the  rise  of  inertia  perceived  when  the  speed  approaches 
within  hail  of  that  of  light. 

We  will  now  enter  more  into  detail  concerning  this 
important  matter. 


Proof  of  the  purely  electrical  nature  of  the  inertia 
of  the  ft  particles  shot  out  by  Radium. 

There  is  every  reason  to  believe  that  the  /3  rays 
emitted  by  radium  are  identical  with  the  cathode 
rays  observable  in  a  vacuum  tube ;  for  both  consist 
of  a  multitude  of  electrons  or  corpuscles  travelling  at 
excessively  high  speed ;  and  if  a  determination  be 
made  of  this  speed  and  of  the  electro-chemical  equiva- 
lent for  the  case  of  P  rays — for  instance,  by  the 


132  ELECTRIC  THEORY  OF  INERTIA   [CH.  xm. 

method  of  subjecting  them  both  to  magnetic  and  to 
electrostatic  deflexions,  which  is  the  easiest  way — the 
numbers  come  out  quite  similar  to  the  number 
obtained  for  cathode  rays,  viz.,  for  m/e  the  value 
10  ~7  in  E.M.  units,  and  for  u  something  of  the  order 
109  centimetres  per  second. 

But  radium  under  favourable  conditions  is  found 
to  shoot  out  its  particles  with  a  speed  exceeding  even 
this,  and  in  some  cases  to  approach  within  hail  of 
the  limiting  speed,  the  velocity  of  light.  This  is 
the  very  important  result  obtained  by  the  German 
physicist  W.  Kaufmann,  who  has  made  an  admirable 
series  of  determinations  of  speed  and  of  electro- 
chemical equivalent  for  this  case.  The  importance 
of  obtaining  these  excessively  high  speeds  should  be 
obvious,  for  thereby  we  are  enabled  to  test  the  elec- 
trical theory  of  inertia.  Theoretically  the  inertia  at 
high  speeds  is  not  constant,  but  increases  according 
to  a  complicated  but  calculated  law ;  we  cannot 
suppose  that  the  electric  charge  varies  in  any 
way  with  motion ;  hence  the  electrochemical  equiva- 
lent m/e  is  proportional  simply  to  the  mass,  and 
ought  to  be  a  function  of  the  velocity  u,  nearly 
constant  for  ordinary  values,  but  increasing  rapidly 
as  it  approaches  within  hail  of  the  velocity  of 
light. 

To  obtain  numerical  values  we  may  apply  the 
theory  developed  by  Mr.  Heaviside  and  by  Prof.  J. 
J.  Thomson,  with  regard  to  the  increase  in  momentum 
of  a  flying  electric  charge,  over  and  above  the  natural 
mu  value,  with  m  considered  constant,  which  is  the 
value  at  all  ordinary  speeds. 

The  formula  which  the  latter  used  for  the  purpose 
of  numerical  calculation  is  one  of  those  given  in  his 
Recent  Researches ;  it  is  quoted  in  his  American 


CH.  xm.]  VARIATION   OF   INERTIA  133 

Lectures    on    Electricity    and    Matter,    p.    44,    as 

/•»    11 

mu  =  electric  momentum  = 


where  sin  0  =  ^/-y  ;  and  we  may  express  it  in  a  fairly 
simple  form  thus  : 

The  momentum  of  a  particle  of  electricity  moving 
at  excessive  speed  is  greater  than  the  momentum 
of  the  same  particle  estimated  on  the  hypothesis 
that  its  mass  is  constant,  in  a  numerical  ratio  given 
by  the  following  expression  ;  where  the  ratio  of  the 
speed  to  that  of  light,  u/v9  is  expressed  as  the  sine 
of  a  certain  angle  0  : 


4  sm20  sin  20 

We  will  call  this  the  ratio  <£(#).  It  is  the  measure 
of  the  spurious  or  extra  inertia  due  to  rapid  motion  ; 
the  ratio  of  the  mass  at  speed  u  to  the  stationary 
mass.  We  may  also  write  it,  rather  more  conveniently 
perhaps  for  calculation,  thus  : 

3l~~2GOs20      2°        2  ~  COS  2e 


l-cos20~sin20     l-cos20/ 

Now   the   highest  speeds  measured  by  Kaufmann 
were  such  as  the  following  : 

2'36,  2'48,  2-59,  272,  2*85  times  1010  cm.  per  sec. 

while  the  speed  of  light  is  well  known  to  be  3*0  x  1C10 
cm.  per  sec.  ;  so  the  ratios  u/v,  corresponding  to  the 
above  observed  speeds,  are  respectively 

787,  '817,  '863,   '907,  '95. 

These  numbers  therefore  represent  the  values  of  sin  #, 
to  be  inserted  in  the  above  formula  for  obtaining  the 


134  ELECTRIC  THEORY  OF  INERTIA   [CH.  xm. 

theoretical  ratio  </>  (0) ;  namely,  the  ratio  which 
expresses  the  number  of  times  the  mass  of  an  electric 
charge,  at  specified  high  speed,  exceeds  its  mass  at 
low  or  zero  speed. 

The  successive  values  of  <£(#)  come  out,  according 
•o  J.  J.  Thomson,  for  the  above  set  of  velocities, 

1-5,   1'66,  2*0,  2-42,   3'1, 

and  these  are  what  must  be  compared  with  direct 
observation  or  measurement  of  the  apparent  or 
effective  mass  in  each  case. 

Now  the  corresponding  values  observed  experi- 
mentally by  Kaufmann  for  these  same  quantities — that 
is  to  say  the  factor  by  which  the  moving  mass 
exceeded  the  same  mass  when  stationary — were 

1'65,   1*83,  2-04,  2'43,  3'09, 

showing  a  very  remarkable  degree  of  approximate 
agreement  between  experiment  and  theory, — especi- 
ally at  the  higher  speeds. 

Thus  at  the  highest  speed  ever  yet  observed  for 
what  may  be  called  a  particle  of  matter,  at  any  rate 
for  an  electron — namely  2*85  x  1010  cm.  per  sec.  or 
six  hundred  million  miles  per  hour — the  mass  of  the 
particle  is  three  times  as  great  as  its  usual  value ; 
and  naturally  its  momentum  and  energy  are  increased 
in  the  same  proportion. 

Such  a  surprising  agreement  as  the  above,  between 
theory  and  observation,  removes  from  my  mind  all 
reasonable  doubt  as  to  the  truth  of  the  hypothesis 
that  the  inertia  of  electrons  is  electrical  inertia. 
I  regard  this  closeness  of  agreement  as  specially 
surprising,  for  it  was  not  the  first  deduction  of  the 
experimenter,  W.  Kaufmann,  himself:  his  deduction 
rather  was  that  the  electrical  mass  constitutes  about 
one-third  or  one-fourth  of  the  whole;  but  then  he 


CH.  XIIL]          VARIATION   OF   INERTIA  135 

used  another  formula  for  calculating  it  (given  in 
Appendix  K),  which  assumes  that  the  charged  body 
behaves  like  a  conducting  sphere.  But  when  the 
correct  deductions  from  the  Heaviside  expressions 
above  referred  to  were  applied,  with  the  collaboration 
of  M.  Abraham,  results  practically  equivalent  to  the 
above  were  obtained.  The  above  agreement  is  attained 
by  Professor  J.  J.  Thomson,  who  applied  his  own 
theory  to  the  results  of  Kaufmann,  working  it  out  on 
the  assumption  that  the  charge  behaves  like  an  actual 
point. 

If  it  is  to  be  urged  in  future  that  an  electron 
contains  a  material  nucleus  in  addition  to  its  electric 
charge,  the  burden  of  proof  rests  with  those  who 
maintain  that  thesis.  The  hypothesis  which  now 
holds  the  field  is  the  purely  electrical  one. 

But  it  must  be  remembered  that  this  is  not  the 
same  thing  as  establishing  an  electrical  theory  for 
all  matter.  The  inertia  of  an  electron  is  purely 
electrical,  but  what  about  the  inertia  of  an  atom  ? 
Who  knows  that  the  atom  is  wholly  composed  of 
electrons  ?  We  do  not  know  that  as  yet. 

Nevertheless  we  are  now  in  a  very  central  chapter 
of  modern  physics,  and  it  is  desirable  to  enter  into 
the  matter  somewhat  more  in  detail  than  in  the 
above  preliminary  sketch. 


CHAPTER  XIV. 

MORE  ADVANCED  DEVELOPMENT  OF  THE  COM- 
BINED ELECTRIC  AND  MAGNETIC  DEFLEXION 
METHOD  FOR  MEASURING  VELOCITY  AND  MASS 
OF  THE  PARTICLES  IN  COMPOUND  RAYS. 

THE  methods  given  in  Chaps.  V.  and  VI.  and  Chap. 
IX.,  for  measuring  u  and  e/m,  made  the  determina- 
tion look  very  simple,  if  the  precaution  is  taken  of 
having  the  apparatus  in  vacua,  so  as  to  eliminate 
the  troublesome  conducting  power  of  the  air  and 
obtain  the  electric  deflexion  undiluted,  as  J.  J. 
Thomson  first  found  feasible.  But  then  the  simple 
theory,  there  given,  assumed  that  the  quantities  to 
be  measured  were  constant,  and  that  the  deflexion 
to  be  observed  in  each  case  was  a  single  deflexion 
capable  of  accurate  measurement ;  but  this  is  often 
far  from  being  the  case,  since  the  velocities  of  the 
particles  differ ;  and  when,  as  in  the  case  of  radium, 
some  of  the  speeds  approximate  to  that  of  light,  it  is 
impossible  that  it  can  be  the  case,  for  the  inertia  itself 
then  changes  in  a  complicated  way  with  the  speed 
and  must  be  treated  as  variable.  It  is  easy  to  forget 
that,  because  it  is  an  unusual  feature  in  mechanics. 
So  the  deflexion  cannot  be  a  simple  deflexion,  the  rays 
must  be  fanned  out  as  it  were  into  a  spectrum  (see 
fig.  18);  and,  since  this  spectrum  is  continuous, 


CH.  xiv.]  RADIUM   RAYS  137 

it  will  possess  no  features  which  enable  anything 
like  measurement  to  be  made  on  it,  unless  some 
still  further  ingenious  device  be  employed,  such  as, 
for  instance,  that  of  Kundt  for  making  experiments 
on  anomalous  dispersion. 

The  experiments  of  W.  Kaufmann  at  Gottingen 
were  conducted  after  this  very  fashion,  and  may  be 
summarised  thus: — an  electric  and  a  magnetic  field 
were  simultaneously  applied,  in  such  a  way  as  not  to 
neutralise  each  other's  effect  but  to  cause  deflexions 


FIG.  18.— Diagram  of  the  deflexion  of  high-velocity  rays  from  radium. 
The  radium  is  in  a  cavity  in  a  lead  block  a ;  the  rays  pass  through  an 
aperture  6,  and  are  spread  out  by  a  magnetic  field  into  a  spectrum  d:d2 ; 
the  gamma  rays  or  any  uncharged  rays  produce  an  impression  at  c  on 
the  photographic  plate,  cd,  placed  to  receive  all  the  rays.  In  a  uniform 
field  each  of  the  lines  abd  is  a  circle. 

at  right  angles  to  each  other.  In  that  case  if  the  rays 
from  a  small  point  source,  after  traversing  the  double 
field,  are  received  upon  a  photographic  plate  at  a 
little  distance,  it  may  be  expected  that  the  two 
spectra  will  be  compounded  into  a  single  spectrum 
inclined  at  some  angle  corresponding  to  the  relative 
strength  of  the  two  fields.  But  whether  the  inclined 
spectrum  thus  produced  will  be  a  straight  line  or  a 
curve  must  depend  upon  circumstances.  All  that 
can  be  said,  without  further  consideration,  is  that  each 
point  of  the  spectrum  would  represent  a  definite 
ratio  of  deflexion,  and  therefore  a  definite  inertia  and 


138  VARIABLE   MASS  [CH.  xiv. 

velocity,  for  each  of  the  particles  which  have  produced 
the  impression  at  that  point.  And  inasmuch  as  the 
particles  of  different  speeds  will  be  sorted  out  to 
different  parts  of  the  spectrum,  it  may  be  possible 
to  select  those  points  which  correspond  to  the  highest 
speeds,  and  indeed  to  compare  the  ratio  of  the  two 
deflexions  for  various  speeds,  if  by  any  means  the 
velocity  corresponding  to  each  point  can  be  determined. 
A  little  calculation  is  needed  to  bring  out  the  details 
of  the  theory,  and  that  shall  be  given  directly,  but 
first  I  will  give  an  idea  of  the  kind  of  apparatus  used. 

Experimental  Device  used  by   W.  Kaufmann. 

A  minute  quantity  of  radium  salt  in  a  little 
brass  box  acts  as  source,  and  a  pencil  of  its  rays 
penetrates  a  small  hole,  about  half  a  millimetre 
diameter,  in  a  plate  of  platinum  at  a  distance  of 
2  centimetres  from  the  source ;  on  the  way,  they 
pass  between  a  pair  of  parallel  and  insulated  plates 
of  brass  which  are  separated  by  about  2  millimetres 
from  each  other  and  connected  to  a  high-tension 
battery  of  from  2,000  to  5,000  volts.  After  then 
travelling  another  2  centimetres,  they  encounter 
the  photographic  plate  placed  to  receive  them.  The 
apparatus  is  contained  in  a  thoroughly  exhausted 
vessel,  and  the  whole  is  placed  between  the  poles  of 
a  large  electromagnet  giving  a  nearly  uniform  field,  so 

FIG.  19. — Kaufmann's  apparatus  for  measuring  simultaneously  the 
electric  and  magnetic  deflexions  of  particles  possessing  very  high  velocity. 
The  source  of  radiation  is  a  minute  quantity  of  radium  placed  in  a  box 
at  C.  All  except  the  highest-velocity  rays  are  deflected  out  of  action  by 
the  magnet  NS ;  some  of  the  highest-velocity  rays  pass  upwards  through 
the  aperture  D,  being  deflected  forward  by  the  magnetic  field,  and  side- 
ways by  an  electric  field,  whose  lines  are  coincident  with  the  magnetic 
lines,  between  the  adjustable  plates  PiP2,  which  are  kept  as  highly 
electrified  as  possible  through  the  electrodes  R.  These  thus  doubly- 
deflected  rays  then  fall  upon  the  photographic  plate  E,  where  they  are 
spread  out  into  an  oblique  sort  of  very  minute  spectrum,  more  or  less  in 
accordance  with  diagram  18 ;  on  which  spectrum  micrometric  measure- 
ments are  subsequently  made. 


KAUFMANN'S   APPARATUS 


139 


nEWtl     H      5tfui7 


140  VARIABLE   MASS  [CH.  xiv. 

that  the  magnetic  and  electric  fields  are  superposed  in 
the  same  direction,  their  lines  of  force  being  coincident. 

Under  these  circumstances  the  particles  will 
describe  the  beginning  of  a  spiral,  being  curved 
round  the  magnetic  lines  and  deflected  along  the 
electric  lines,  until  they  escape  from  the  combined 
field  and  travel  in  their  deflected  direction  to  the 
photographic  plate  as  target.  The  slow-moving 
particles,  if  any,  will  presumably  strike  the  bounding 
surfaces  and  be  stopped, — only  the  very  rapid  ones 
will  reach  the  plate;  which  is  protected  from  alpha-rays 
by  aluminium  foil,  while  the  undeflected  gamma-rays 
would  probably  mark  the  direct  line  of  fire,  and  thus 
give  the  geometrical  "origin"  of  the  curve  or  trace 
which  would  be  found  on  the  plate  after  long  ex- 
posure,— a  curve  which  we  may  write  y—f(^)->  where 
y  signifies  the  electric  deflexion  and  x  the  magnetic. 

This  method  may  be  called  the  method  of  the 
crossed  spectra. 

The  theory  can  then  be  expressed  somewhat  as 
follows : 

Let  the  measured  coordinates  of  any  point  in  the 
spectrum,  as  developed  on  the  photographic  plate,  be 

y '     x  being  the  magnetic  deflexion, 
and  y  the  electric. 

These  deflexions  may  be  taken  to  represent 
inversely  the  radii  of  curvature  r  and  rf  produced 
in  the  rays  by  the  respective  fields  H  and  E, 
in  accordance  with  the  simple  mechanical  equations 

mu2  ,  mu2 


TT  ,  -r, 

u.e}±u,  and  —  7-  =  Le, 

T 


if.  XT       fJLtiU       U 

wherefore 


y     r       E 


CH.  xiv.]  AT   HIGH   SPEEDS  141 

where  ki  is  a  constant  depending  on  the  relative 
effective  strengths  of  the  fields  applied. 

In  so  far,  therefore,  as  the  particles  which  reach 
the  plate  are  all  emitted  with  nearly  the  same  velo- 
city, the  photographic  trace  will  be  an  approximate 
straight  line,  whose  slope  is  a  measure  of  that 
velocity. 

But  to  get  the  electrochemical  equivalent  we  must 
also  write,  from  the  above  equations, 

r»        y  (  } 

~       2'' 


e~  u*~     E 

where  k  is  another  constant  expressive  of  experi- 
mental conditions  ;  so  in  so  far  as  the  masses  of  the 
particles  are  all  the  same,  the  photographic  trace  or 
spectrum  will  be  a  parabola. 

But  at  the  highest  speeds  mfe  is  not  a  constant, 
but  a  function  of  u,  —  such  a  function  as  is  given  on 
page  133,  —  with  u  =  v  sin  0. 

So   calling;    this    function    —  =  0(-  1  =  </>(—  -|   we 

m0     T\vj     T\v  y) 

arrive  at  the  conclusion  that  the  actual  equation  to 
the  photographic  curve  should  be 


y   \o  y 

with  k2  another  constant. 

At  the  highest  speeds,  when  u  approaches  v  the 
velocity  of  light,  u  cannot  vary  much,  since  it 
is  approaching  a  limit,  and  accordingly  the  curve 
to  be  expected  will  be  approximately  a  straight  line  ; 
the  only  rapid  variable  will  then  be  the  mass,  which  is 
getting  near  to  its  asymptotic  approach  to  infinity, 
and  therefore  varies  much  more  rapidly  than  u. 

The  determination  consists  therefore  in  getting  as 


142  VARIABLE   MASS  [CH.  xiv. 

clear  a  trace  as  possible,  for  purposes  of  measurement, 
and  then  by  trial  and  error  choosing  a  constant  kl9 
such  as  to  make  the  squares  of  discrepancies  of  the 
ratio  here  called  k2,  from  its  mean  value,  as  small  as 
possible. 

If  it  is  possible  to  find  a  value  for  the  constant  kt 
which  shall  bring  out  the  calculated  value  k2  constant 
within  the  limits  of  experimental  uncertainty,  then 
the  form  of  the  theoretical  function  ^  is  to  that 
extent  verified ;  and  inasmuch  as  that  function  was 
calculated  on  the  hypothesis  of  purely  electrical 
mass,  the  hypothesis  of  the  purely  electrical  nature 
of  the  inertia  of  ft  rays  is  thereby  similarly  verified. 

Kaufmann  in  one  of  his  papers  says  the  experimental 
errors  in  his  concluding  series  only  amounted  to  1*4 
per  cent. ;  which,  considering  the  difficulties  to  be 
overcome,  is  remarkably  good. 

It  is  also  of  interest  to  record  that  the  numerical 
value  obtained  for  the  normal  or  low  speed  value 

S) 

of  —  for  the  ft  rays  from  radium  is  1'84  x  107  c.g.s.  ; 

mQ 

while  Dr.  Simon's  independent  determination,  by 
other  means,  of  the  same  quantity  for  cathode  rays 
was  l*865x!07;  which  is  likewise  a  satisfactory 
agreement.  It  is  needless  to  emphasise  the  agreement 
with  J.  J.  Thomson's  much  earlier  measurement  of  the 
same  quantity  for  rays  from  other  sources. 

The  formula  employed  by  Dr.  Kaufmann,  as  repre- 
senting the  inertia,  was  erroneously  deduced  from 
results  in  a  paper  by  Mr.  Searle  of  Cambridge ;  and  on 
the  strength  of  that  he  concluded  at  first  that  only  a 
fraction  of  the  mass  was  electric.  But  it  was  pointed 
out  by  Dr.  Abraham  of  Gottingen  that  the  inertia  thus 
calculated  was  only  appropriate  to  direct  acceleration, 
or  acceleration  in  the  line  of  motion  ;  whereas  what 


i  H.  xiv.]  AT   HIGH   SPEEDS  143 

was  wanted  was  the  transverse  inertia,  or  the  inertia 
appropriate  to  a  deflecting  force  at  right  angles  to 
the  line  of  motion.  This  is  to  be  obtained  from  the 
expression  for  the  tran verse  force,  derivable  from  the 
expression  for  the  energy  in  the  ordinary  manner  by 
Lagrange's  dynamical  equations  :  at  high  speeds  its 
value  comes  out  different ;  and  when  the  formula 
supplied  for  it  by  Dr.  Abraham  was  subsequently 
applied  by  Kaufmann  in  his  calculations,  it  was  found 
to  correspond  very  nearly  with  the  view  that  the 
whole  of  the  inertia  is  electric. 

This  formula,  which  in  fact  applies  to  any  solid 
aggregation  of  electricity  stratified  spherically,  is 
that  the  transverse  inertia  of  a  flying  particle,  m,  is 
to  the  inertia  of  the  same  particle  stationary  or 
moving  slowly,  m0,  in  the  following  ratio  : 

m 


where  /3  is  the  ratio  of  the  velocity  of  the  particle 
to  the  velocity  of  light. 

This  formula  is  not  identical  with  that  employed  by 
Thomson,  possibly  because  the  latter  worked  with  a 
different  idea  of  an  electron,  though  it  gives  numerical 
results  not  exceedingly  different.  Primarily,  how- 
ever, it  was  employed  not  so  much  as  an  absolute 
expression,  as  a  form  of  function  to  be  verified : 
though  it  was  used  absolutely  too.  Kaufmann  was 
ultimately  satisfied  by  finding  out  that  his  observed 
mass  varied  if  anything  more  rapidly,  not  less  rapidly, 
than  theory  required ;  so  that  if  the  particles  con- 
tained any  outstanding  inertia  of  a  non-electrical 
character,  such  unexplained  inertia  must  have  a 
negative  value, — which  presumably  would  be  absurd. 

I    do   not    myself   find  that   Abraham's    function 


144  VARIABLE   MASS  [CH.  xiv. 

agrees  with  observation,  in  absolute  numerical  value, 
any  better  than  Thomson's  formula  does ;  nor  do  I 
obtain  even  from  Thomson's  formula  exactly  the 
numbers  that  he  quotes  in  his  American  lectures  ; 
but  to  go  into  the  whole  matter  would  be  inappro- 
priate here, — nor  is  it  necessary,  since  the  theoretical 
differences  only  concern  details  that  could  doubtless 
be  removed  by  a  little  discussion :  it  will  only  become 
necessary  to  go  into  them  more  fully  when  the 
difficulties  of  the  experimental  observation  are  still 
further  overcome,  and  when  even  more  accurate  and 
trustworthy  results  are  obtained.  * 

I  have  taken  the  table  of  Kaufmann's  best  results, 
as  published  in  the  Physikalische  Zeitschrift  4, 
1902-3,  p.  55,  and  calculated  them  out  by  aid  of 
the  0  expression  given  above  on  p.  133. 

The  results  are  tabulated  below.  I  quote  his  given 
experimental  values  for  x  and  y,  together  with  the 
values  he  gives  for  /3,  or  u/v,  or  what  I  have  called 
sin  0;  and  then  after  reckoning  out  <£(#),  which  repre- 
sents the  theoretical  ratio  m/m0  according  to  Thomson's 
theory,  I  have  put  a  column  of  y/x2 ;  which  should 
correspond,  at  least  proportionally,  to  the  same 
quantity  as  experimentally  determined ;  and  I  like- 
wise quote  a  column  of  f^(/#),  which  represents  the 
same  quantity  calculated  according  to  Abraham's 
formula  (p.  143).  (The  numerical  agreement  of  y/x2 
with  a  mean  mass  ratio,  without  any  constant  factor 
other  than  unity,  must  be  accidental.) 

*The  results  of  Kaufmann's  subsequent  work  will  be  discussed  in 
Appendix  M. 


AT   HIGH   SPEEDS 


145 


II 

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CHAPTER  XV. 
ELECTRIC  VIEW  OF  MATTER. 

WHAT  has  been  proved,  by  the  combination  of  experi- 
ment and  theory  now  summarised,  is  that  the  most 
important  variety  of  rapidly  flying  corpuscle — the 
cathode  rays  in  a  Crookes  tube,  the  /3  rays  emitted 
by  radium  and  other  radio-active  substances,  the 
particles  thrown  off  by  most  clean  surfaces  when 
negatively  charged  and  stimulated  by  ultra-violet  light, 
the  carriers  of jbhe  negative  discharge  from  incandescent 
bodies,  and  likewise  the  revolving  or  vibrating  portion 
of  an  atom  to  which  the  emission  of  radiation  or 
ethereal  wave-motion  is  due — that  these  are  all  of  an 
identical  nature  and  all  possess  an  inertia  of  purely 
electromagnetic  character  ;  that  is  to  say  that  they 
are  all  pure  electrons  without  any  admixture  of 
ordinary  or  unexplained  matter, — that  they  are 
simply  electrical  charges  without  any  material  or 
non- electrical  nucleus. 

We  thus  reach  the  very  important  deduction  that 
negative  electricity  can  exist  apart  from  matter  in 
little  isolated  identical  portions,  each  of  exceedingly 
minute  known  size,  known  charge,  and  known  inertia ; 
and  that  the  laws  of  mechanics,  applied  to  such 
particles  in  given  fields  of  electric  and  magnetic  force, 
should  carry  us  on  towards  explaining  the  fun  da- 


CH.  xv.]  CONSTITUTION   OF   ATOM 

mental  phenomena  of  electric  currents,  of  magnetism, 
and  of  the  production  of  light.  But  in  order  to  explain 
chemical  action,  the  details  of  radiation — such  as 
groups  of  spectrum  lines  and  the  like, — the  differences 
observable  between  conductors,  and  the  properties  of 
magnetic  bodies,  it  is  necessary  to  treat  of  matter  also  ; 
and  to  consider  whether  its  inertia  too,  and  therefore 
its  whole  nature  and  properties,  can  be  reduced 
and  simplified  and  explained  as  electromagnetic 
phenomena. 

For  observe  that  though  an  electron  has  been 
shown  to  possess  purely  electrical  inertia,  the  same 
proof  has  not  yet  been  extended  to  an  atom  :  the 
constitution  of  an  atom  is  so  far  unknown,  and  is  the 
subject  of  hypothesis  only.  Moreover  the  only 
electron  observed,  so  far,  has  been  the  negative 
electron  ;  the  positive  has  hitherto  escaped  observa- 
tion in  any  isolated  form,  since  it  has  never  been  met 
with  apart  from  a  mass  comparable  with  an  atom  in 
bulk  and  weight.  It  may  be  that  it  can  have  no 
separate  existence  apart  from  the  atom  of  matter, 
but  in  that  case  it  will  hardly  be  proper  to  speak  of 
it  as  an  electron  at  all ;  it  may  be  that  an  indi- 
visible positive  charge  itself  constitutes  the  bulk  of 
an  atom  of  matter ;  in  any  case  its  nature  must  be 
investigated,  and  many  have  been  the  attempts 
made  in  that  direction, — among  the  best  known  in 
recent  times  being  the  experiments  of  Prof.  Wien 
and  others  on  "  Canal  rays."  According  to  Larmor 
positive  electricity  must  be  the  mirror  image  of 
negative,  and  experimental  results  must  be  inter- 
preted to  suit  that  theoretical  conclusion.  The 
relations  of  positive  electricity  constitute  in  fact  the 
main  outstanding  problem  of  Physics  at  the  present 
time,  and  until  they  can  be  probed,  further  progress 


148  ELECTRIC  VIEW  OF  MATTER       [CH.  xv. 

towards  understanding  the  constitution  of  an  atom 
must  remain  in  a  state  of  suspended  animation. 

The  only  portion  of  an  atom  that  has  been  really 
analysed,  and  so  to  speak  understood,  is  that  minute 
but  significant  fraction  of  its  mass  which  confers 
upon  it  an  electric  charge,  consequent  chemical 
affinity,  and  radiating  power ;  and,  when  we  come  to 
ask  what  all  the  rest  of  the  atom  is  composed  of,  all 
we  can  say  definitely  is  that  the  specific  structure 
must  depend  on  the  nature  of  the  chemical  element 
under  consideration.  But  if  we  consider  the  simplest 
known  atom,  namely  that  of  Hydrogen,  we  can  make 
various  hypotheses  somewhat  as  follows  : 

(1)  The  main  bulk  of  the  atom  may  consist  of 
ordinary  matter  (whatever  unknown  entity  is  hidden 
by  that  familiar   phrase),  associated  with  sufficient 
positive     electricity    (whatever     that    may    be)    to 
neutralise  the  charge  belonging  to  the  electron  or 
electrons  which  undoubtedly  exist  in  connection  with 
each  atom. 

(2)  Or  the   bulk  of  the  atom  may  consist  of  a 
multitude  of  positive  and  negative  electrons,  inter- 
leaved, as  it  were,  and  holding  themselves  together 
in  a  cluster  by  their  mutual  attractions,  either  in  a 
state  of  intricate  orbital  motion,  or  in  some  static 
geometrical  configuration,  kept  permanent  by  appro- 
priate connexions. 

(3)  Or  the  bulk  of  the  atom  may  be  composed  of 
an  indivisible  unit  of  positive  electricity,  constituting 
a  presumably  spherical  mass  or  "jelly,"  in  the  midst 
of  which  an  electrically  equivalent  number  of  point 
electrons   are   as    it    were    '  sown ' ;    these    electrons 
probably  distributing  themselves  in  rings,  after  the 
fashion  of  Alfred  Mayer's  floating  magnetic  needles, 
and  revolving  in  regular  orbits  about  the  centre  of 


CH.  xv.]  CONSTITUTION   OF   ATOM  149 

the  jelly,  with  a  force  directed  to  that  centre,  and 
varying  as  the  direct  distance  from  it. 

This  hypothesis,  in  spite  of  obvious  weaknesses  con- 
nected with  the  nature  of  the  positive  unit,  has  great 
attractiveness  : — for  it  explains  the  constant  period 
of  an  orbit ;  it  can  explain  the  occurrence  of  visible 
radiation  by  perturbations  of  the  orbit  during 
collision ;  and  it  has  been  shown  by  J.  J.  Thomson 
to  be  capable  of  carrying  us  a  long  way  towards  a 
rational  electrical  theory  of  Mendele*efFs  series  of 
the  chemical  elements,  together  with  some  of  their 
chemical — especially  their  electro-chemical — proper- 
ties, and  some  features  of  their  spectra.  Moreover 
it  goes  further  and  explains  in  a  fairly  natural 
manner,  and  without  artificiality,  the  gradual  degra- 
dation of  atomic  energy  by  slow  uncompensated 
and  unperceived  radiation ;  the  consequent  gradual 
oncoming  of  instability ;  and  the  occasional  cata- 
clysmic transmutation  of  one  element  into  another, 
or  rather  into  others,  with  explosive  violence, — as 
observed  in  the  facts  of  radio-activity.  It  gives  in 
fact  a  rational  though  preliminary  view  of  the 
hypothetical  evolution  of  all  matter,  which  many 
known  circumstances  now  tend  to  support;  and  it 
accounts  in  a  kinetic  fashion  for  the  immense  store 
of  intra-atomic  energy.  Nevertheless  it  is  very  far 
from  being  an  established  theory,  and  another  view 
that  can  be  taken  of  the  rest  of  the  atom  is : 

(4)  That  it  consists  of  a  kind  of  interlocked 
admixture  of  positive  and  negative  electricity, 
indivisible  and  inseparable  into  units,  and  incapable 
of  being  appreciably  sheared  by  applied  forces,  but 
incorporated  together  as  a  continuous  mass ;  in  the 
midst  of  which  one  or  more  isolated  and  indi- 
vidualised electrons  may  move  about  and  carry  on 


150  ELECTRIC  VIEW  OF  MATTER       [CH.  xv. 

that  display  of  external  activity  which  confers  upon 
the  atom  its  observed  properties. 

(5)  A  fifth  view  of  the  atom  would  regard  it  as  a 
central  '  sun,'  of  extremely  concentrated  positive 
electricity  at  the  centre,  with  a  multitude  of  electrons 
revolving  in  astronomical  orbits,  like  asteroids,  within 
its  range  of  attraction.  But  this  would  give  a  law  of 
inverse  square  for  the  force,  and  consequently  periodic 
times  dependent  on  distance,  which  appears  not  to 
correspond  with  anything  satisfactorily  observed. 

All  these  views  however  are  painfully  indefinite, 
except  the  third  one,  which  regards  positive  electricity 
as  an  indivisible  unit  of  perfectly  unresisting  uniform 
material  (though  '  material '  is  not  the  right  word),  of 
spherical  form  the  size  of  an  atom,  in  the  midst 
of  which  a  definite  geometrical  arrangement  of 
electrons  are  revolving  with  known  frequency  in 
specified  groups  or  rings.  The  amount  of  outstanding 
vagueness  in  this  view  is  obvious ;  and  is  necessary,  so 
long  as  we  know  little  or  nothing  about  the  intrinsic 
nature  of  what  we  experience  as  positive  electricity ; 
but  at  the  same  time  all  the  rest  of  this  hypothesis  is 
definite  enough,  and  enables  mechanical  laws  and 
calculations  to  be  applied  with  considerable  fulness  to 
the  elucidation  of  the  phenomena  that  would  be 
displayed  by  such  a  '  model '  or  hypothetical  com- 
bination. And  if  the  so-calculated  phenomena  are 
found  to  correspond  with  fact,  it  assuredly  lends 
some  strength  to  the  hypothetical  basis  on  which  the 
calculation  is  founded;  although  it  is  certain  to  have 
to  be  modified  somewhat  in  the  light  of  growing 
experience  as  discovery  proceeds. 

Whatever  it  may  be  worth,  this  is  the  only  theory 
of  the  nature  of  the  atom  which  has  been  to  any  great 
extent  elaborated;  and,  extremely  imperfect  though  it 


CH.  xv.]  CONSTITUTION   OF   ATOM  151 

is  at  present,  it  is  worthy  of  some  attention  from  its 
own  intrinsic  interest.  It  will  be  found  developed  by 
Professor  J.  J.  Thomson  in  the  Philosophical  Maga- 
zine for  Dec.  1903  and  March  1904;  and  a  general 
idea  of  its  main  features  can  be  gathered  from  his 
American  "  Silliman  Lectures,"  published  in  1904  by 
Constable  as  a  book  called  Electricity  and  Matter. 

Were  it  less  hypothetical  a  further  account  of  it 
would  be  given  here,  but  an  extremely  recent  paper 
by  the  same  great  Physicist  has  tended  to  reduce  the 
whole  subject  to  a  state  of  exaggerated  uncertainty; 
since  he  gives  reasons,  which  appear  to  be  sound 
ones,  in  the  Philosophical  Magazine  for  June  1906, 
for  assuming  that  only  one  active  electron  is  contained 
in  a  hydrogen  atom,  and  that  all  other  elements  contain 
a  number  of  electrons  comparable  to  their  atomic 
weight,  reckoned  on  the  basis  that  H  =  1  (see 
Appendix  L).  This  is  an  extraordinary  and  un- 
suspected result,  and  at  first  sight  appears  very 
unlikely,  since  the  ordinary  chemical  assumption  of 
a  unit  atomic  weight  for  Hydrogen  has  always  been 
known  to  be  a  pure  convention,  made  for  convenience 
alone,  and  not  likely  to  correspond  with  anything  in 
nature.  I  do  not  suppose  that  anyone  imagined 
that  it  would,  even  provisionally,  be  found  to  have 
a  physical  and  rational  basis.  The  subject  is  further 
referred  to  in  Chapters  XVII.  and  XIX.  below. 

In  that  state  of  uncertainty  the  matter  must  be 
left  for  the  present ;  but  we  may  go  on  to  indicate 
roughly  how  some  of  the  known  properties  of  matter 
could  be  expected  or  explained,  on  a  view  of  the 
electrical  constitution  of  matter  which  supposes  it 
composed  of  a  large  number  of  positive  and  nega- 
tive electric  charges,  irrespective  of  the  particular 
mode  of  their  aggregation  and  distribution. 


CHAPTER  XVI. 
ELECTKIC  VIEW  OF  MATTER  (CONTINUED). 

Nature  of  Cohesion. 

WE  shall  now  try  to  trace  some  of  the  consequences 
of  the  view  that  all  atoms  of  matter  are  built  up  of 
the  same  fundamental  units,  and  are  composed 
of  aggregates  of  a  definite  number  of  variously 
grouped  negative  and  positive  charges, — which  for 
present  purposes  we  may  call  electrons,  even  though 
some  are  positive — arranged  in  kinetic  patterns  and 
keeping  apart  by  reason  of  the  vigour  of  their  own 
orbital  motions. 

At  first  it  is  not  easy  to  do  more  than  imagine 
the  electrons  to  be  statically  grouped  into  regular 
patterns.  It  is  easy  to  conceive  this  on  the  hypo- 
thesis No.  3  of  last  chapter ;  for  though  in  free  space 
they  would  be  unstable  or  disperse,  their  possible 
groupings  are  easily  calculated  in  a  positive  men- 
struum ;  for  instance  they  might  be  arranged  in 
triangular  or  square  or  hexagonal  order ;  with 
other  allied  three-dimensional  possibilities  familiar 
to  students  of  crystallography.  See,  for  instance, 
William  Barlow,  Brit.  Assoc.  Report,  1896,  p.  731; 
also  Lord  Kelvin,  Phil.  Mag.,  March  1902,  and 
elsewhere. 


CH.  XVL]  MOLECULAR   FORCES  153 

On  Chemical  and  Molecular  Forces. 

The  force  of  chemical  affinity  has  long  been  known 
to  be  electrical.  This  opinion  was  propounded  by 
Berzelius,  and  was  also  held  previously  by  Davy 
and  afterwards  by  Faraday.  Ordinary  electrical 
attraction  between  charged  bodies  may  be  called 
molar  chemical  action ;  only  there  is  no  combination 
in  ordinary  cases,  because  the  opposing  charges 
spark  into  one  another,  and  so  the  attraction  ceases 
when  a  certain  proximity  is  reached.  This  dis- 
charge and  cessation  of  attraction  does  not  seem  to 
occur  among  atoms ;  the  difference  of  potential 
between  them  is  too  low  to  permit  of  mutual 
exchange  or  neutralisation  of  charge,  so  the  combi- 
nation is  permanent.* 

Keal  chemical  attraction  occurs  between  two  atoms 
each  of  which  contains  an  unbalanced  electron — one 
extra,  or  it  may  be  more  than  one  extra,  electron  of 
given  sign.  Such  an  atom  thus  has  a  centre  of  force 
whereby  it  can  attach  itself  to  other  atoms  and  enter 
into  pairing  or  chemical  combination  with  them.  It 
is  probable  that  a  negative  charge  is  an  excess,  and  a 
positive  charge  a  defect ;  and  that  when  pairing 
occurs  the  excess  charge  of  one  fills  up  the  deficiency 
of  the  other,  and  composes  a  complete  and  neutral 
molecule. 

Union  of  this  kind,  however,  never  seems  quite  as 
strong  and  permanent  as  the  union  of  the  electrons  in 
the  atom  itself:  the  molecule  easily  separates  at  the 
same  place  again,  under  the  influence  of  decomposing 
influences,  and  does  not  seem  able  to  split  up  in 
other  ways  into  new  substances ;  except  in  organic 
chemistry,  where  various  modes  of  splitting  up  a 

*See  Lodge,  Brit.  Assoc.  Report,  1885,  pp.  744,  5. 


154  ELECTRIC  VIEW  OF  MATTER      [CH.  xvi. 

complex   molecule   can   be   brought   about,   and  are 
practically  utilised  for  the  generation  of  new  com- 

CH3 .  CH3  =  C2H5 .  H. 

It  is  probable  that  the  same  sort  of  thing  is  possible 
with  simple  bodies,  but  that  the  so-called  "elements" 
constitute  a  peculiarly  stable  group,  the  ingredients  of 
which  so  far  have  only  partially  been  re-associated 
into  isomeric  or  allotropic  forms,  and  have  not  yet 
been  detached  from  each  other. 

When  chemical  combination  occurs  between  two 
oppositely  charged  atoms,  there  is  no  electric  dis- 
charge between  them  :  the  two  atoms  retain  each  its 
own  charge,  and  cling  together  for  that  reason. 
When  they  are  separated,  each  is  an  ion  and  possesses 
its  appropriate  charge. 

It  is  possible  to  charge  an  assemblage  of  neutral 
molecules  with  an  excess  or  with  a  defect  of  one  or 
more  electrons,  by  processes  of  ordinary  electrification, 
such  as  friction ;  but  the  attachment  of  these  super- 
numerary electrons  is  loose — and  they  can  be  shaken 
away  by  the  agitation  of  ultra-violet  light  and  in 
many  other  ways.  Even  splashing  of  water  into 
spray  shakes  some  loose,  and  can  thus  perturb  an 
electroscope,  although  the  liquid  was  not  charged 
beforehand ;  *  a  fact  which  adds  to  the  probability 
that  the  water  unit  is  a  molecular  aggregate.  And 
in  the  case  of  massive  atoms,  of  high  atomic  weight, 
they  occasionally  appear  automatically  to  reach  a 
condition  of  instability,  and  rearrange  themselves 
in  such  a  way  as  to  throw  off  one  or  more  electrons 
spontaneously,  which  then  fly  off  tangentially  with 
whatever  orbital  velocity  they  may  have  had,  giving 

*Lenard  on  electrification  near  waterfalls.      See  also  Chap.  VII.,  . 
above,  on  ionisation. 


CH.  XVL]  COHESION  155 

rise  to  part  of  phenomena  recently  discovered  under 
the  name  of  radio-activity.  But  instead  of  suppos- 
ing that  their  violence  of  ejection  is  due  to  velocity 
previously  possessed  by  them,  it  is  possible  to  suppose 
that  they  are  driven  away  by  intrinsic  static  force, 
so  that  their  previous  energy  was  potential ;  and 
this  is  the  form  of  hypothesis  favoured  by  Lord 
Kelvin.  See  Phil.  Mag.  for  March  1902. 

Molecular  Forces,  Cohesion. 

But  there  is  another  kind  of  adhesion  or  cohesion  of 
molecules,  not  chemical  but  what  is  called  molecular. 
This  occurs  between  atoms  not  possessing  ionic  or 
extra  charges,  but  each  quite  neutral,  consisting  of 
paired-off  groups  of  electrons.  At  any  moderate 
distance  the  force  of  attraction  between  paired  elec- 
trons will  be  next  to  nothing,  but  at  very  minute 
distances  it  may  be  very  great ;  ultimately  becoming 
almost  indistinguishable  from  chemical  combination, 
except  that  the  cling  will  be  a  weak  cling  at  a 
multitude  of  points  instead  of  an  intense  cling  at 
only  one. 

Consider  the  outer  surface  of  an  atom  consisting 
of  a  regular  group  of  interleaved  electrons  of  alter- 
nately opposite  sign.  Its  equipotential  surfaces  will 
be  dimpled  or  corrugated  or  pimply  sheets,  which  at 
a  little  distance  away  will  be  almost  plain ;  but  the 
dimples  will  increase  rapidly  in  depth  and  become 
like  the  cover  of  a  mattrass,  when  something  less 
than  molecular  distance — something  approaching  the 
internal  electron  distances  apart — is  reached. 

Two  such  atoms  will  therefore  tend  to  settle  down 
with  their  equipotential  surfaces  adjusted  into  uni- 
formity, the  pimples  of  the  one  fitting  into  the  hollows 
•  of  the  other  ;  and  this  is  the  state  of  things  suggested 


156  ELECTRIC  VIEW  OF  MATTER      [CH.  xvi. 

by  the  facts  of  cohesion.     For  a  diagram  representing 
the  state  of  things  intended,  see  fig.  20. 

To  investigate  the  actual  law  of  force  would  be 
difficult,  and  too  many  assumptions  would  have  to  be 
made  for  the  geometrical  arrangement  of  the  electrons 
in  the  adjacent  atoms ;  it  could  only  be  approximate, 
because  we  should  probably,  at  least  in  the  first 
instance,  have  to  assume  a  static  distribution. 
Nevertheless  the  attempt  might  be  instructive,  and 
might  in  a  developed  form  be  suitable  for  an  Adams 
Prize  Essay. 

•    o    •    o    •    o    •  0*0*0*0 

0*0*0*0  •    o    •    o    •    o    • 

*•     0*0*0*  0*0*0*0 

0*0*0*0  •    o    •    o    •    o    • 

•0*0*0*  0*0*0*0 

A  B 

FIG.  20. — Ordinary  Cohesion  between  two  Neutral  Atoms  A  and  B : 
each  atom  supposed  to  consist  of  interleaved  electrons  of  opposite  sign — 
depicted  in  any  convenient  way — which  attract  each  other  by  residual 
or  spare  affinity.  This  is  due  to  a  few  of  the  lines  of  force  which  stretch 
across  the  interspace,  and  hold  the  pair  of  atoms  together.  The  maxi- 
mum distortional  shear  permissible  depends  on  the  ratio  of  the  electronic 
to  the  atomic  distance. 

It  is  quite  plain,  however,  that  the  result  would  be 
a  force  rapidly  increasing  and  becoming  great  at 
small  distances,  and  practically  nil  at  any  perceptible 
distance. 

A  theory  of  cohesion  cannot  really  be  given  until 
the  structure  of  an  atom  is  better  known,  but  in 
all  probability  it  will  proceed  on  lines  not  wholly 
unlike  the  above. 

Molecular  forces  on  this  view  are  electrical,  just  as 
much  electrical  as  are  chemical  forces  ;  but  they  occur 
between  chemically  saturated  molecules,  and  are  due 
to  the  interaction  or  distant  influence  of  paired 


CH.  xvi.]  UCOHERER  157 

electrons  on  each  other  across  molecular  distances. 
It  may  be  said  to  be  a  result  of  "residual  affinity."* 

Ions  cannot  thus  combine ;  because  if  they  were 
oppositely  charged  their  combination  would  be 
chemical,  and  if  they  were  similarly  charged  they 
would  strongly  repel  each  other.  But  if  ions  arrive 
at  a  metallic  electrode,  or  are  provided  with  other 
means  of  passing  on  their  free  charges,  they  cease 
to  be  ions ;  and  then  the  diselectrified  atoms  can  and 
do  combine  molecularly  with  each  other. 

It  is  of  course  possible  for  an  ion  to  have  more 
than  one  free  electron,  forming  a  dyad  or  a  triad 
radical ;  and  the  way  in  which  a  neutral  group  can 
receive,  and  by  rapid  re-adjustment  pass  on,  an^  extra 
foreign  electron,  reminding  one  of  the  re-adjustment 
of  the  films  in  a  lather  when  one  compartment  bursts, 
is  doubtless  instructive. 

The  effect  of  electric  polarisation  on  such  a 
neutral  group  of  electrons  is  noteworthy.  The  effect 
of  a  charged  body  in  the  neighbourhood  is  at  once  to 
disturb  the  equilibrium,  and  to  perturb  the  grouping 
throughout  the  atom,  more  or  less  :  it  will  cause  the 
negative  electrons  to  protrude  slightly  on  one  side 
and  the  positive  on  the  other  (see  fig.  21  where  two 
different  but  very  complete  kinds  of  polarisation  are 
shown). 

If  two  molecules  were  beyond  each  other's  molecular 
range,  and  if  the  neighbouring  surfaces  could  by  any 
means — as  by  the  supply  of  electricity  from  without 
— be  oppositely  electrified,  the  forces  of  cohesion 
would  be  intensified  momentarily,  by  something  akin 
to  chemical  affinity,  and  cohesion  would  set  in  over 
ultra-molecular  distances.  This  appears  to  be  what 
goes  on  in  a  "  coherer."  The  opposite  charges 

*  See  Lodge  in  Nature,  1904,  vol.  70,  p.  176. 


158  ELECTRIC  VIEW  OF  MATTER      [CH.  xvi. 

cannot  be  maintained  electrostatically  between  two 
neighbouring  metallic  surfaces,  but  they  can  be 
momentarily  imparted,  by  a  sudden  jerk  or  disruptive 
discharge  or  received  electric  impulse ;  and  these  are 
the  things  which  are  effective  in  promoting  cohesion. 
In  the  two  diagrams ; — fig.  20  represents  a  couple 
of  atoms  with  interleaved  electrons  of  opposite  sign 


c 

o 


0000 


FIG.  21.— Two  Polarised  Atoms,    illustrating  electrically  intensified 
cohesion. 

in  square  order,  the  atoms  being  within  range  of 
one  another  and  so  cohering  by  molecular  or  non- 
chemical  forces.  They  have  adjusted  themselves  into 
a  cohering  position ;  but  a  vertical  shear  through  half 
the  distance  apart  of  the  electrons  would  disintegrate 
them.  An  angle  represented  by  half  the  electron- 
distance  divided  by  the  molecular  distance,  is  therefore 
a  measure  of  the  maximum  distortion  a  substance  can 
undergo. 


CH.  XVL]  COHESION  159 

Fig.  21  shows  a  couple  of  atoms  both  electrically 
polarised,  as  by  a  positively  charged  rod  held  above 
both.  To  vary  the  illustration,  the  constituents  of  C 
are  shown  polarised  into  hexagonal  order — an  effect 
such  as  might  also  be  caused  by  lateral  pressure 
in  some  cases ;  while  the  constituents  of  D  are 
depicted  in  diagonal  square  order — which  has  the 
effect  of  violent  electric  polarisation.  In  any  case 
polarised  atoms  such  as  C  and  D  are  clinging  by 
forces  much  stronger  than  the  force  of  ordinary 
cohesion  at  that  distance.  They  represent  adjacent 
atoms  of  a  momentarily  polarised  coherer. 

It  is  not  to  be  supposed  that  the  electrons  in  a 
polarised  atom  need  really  ever  be  disturbed  as 
much  as  is  shown  in  the  diagram,  nor  any  more 
than  an  almost  imperceptible  amount,  in  order  to 
produce  this  chemical  cohesion  effect.  For  that  is 
what  polarisation  accomplishes  :  it  converts  ordinary 
molecular  force,  or  cohesion,  into  incipient  but  real 
chemical  affinity ;  both  kinds  of  forces  being  on  the 
above  hypothesis  electrically  explicable. 


CHAPTER  XVII. 

FURTHER  CONSIDERATIONS  REGARDING  THE 
STRUCTURE  OF  AN  ATOM. 

THE  hypothesis  that  has  been  already  referred  to, 
No.  3  in  Chap.  XV.,  that  an  atom  consists  of  a 
globular  mass  of  positive  electricity  with  minute 
negative  electrons  embedded  in  it — either  at  rest,  or 
vibrating  about  a  position  of  equilibrium,  or  revolving 
in  regular  annular  orbits, — is  obviously  not  free  from 
difficulties ;  though  its  success  in  explaining  many 
observed  facts  seems  to  justify  an  attempt  to  mini- 
mise those  difficulties,  and  to  render  hopeful  an 
effort  ultimately  to  overcome  them. 

One  objection  that  can  easily  be  raised  is  to  ask 
how  a  mass  of  positive  electricity  can  hold  together 
against  the  mutual  repulsion  of  its  parts.  This  diffi- 
culty is  felt  more  in  the  case  of  positive  electricity 
than  in  the  case  of  negative,  because  by  hypothesis 
the  positive  charge  has  some  perceptible  bulk,  namely 
the  size  of  an  atom,  whereas  the  negative  charge  or 
electron  is  exceedingly  small.  But  however  small  an 
electron  is,  it  must  be  supposed  to  have  parts,  and 
there  is  just  as  much  reason  for  supposing  the  parts 
of  a  negative  unit  to  be  mutually  repulsive  as  there 
is  in  supposing  the  parts  of  the  positive  unit  to  be 
mutually  repulsive.  Hence  the  question  is  equally 


CH.  XVIL]  STRUCTURE   OF   ATOM  161 

valid,  how  do  the  parts  of  an  electron  hold  together  ? 
But  nobody  seems  to  ask  this  question  ;  and  I  see  no 
reason. why  it  should  be  asked,  because  there  is  no 
evidence  that  the  parts  of  an  electron  are  mutually 
repulsive — there  is  no  real  evidence  as  yet  that  it 
has  parts  at  all.  What  we  know  is  that  different 
electrons  repel  each  other,  and  are  attracted  by 
positive  charges,  but  we  do  not  know  that  the  parts 
of  one  electron  repel  each  other ;  in  fact  we  know 
nothing  about  the  parts  of  an  electron.  The  lines 
of  force,  or  field  of  force,  representing  the  activity 
of  an  electron,  may  be  entirely  outside  itself,  and 
need  not  penetrate  into  its  interior  at  all :  it  may 
be  for  all  electrical  purposes  an  indivisible  unit. 

But  then,  supposing  all  this  admitted  for  a  negative 
charge,  why  should  it  not  be  extended  to  cover  a 
positive  charge  also  ?  Why  should  the  parts  of  a 
positive  unit  be  mutually  repulsive  ?  It  is  no  answer 
to  say  that  the  unit  is  bigger,  unless  the  electron  is 
thought  of  as  a  geometrical  point ;  the  argument 
about  parts  is  just  as  valid  in  the  one  case  as  in 
the  other,  and  no  more  so.  What  we  require  is  some 
conception  as  to  the  nature  of  the  positive  charge, 
— and  that  I  confess  is  wanting ;  though  "  an 
entanglement  of  finite  size"  seems  to  Larmor  quite 
possible  and  natural ;  and  anyhow  an  argument 
against  its  existence  based  upon  the  assumed  repul- 
siveness  of  its  parts  does  not  seem  to  be  an  argument 
of  any  weight. 

Another  suggestion  can  be  made :  and  that  is  that 
the  main  bulk  of  the  atom,  in  which  electrons  are 
embedded,  consists  not  of  positive  electricity  alone 
but  of  a  close  admixture  or  combination  of  positive 
and  negative  electricities — inseparable  and  as  it  were 
rigidly  connected — behaving  to  outside  forces  like  the 


L.E. 


162  THE  STRUCTURE  OF  AN  ATOM  [CH.  xvn. 

oxygen  and  hydrogen  interlocked  together  in  a  gallon 
of  water  ;  in  which  water  a  few  extra  atoms  of  oxygen 
might  easily  be  dissolved,  in  a  relatively  free  condi- 
tion— that  is  to  say,  not  forming  part  of  the  fixed 
constituent- oxygen — just  as  a  few  outstanding  elec- 
trons may  exist  in  the  general  mass  of  an  atom. 

This  is  the  hypothesis  numbered  4  in  that  list  of 
alternative  schemes  which  was  exhibited  in  Chap. 
XV.;  and  the  latest  results  of  Thomson,  there  also 
mentioned,  tend  towards  supporting  it. 

If  any  lines  of  force  are  then  postulated  between 
the  constituent  positive  and  negative  fluids  inside  an 
atom  they  would  be  entirely  of  an  internal  character, 
and  only  those  belonging  to  some  free  unbalanced 
charges  would  emerge  and  produce  ionic  activities  : 
the  internal  lines  of  force  would  be  wholly  occupied 
in  holding  the  atom  together,  and  would  have  no 
influence  on  neighbouring  atoms — not  even  molecular 
or  residual  influence.  The  main  bulk  of  atom  in 
that  case  would  be  like  a  finely  interleaved  condenser, 
incapable  of  discharge  or  of  decomposition, — except 
by  actual  disintegration  such  as  might  occasionally 
accompany  or  cause  radio-activity. 


CHAPTER  XVIII. 

SUMMARY  OF  OTHER  CONSEQUENCES  OF  ELECTRON 

THEORY. 

Radio-activity. 

IF  many  atoms  of  a  substance  have  electrons  attached 
to  them,  and  if  these  are  performing  orbital  revolutions; 
it  is  natural  to  ask  how  then  can  it  be  that  substances 
are  not  constantly  emitting  waves  and  radiating  away 
their  energy.  For  we  have  seen  in  Chap.  X. 
that  electric  charges  in  revolution  or  vibration 
constitute  radiators,  and  must  emit  more  or  less 
radiation ;  thereby  dissipating  their  kinetic  energy 
and  gradually  either  coming  to  rest  or  effecting 
some  other  change.  Fortunately,  owing  to  the 
brilliant  researches  of  Becquerel,  Curie,  and  others, 
certain  substances  have  been  found  in  which  the 
radiation  intensity  reaches  a  very  perceptible  mag- 
nitude ;  and  it  appears  that  this  radiation  may 
be  of  several  kinds — 

1st,  of  waves  or  pulses  analogous  to  Rontgen 
radiation  :  called  7  rays  ; 

2nd,  of  rays  analogous  to  cathode  rays  consist- 
ing of  electrons  bodily  shot  off:  called  ft 
rays; 

3rd,    of  positively   charged   ions   or   atoms,    or 


164    SUMMARY  OF  ELECTRON  THEORY  [CH.  xvm. 

semi-atoms,  consisting  of  something  like 
helium  apparently,  likewise  shot  off  with 
great  energy  :  called  a  rays ; 
4th,  as  a  consequence  of  all  this  radiation, 
detached  portions  of  the  residue  of  the 
substance  drift  away,  not  charged  with 
electricity,  but  emanating  something  after 
the  fashion  of  an  odour.  This  gaseous 
emanation  is  found  itself  to  possess  a 
very  high  intrinsic  radiating  power,  and 
to  be  capable  of  attaching  itself  to,  or 
causing  a  deposit  on,  other  materials  in 
the  neighbourhood,  so  that  they  too  acquire 
temporary  radiating  power :  a  deposit  at 
one  time  spoken  of  as  induced  or  excited 
activity.* 

The  substances  which  possess  any  noteworthy 
amount  of  this  radiating  power  are  substances  with 
very  high  atomic  weight ;  and  their  emitting  power 
would  appear  to  be  probably  due  to  an  internal 
commotion  or  convulsion,  of  sufficient  violence  to 
detach  and  expel,  every  now  and  then,  some  particle 
or  fragment ;  and  also,  by  the  shock  of  the  expulsion, 
to  generate  some  feeble  but  exceedingly  penetrating 
Eontgen  rays. 

witn  quantitative  determinations  concerning  it.  Also  in  mil. 
Mag.,  July  and  November,  1902.  Other  references  are  M.  and 
Mme.  Curie,  Comptes  Rendus,  November,  1899  ;  Hon.  R.  J.  Strutt, 
Phil.  Trans.,  A  1901,  vol.  196,  p.  525;  Sir  W.  Crookes,  Proc.  Roy. 
Soc.,  vol.  66,  p.  409  (1900),  vol.  69,  p.  413  (1902),  also  "Electrical 
Evaporation,"  1891,  Proc.  Roy.  Soc.,  vol.  50,  p.  88;  and  many  other 
workers.  References  to  them  are  now  conveniently  collected  in 
Professor  Rutherford's  excellent  treatise. 

Madame  Curie's  original  Thesis  on  Radio-activity  for  her  Doctorate, 
of  date  1903,  is  a  masterly  production. 


CH.  XVIIL]  ATOMIC   RADIATION  165 

It  is  easy  to  grant  that,  whenever  there  are  actual 
collisions  of  sufficient  suddenness,  some  radiation  must 
be  emitted ;  but  we  cannot  help  asking,  why  does 
not  the  quiet  orbital  revolution  of  electrons  round 
atoms,  in  a  substance  not  in  a  high  state  of 
thermal  disturbance  and  not  possessing  specially 
massive  atoms,  why  does  not  this  also  give  rise  to 
a  perceptible  amount  of  true  radiation  and  loss  of 
energy  ?  One  answer  that  has  been  given  is  as 
follows  : — 

The  radiators  are  not  isolated  or  independent,  and 
surface  radiation  is  maintained  by  layers  at  greater 
depth  in  the  substance.  Moreover  the  radiators  are 
so  close  together  that  they  are  in  all  sorts  of  phases 
within  the  first  quarter  wave  length,  a  length  which 
embraces  a  multitude  of  them;  wherefore  a  multitude 
is  a  worse  radiator  than  one,  because  they  interfere 
and  produce  but  little  external  or  distant  effect ;  like 
the  two  prongs  of  a  fork,  or  two  neighbouring  organ 
pipes,  or  the  front  and  back  of  a  vibrating  wire.  See 
Larmor,  Ether  and  Matter,  page  232  ;  the  proposition 
by  which  he  considers  the  question  settled  is  that  the 
vector  sum  of  accelerations  equals  zero. 

Of  course  it  must  not  be  forgotten  that  radiation 
of  a  low  temperature  order  is  as  a  matter  of  fact 
always  going  on  from  all  substances  ;  that  energy  is 
conserved,  and  constancy  of  temperature  persists, 
merely  because  loss  is  equal  to  gain,  because  absorption 
compensates  radiation,  not  because  radiation  ceases ; 
and  that  to  make  an  estimate  of  the  amount  of 
radiation,  so  occurring,  it  would  be  necessary  to 
suppose  the  body  in  an  enclosure  at  absolute  zero  : 
when  undoubtedly  its  kinetic  energy  would  rapidly 
leak  away,  and  be  dissipated.  But  this  refers  to 
questions  connected  with  ordinary  radiation,  whereas 


166    SUMMARY  OF  ELECTRON  THEORY  [CH.  xvm. 

we  are  now  dealing  with  the  extraordinary  variety 
known  as  radio-activity. 

If  radiation  goes  on  at  the  expense  of  the 
internal  energy  of  an  atom,  as  it  must  if  the  atom 
contains  revolving  electrons, — still  more  if,  as  on 
the  electric  theory  of  matter,  it  is  wholly  composed 
of  electric  charges, — it  becomes  necessary  to  ask 
further : — Why  are  not  all  atoms  temporary  and 
unstable  ?  Why  are  they  not  all  liable  to  internal 
catastrophe  and  disruption,  akin  to  earthquakes  and 
volcanoes?  Why  do  they  not  all  exhibit  the  phe- 
nomena of  radio-activity  ? 

The  whole  subject  of  radio-activity  is  a  large 
one,  upon  which  I  do  not  propose  to  enter  at  any 
length  here.  Suffice  it  to  realise  that  any  difficulty 
of  explanation,  in  connection  with  it,  is  not  the  fact 
itself,  but  rather  the  question  why  it  is  not  more 
notorious. 

However,  so  far  as  that  most  striking  and  interest- 
ing phenomenon — the  excessive  photographic  and 
electric  radio-activity  of  certain  rare  substances — is 
concerned,  it  has  been  already  hinted  that  the  greater 
part  of  that  does  not  consist  so  much  in  the  emission 
of  radiation  proper — whether  in  the  form  of  pulses  of 
X-rays  or  any  other  form — as  in  the  flinging  off  of 
particles ;  sometimes  negatively  charged  particles  or 
electrons,  sometimes  positive  ions.  And  these  ex- 
pelled particles,  when  they  strike  a  photographic  plate, 
appear  to  generate  by  the  concussion  electric  waves 
which  affect  the  silver  salt.  The  faint  photographic 
influence  of  ordinary  substances,  observed  by  Dr.  W. 
H.  Russell,  seemed  to  suggest  that  incipient  power  of 
this  kind  is  not  limited  to  bodies  with  heavy  atoms, 
like  Uranium,  Radium,  Polonium,  etc.,  as  described 
by  Becquerel  and  the  Curies,  though  these  substances 


€H.  xvni.]  RADIO-ACTIVITY  167 

show  it  to  an  extraordinary  degree  :  Dr.  Russell, 
however,  appears  to  have  traced  his  at  first  interesting 
effects  to  the  merely  chemical  action  of  hydrogen 
peroxide.  He  has  quite  recently  shown  that  leaves 
of  growing  plants  have  a  spontaneous  photographic 
power  of  the  same  kind. 

The  whole  subject,  together  with  the  allied  one  of 
the  loss  of  charge  from  hot  bodies,*  first  discovered  by 
Dr.  Guthrie  long  ago  (see  Phil.  Mag.,  [4],  xlvi.  p.  273), 
is  one  that  demands  special  attention  and  treatment. 

Crookes  discovered  that  the  alpha  rays,  or  particles 
projected  by  radium,  polonium,  and  other  strongly 
radio-active  substances,  were  able  by  their  concussion 
with  a  target  of  zinc-sulphide  to  produce  luminous 
flashes,  visible  under  slight  magnification  :  and  the 
evidence  on  the  whole  is  in  favour  of  the  view  that 
many  of  the  impinging  atoms  may  have  speed  enough 
to  be  able  to  cause  a  separate  flash,  by  its  own 
individual  action  on  the  crystalline  compound  :  a 
phenomenon  popularised  in  the  little  pocket-instru- 
ment called  a  *  spinthariscope.'  When  we  consider 
the  speed  with  which  these  particles  are  ejected,  such 
an  idea  is  not  surprising,  although  it  is  novel  to  have 
to  contemplate  any  perceptible  effect  produced  by  a 
single  atom.  But  taking  these  projectiles  to  be 
atoms  of  hydrogen  or  helium,  of  mass  10~24  grammes, 
flying  with  say  one-tenth  the  speed  of  light,  —  the 
stoppage  of  one  of  them  within  molecular  dimension, 
that  is  within  its  own  thickness  as  ordinarily  estimated, 
10~8  centimetre,  would  require,  for  an  exceedingly  v 
minute  fraction  of  time,  the  expenditure  of  80  horse- 
power. 


*  See,  for  instance,  Strutt  on  leakage  from  hot  bodies,  Phil. 
July,  1902  ;  J.  J.  Thomson,  ditto,  Phil.  Mag.,  August,  1902  ;  further 
•developed  by  O.  W.  Richardson,  Phil.  Trans.,  vol.  201,  p.  516  (1903). 


168    SUMMARY  OF  ELECTRON  THEORY  [CH.  XVIIL 

Solar  Corona,  Magnetic  Storms,  and  Aurorce. 

Another  subject  on  which  it  is  tempting  to  enlarge 
is  the  explanation  of  various  astronomical  and 
meteorological  phenomena  by  the  electron  theory. 

The  theory  of  Aurorse  has  recently  been  elaborated 
by  Arrhenius ;  but  the  whole  doctrine  of  emanations 
from  the  sun,  and  of  repulsion  of  small  particles  both 
by  his  light  and  by  his  probable  electrification,  is  a 
matter  that  has  been  familiar  to  me  for  many  years, 
through  conversation  with  FitzGerald  and  others. 
See,  for  instance,  Larmor,  Phil.  Trans.,  1894,  vol. 
185,  p.  813;  Lodge  on  Sunspots,  Magnetic  Storms,. 
Comets'  Tails,  Atmospheric  Electricity,  and  Auroras, 
in  the  Electrician  for  December  7,  1900,  vol.  46,  p. 
250;  FitzGerald,  Electrician,  December  14,  1900, 
with  reference  to  his  review  of  a  Heaviside  volume  in 
1893  (Electrician,  vol.  31,  p.  390).  See  also  Fitz- 
Gerald's  collected  "Scientific  Writings,"  at  date  1882. 

The  earth  is  in  fact  a  target  exposed  to  cathode 
rays,  or  rather  to  electrons,  emitted  by  a  hot  body, 
viz.  the  sun.  The  sun  is  evidently  intensely  radio- 
active :  and  the  result  of  its  discharge  of  electrons 
into  the  approximate  vacuum  of  its  immediate 
neighbourhood  is  not  unlikely  to  be  the  appearance 
known  as  the  corona.  The  gradual  accumulation 
of  negative  electricity  by  the  earth  is  a  natural 
consequence  of  this  electron  bombardment  extending 
to  greater  distances  across  space,  where  no  residual 
matter  exists  ;  and  the  fact  that  the  torrent  of  particles 
constitutes  an  electric  current  of  fair  strength  gives  an 
easy  explanation  of  one  class  of  magnetic  storms ; 
these  storms  having  long  been  known,  by  the  method 
of  concomitant  variations,  to  be  connected  with  sun- 
spots  and  aurorse.  The  electric  nuclei,  when  they 


CH.  XVIIL]  AURORA  169> 

form  ions,  would  also  serve  as  centres  for  condensation 
of  atmospheric  water  vapour  at  high  altitudes,  and  so? 
be  liable  to  affect  rainfall.  Moreover,  the  fact  that 
water  vapour  condenses  more  readily  on  negative 
than  on  positive  ions,  seems  to  furnish  us  with  one  ./ 
explanation  of  atmospheric  electricity ;  for  a  fall  of 
rain  would  bring  down  with  it  a  negative  charge, 
and  would  leave  the  upper  regions  positively 
electrified  with  respect  to  the  earth's  surface  :  and 
this  agrees  with  the  known  sign  of  the  normal  field 
of  electric  force  in  the  atmosphere. 

These  early  perceptions  have  been  well  elaborated 
of  late  by  Arrhenius ;  and  his  explanation  of  the 
aurora—by  means  of  the  catching  and  guiding  of 
rapidly  moving  electrons  by  the  earth's  magnetic 
lines  of  force,  so  as  to  deflect  them  away  from  the 
tropical  sunshine,  and  to  guide  them  in  long  spirals, 
along  the  lines,  to  the  poles, — there  to  reproduce  the 
phenomena  of  the  vacuum-tube  in  the  rarified  upper 
regions  of  the  atmosphere — is  particularly  definite  and 
pleasing.  Some  of  the  other  astronomical  suggestions 
he  has  made  are  likewise  of  considerable  interest. 

Transformations  of  Radium,  etc. 

The  following  details  are  given  by  Rutherford  for 
the  spontaneous  transformations  which  radium  under- 
goes, together  with  the  lifetime  constant  of  the 
various  products — that  is  to  say  the  time  required 
for  the  activity  of  the  product  to  fall  to  one-half  its 
value, — and  also  the  kind  of  particles  or  rays  which 
are  thrown  off. 

Certain  of  the  changes  are  rayless  changes,  and 
may  be  considered  to  result  in  an  allotropic  modi- 
fication, without  change  of  atomic  weight ;  but 
whenever  an  alpha  particle  is  thrown  off,  the  atomic 


170    SUMMARY  OF  ELECTRON  THEORY  [CH.XVIII. 

weight  must  change,  presumably  by  an  amount 
appropriate  to  the  loss  of  an  atom  of  helium.  It 
will  be  observed  that  the  gamma  or  Rontgen  rays 
always  accompany  the  emission  of  a  beta  particle  or 
electron,  and  never  appear  otherwise ;  also  that  it  is 
only  in  some  of  the  changes  that  electrons  are  thrown 
off.  It  will  be  understood  that  the  so-called  "  emana- 
tions" are  all  of  the  nature  of  gas,  while  the  other 
products  are  like  a  solid  deposit  or  coating.  These 
active  deposits,  or  "  excited  activities,"  can  be  sub- 
jected to  ordinary  chemical  tests  :  some  of  them  are 
soluble  in  acids,  some  in  ammonia ;  some  of  them 
are  volatile  at  a  high  temperature,  some  are  not 
readily  volatile.  The  following  table  contains  the 
principal  features  of  the  transformations  of  the  more 
remarkable  radio-active  substances ;  for  more  details 
Rutherford's  book  must  be  referred  to.  The  product 
here  called  Radium  F  appears  to  be  the  same  as  that 
called  by  other  observers  Radio-tellurium,  or  by  its 
original  discoverer,  Mme.  Curie,  Polonium  : 


The  substance 

has  a  life-constant 

it  shoots  off 

and  changes  into 

Uranium 
Ur.  X 

(say)  600  million 
years 
22  days 

an  a  particle  or 
(?)  helium  atom 
Py  rays 

Ur.  X 

Thorium 
Th.  X 
Emanation 
Th.  A 
Th.  B 

24  x  109  years 
4  days 
54  sees. 
11  hours 
55  mins. 

an  a  particle 
a  particle 
a  particle 
no  rays 
a/3y  rays 

Th.  X 
Emanation 
Th.  A 
Th.  B 

Actinium 
Act.  X 
Emanation 
Act.  A 
Act.  B 

10  days 

4  sees. 
36  mins. 
2  mins. 

no  rays 
a  particle 
a  particle 
no  rays 
afty  rays 

Act.  X 
Emanation 
Act.  A 
Act.  B 

€H.  XVIII.] 


RADIO-ACTIVITY 


171 


The  substance 

has  a  life-constant 

it  shoots  off 

and  changes  into 

Radium 

1300  years 

a  particle 

Emanation 

Emanation 

4  days 

a  particle 

Radium  A 

Radium  A 

3  mins. 

a  particle 

Radium  B 

Radium  B 

21  mins. 

no  rays 

Radium  C 

Radium  C 

28  mins. 

afiy  rays 

Radium  D 

Radium  D 

40  years 

no  rays 

Radium  E 

Radium  E 

6  days 

fiy  rays 

Radium  F 

Radium  F 

143  days 

a  particle 

Possibly  Lead 

Emanations. 

The  discovery  of  thorium  and  radium  emanations 
was  made  by  Rutherford  and  Dorn  respectively  in 
consequence  of  an  observation  of  Owens  on  the 
irregularity  of  thorium  rays  in  producing  ionisation, 
the  fact  being  that  any  of  these  materials  are  more 
active  when  the  emanation  has  been  allowed  to 
accumulate  than  soon  after  it  has  been  removed. 
For  the  emanation,  although  so  infinitesimal  in 
quantity,  is  considerably  more  active  than  the  sub- 
stance itself;  and,  being  a  gas,  it  can  readily  be 
drawn  away  or  otherwise  expelled  from  the  pores  or 
neighbourhood  of  the  salt.  But  it  accumulates  again, 
being  evidently  generated  in  situ,  and  presently  the 
full  activity  of  the  substance  is  restored.  Radium 
emanation  is  shown  by  Rutherford  and  Soddy  to 
liquefy  at  a  temperature  of  about  150  degrees  below 
zero;  thorium  emanation  liquefies  at  about  —  120°  C. 
They  appear  to  be  quite  definite,  though  transitory 
and  very  unstable  and  disintegrating,  materials. 

Deflexion  of  Alpha-rays. 

When  alpha-rays  are  submitted  to  a  strong 
magnetic  field  they  are  deflected,  though  very 


172    SUMMARY  OF  ELECTRON  THEORY  [CH.  XVIIK 

slightly,  in  a  direction  indicating  that  they  are  posi- 
tively charged  particles.  Rutherford  and  Becquerel 
have  both  observed  this  fact,  and  Strutt  has  confirmed 
the  fact  of  positive  charge.  But  quite  recently* 
Soddy  has  surmised  that  this  positive  charge  might 
be  acquired  by  ionisation  in  travelling  through  the 
air,  and  that  in  a  high  enough  vacuum  no  deflexion 
would  be  observed ;  thereby  showing  that  intrinsi- 
cally they  did  not  possess  a  charge.  He  believes 
himself  to  have  confirmed  this  by  careful  though 
difficult  experiment.  So  important,  and  in  some 
respects  improbable,  a  conclusion,  however,  cannot 
yet  be  regarded  as  at  all  certain. 

Rutherford  was  the  first  to  observe  the  fact  and 
the  sign  of  the  magnetic  deflexion  or  curvature  of 
alpha  rays,  and  to  make  an  estimate  of  its  amount. 
He  invented  the  device  of  sending  them  through  a 
magnetic  field,  up  a  stream  of  rarified  hydrogen, 
between  a  set  of  narrow  plates  set  edgeways ;  which 
latter  constituted  a  grid  that  would  be  opaque 
unless  the  trajectories  of  the  flying  particles  were 
rigorously  straight.  He  thus  made  the  discovery  that 
the  rays  consisted  of  positively  charged  particles,  and 
arrived  at  a  rough  estimate  of  their  atomic  weight. 

Becquerel  measured  the  magnetic  deflexion  of 
alpha  rays,  at  different  distances  from  the  source, 
by  letting  them  graze  a  photographic  plate  at  a 
known  angle.  The  actual  trace  observed  was  a 
short  slant  line  with  a  slight  curvature ;  reversal  of 
the  field  slanted  the  line  the  other  way,  thus  giving 
a  resultant  impression  like  the  conventional  two  wings 
of 'a  flying  bird  drawn  at  a  very  acute  angle.  Subse- 
quent measurement  of  the  distance  apart  of  different 
positions  of  the  two  wings  gave  the  data  sought. 

*  See  Nature,  2nd  August,  1906. 


CH.  xviii.]  RADIO-ACTIVITY  173 

Eutherford  has  examined  the  deflexion  of  alpha 
particles  from  radium  in  a  careful  manner.  Previous 
experiments,  such  as  his  own  and  those  of  Becquerel 
and  Des  Coudres,  were  made  on  a  thick  layer  of 
radium  ;  but  under  these  circumstances  the  particles 
are  projected  with  a  considerable  range  of  velocity. 
To  obtain  homogeneous  radiation  it  is  necessary  to 
use  a  very  thin  layer ;  and  Rutherford  employed 
for  this  purpose  the  product  Radium  C, — namely, 
part  of  the  active  deposit  which  appears  on  a  fine 
wire  exposed  for  some  hours  to  radium  emanation. 
This  is  a  deposit  of  utterly  imperceptible  thickness, 
undetectable  by  any  means  save  radio-activity ;  and 
it  consists  of  Radium  A,  B,  and  C.  The  activity  of 
Radium  A  disappears  in  about  a  quarter  of  an  hour ; 
Radium  B  emits  no  rays ;  so  Radium  C  alone  is  left 
active,  and  it  emits  only  alpha  rays.  It  is  true  it 
dies  away  in  about  a  couple  of  hours,  but  there  is 
time  enough  for  an  experiment.  The  method  em- 
ployed is  like  this  : 

Rays  from  the  wire  pass  through  a  narrow  slit,  and 
then  on  to  a  photographic  plate  in  a  vacuum ;  a 
uniform  magnetic  field  is  applied  in  a  direction 
parallel  to  the  slit,  so  as  to  curve  the  rays ;  this  field 
is  reversed  every  ten  minutes,  so  that  on  developing 
the  plate  two  narrow  parallel  lines  are  observed,  the 
distance  between  which  represents  twice  the  de- 
flexion ;  their  sharpness  shows  that  the  rays  were 
homogeneous.  The  path  corresponding  to  a  magnetic 
field  of  9470  C.G.S.  units  had  a  radius  of  curvature 
equal  to  42  centimetres. 

Electric  deflexion  was  not  then  applied ;  but, 
estimating  the  number  of  particles  expelled  from  the 
Radium  C  as  6*2  x  1010  per  second,  and  the  heating 
effect  as  31  calories  per  hour,  Rutherford  calculated 


174    SUMMARY  OF  ELECTRON  THEORY  [CH.  xvm. 

the  emission  of  energy  as  '36  million  ergs  per  second. 
Combining  this  with  the  magnetic  deflexion,  the 
result  is  that  u  =  2'6xlOQ  centimetres  per  second, 
while  e/m  =  6,500  electro-magnetic  units. 

Des  Coudres,  using  both  electric  and  magnetic 
deflexion,  but  employing  more  complex  rays,  obtained 
u=l'65  x  109,  and  e/m  6,400. 

Activity  of  Radium  at  all  Temperatures. 

Messrs.  Dewar  and  Curie  have  shown  that  at  the 
temperature  of  liquid  hydrogen,  252  degrees  below 
zero  centigrade,  the  heat  evolution  of  radium  is  the 
same  as  at  ordinary  temperatures.  It  has  also  been 
shown  to  be  equally  active  in  the  solid  or  in  the 
dissolved  state,  and  elevation  of  temperature  makes 
it  no  more  active. 

The  activity  of  radium,  as  observed  in  Crookes' 
spinthariscope,  is  just  as  marked  at  the  temperature 
of  liquid  hydrogen  as  at  ordinary  temperatures, 
provided  the  luminescent  screen  is  not  likewise 
chilled. 

Spectrum  of  Radium. 

In  speaking  of  the  spectrum  of  radium  there  is  an 
ambiguity  to  be  guarded  against.  We  may  mean 
the  spectrum  of  radium  itself,  when  it  is  put  in  a 
flame  or  subjected  to  the  electric  spark ;  or  we  may 
mean  the  spectrum  of  the  spontaneous  glow  of 
radium  chloride  or  bromide,  which  can  be  seen  in 
the  dark.  The  latter  spectrum  is  very  difficult  to 
observe,  because  of  its  extreme  faintness,  but  the 
experience  of  Sir  William  and  Lady  Huggins  has 
enabled  them  to  examine  it,  and  to  show  that  it 
is  chiefly  the  spectrum  of  atmospheric  nitrogen ; 
which  is  thereby  proved  to  be  ionised  and  violently 


CH.  XVIIL]          SPECTRUM   OF   RADIUM 


175 


disturbed  by  the  neighbourhood  of  radium,  to  the 
extent  of  emitting  luminous  radiation  without  eleva- 
tion of  temperature.  The  spontaneous  radium -glow 
is,  in  fact,  probably  due  to  its  influence  on  other 
substances  ;  and  ordinary  glass,  exposed  to  it,  darkens 
and  becomes  thermo-luminescent, — that  is  to  say,  it 
begins  to  emit  light  when  raised  to  a  temperature 
of  about  500  degrees. 

M.  Eugene  Ne'culcea  gives  the  following  table  of 
the  photographic  spectrum  of  the  radium  spark,  as 
observed  by  M.  Demargay,  the  wave  lengths  being 
given  in  "  tenth-metres."  In  the  visible  spectrum, 
which  is  not  photographed,  there  is  only  one  notable 
ray,  of  wave-length  5665.  For  other  observations^ 
see  Runge,  Astrophysical  Journal,  1900,  p.  1. 


WAVE-LENGTH. 

INTENSITY. 

WAVE-LENGTH. 

INTENSITY. 

f  4826-3 

10 

{4600-3 

3 

4726-9 

5 

4533-5 

9 

Blue- 

4699-8 
4692-1 

3 

7 

4436-1 
(4340-6 

8 
12 

4683-0 

14 

Ultra-violet  \  3814'7 

16 

^4641-9 

4 

(3649-6 

12 

The  detection  of  radium  by  the  spectroscope, 
through  its  strongest  line,  38147,  though  it  may  be 
a  method  perhaps  a  million  times  more  sensitive  than 
ordinary  chemical  analysis,  has  been  shown  to  be  a 
million  times  less  sensitive  than  a  method  of  detec- 
tion by  means  of  an  electroscope,  utilising  the 
extraordinary  ionising  power  of  its  radio-activity. 
For  Rutherford  reckons  that  each  a  particle  expelled  x 
from  radium  is  able  to  generate  some  hundred  thou- 
sand ions  before  it  is  stopped,  or  rather  before  its 


176    SUMMARY  OF  ELECTRON  THEORY   [CH.  xvm. 

immense  initial  velocity  falls  below  a  certain  critical 
speed  at  which  ionisation  ceases  to  be  caused.  A 
charged  electroscope  of  proper  sensitiveness  is  able 
to  indicate  by  its  leak  the  presence  of  this  number  of 
ions,  and  accordingly  is  able  to  signal  the  presence 
of  only  one  a  particle.  But  the  number  of  such 
particles  expelled  by  a  milligramme  of  fully  active 
radium  is  estimated  as  a  hundred  million  every 
second. 

Electric  Production. 

The  power  of  radium  constantly  to  develop  elec- 
tricity was  first  demonstrated  by  W.  Wien,  by 
suspending  a  tube  in  a  vacuum.  Dorn  observed  that 
sometimes  sparks  were  obtained  on  opening  a  tube 
containing  radium.  Strutt  contrived  an  ingenious 
device  for  displaying  this  constant  production  of 
electricity  by  reason  of  the  very  different  penetrating 
power  of  the  +  a  and  the  —  /3  particles,  so  that  one 
set  can  be  trapped  while  the  other  set  escapes. 

Fig.  22  shows  Strutt's  apparatus  and  "perpetual" 
— more  accurately,  perennial — electric  generator  and 
source  of  mechanical  energy.  A  small  tube  contain- 
ing radium  salt,  with  its  outside  made  sufficiently 
conducting,  has  a  pair  of  gold  or  aluminium  leaves 
attached,  to  it,  and  is  insulated  in  a  very  high 
vacuum  by  a  quartz  rod ;  a  metallic  strip,  lining 
the  vacuum  case,  being  connected  to  earth.  The 
radium  fires  off  positive  and  negative  particles  in 
equal  quantities ;  but  the  negative,  being  small  and 
penetrating,  are  many  of  them  able  to  escape,  while 
the  positive  accumulate  and  thus  keep  on  slowly 
charging  the  gold  leaves  with  positive  electricity  till 
they  periodically  overflow.  The  high  vacuum  is 
necessary  to  prevent  the  internal  atmosphere  from 


CH.  XVIII.] 


RADIO-ACTIVITY 


177 


becoming  conducting,  by  ionisation  from  the  shock 
of  the  flying  particles,  and  as  a  consequence  pre- 
venting the  gold  leaves  from  becoming  charged. 

Radio-activity  of  Ordinary  Materials. 

Even  in  the  absence  of  radium,  a  charged  electro- 
scope is  usually  found  to  leak  rather  more  than  any 
creeping  along  the  supports  can  account  for;  this 


FIG.  22. — Strutt's  mode  of  demonstrating  constant  electric  production 
by  radium. 

leakage  must  be  due  to  ionisation  of  the  atmosphere, 
and  a  consequent  kind  of  gaseous  electrolysis  in  the 
air.  The  ionisation  is  partly  due  to  stray  radiation 
from  outside,  but  some  of  it  may  be  due  to  the 
radio-activity  of  materials  with  which  the  interior 
of  the  electroscope  can  be  lined.  Definite  experi- 
ments of  this  kind  have  been  made  by  M'Lennan  and 
Burton  of  Toronto,  and  by  Strutt,  also  by  A.  Wood, 
Rutherford  and  Cooke.  When  cylinders  of  zinc, 
tin,  or  lead  were  used  to  line  the  electroscope,  a 


L.E. 


M 


178    SUMMARY  OF  ELECTRON  THEORY    [CH.  xvm. 

certain  leakage  was  observed,  but  this  was  reduced 
some  thirty  per  cent,  when  the  whole  was  plunged 
into  a  tank  of  water  so  as  to  screen  the  interior 
from  outside  radiation. 

Kutherford  and  Cooke  surrounded  the  electroscope 
with  thick  screens  of  various  kinds,  and  once  with 


K. 


FIG.  23. — Righi  form  of  electroscope  or  electrometer,  of  small  capacity. 
The  vital  parts  DECB,  with  the  gold  leaf,  are  shown  on  a  larger  scale  in 
fig.  24.  They  are  contained  in  a  metal  case,  with  a  movable  wire  G,  by 
which  they  may  be  charged  from  outside.  The  instrument  is  read  by  a 
reading  microscope  R;  an  ordinary  millimetre  scale  being  placed  in  a 
conjugate  focus  and  projected  by  the  lens  L  on  to  the  plane  of  observa- 
tion where  the  gold  leaf  is.  The  radio-active  substances  are  presented 
to  the  box  outside  a  window  of  very  thin  aluminium  foil. 

as  much  as  five  tons  of  lead.  A  moderate  amount 
of  screen,  however,  was  found  to  produce  the  same 
effect  as  a  greater  amount,  showing  that  the  influence 
of  the  outside  penetrating-radiation  could  be  checked 
without  stopping  more  than  thirty  per  cent,  of  the 


CH.  XVIII.] 


RADIO-ACTIVITY 


179 


leakage ;  the  remaining  seventy  per  cent,  seemed  due 
to  internal  radio-activity.  Materials  such  as  brick 
seem  specially  radio-active,  and  any  metals  which 
have  been  exposed  to  the  outside  atmosphere  are 
more  radio-active  than  virgin  metal. 

But,  in  addition  to  this  induced  or  excited  activity, 
Strutt  and  others  tried  a  good  many  materials  and 
found  different  characteristic  effects  with  each. 


D. 


E. 


FIG.  24. — Working  part  of  the  above  electroscope,  magnified  four  times. 
The  rod  AB  with  the  gold  leaf  C  is  cemented  to  a  thin  rod  of  melted 
quartz  D  by  means  of  a  drop  of  mastic  or  guttapercha  at  the  bottom  of  a 
minute  metallic  capsule  E  attached  to  the  rod  AB;  thereby  lessening 
any  tendency  of  the  charge  to  creep,  and  keeping  the  capacity  exceedingly 
small. 

The  question  of  whether  radiation  is  emitted 
spontaneously  by  metals  of  every  kind,  and  not  only 
by  those  few  substances  which  are  conspicuously 
radio-active,  has  been  still  further  examined  by  Mr. 
Norman  E.  Campbell  of  Trinity  College,  Cambridge 
(Phil.  Mag.,  Feb.  7,  1906).  He  adduces  very  strong 
experimental  proof  that  such  radiating  power  actually 
exists,  since  they  all  ionize  the  air  in  their  neigh- 
bourhood. Moreover,  the  experiments  indicate  a 


180    SUMMARY  OF  ELECTRON  THEORY   [CH.  xvm. 

characteristic  or  specific  quality  in  the  radio-activity 
of  the  different  substances :  a  result  tending  to  nega- 
tive the  idea  that  it  is  due  to  some  residual  effect 
of  a  common  impurity,  such  as  an  excessively 
minute  trace  of  radium  common  to  all  metals ; 
the  indication  is  rather  in  favour  of  a  specific 
radio-activity  belonging  to  each  metal,  not  due  to 
any  impurity. 

It  is  not  yet  absolutely  proved  that  this  is  identical 
with  orthodox  radio-activity,  of  the  kind  which  is 
accompanied  by  atomic  change  or  transformation  of 
substance ;  but,  inasmuch  as  the  rays  appear  to  consist 
to  a  great  extent  of  alpha-rays,  there  is  not  much 
doubt  but  that  the  complete  identity  of  the  process 
will  be  established  before  long. 

Population  Analogy. 

Since  radio-activity  is  a  sign  of,  and  is  accompanied 
by,  disintegration  and  loss  of  material,  it  is  manifest 
that  substances  of  exceedingly  high  radio-activity 
must  be  comparatively  scarce.  Ordinary  permanent 
materials  cannot  be  violently  radio-active,  though 
each  gramme  of  them  might  lose  a  few  thousands  of 
atoms  per  second  without  any  probability  of  our 
being  able  to  detect  the  loss  by  weighing — not  even 
by  weighings  continued  through  a  century.  The 
plentifulness  of  a  substance  must  depend  on  its  rate 
of  production,  its  life  time,  and  its  rate  of  decay;  just 
as  the  population  of  a  circumscribed  area  is  deter- 
mined by  the  birth  rate,  death  rate,  and  average  age. 


CHAPTER  XIX. 

EADIATION  FROM  A  RING  OF  ELECTRONS,  AND  ITS 
BEARING  ON  THE  CONSTITUTION  OF  AN  ATOM. 

ALTHOUGH  the  radiating  power  of  a  single  vibrating 
or  revolving  electron  is  considerable,  even  when  the 
speed  is  not  excessively  high,  it  must  be  observed 
that  the  amount  of  radiation  emitted  is  greatly 
diminished  when  a  second  symmetrically  situated 
particle  is  introduced  ;  because,  at  a  distance,  it  will 
be  virtually  in  opposite  phase  to  the  first.  The 
diminution  is  specially  marked  when  the  speed  is 
low.  In  order  to  assist  the  radiation,  the  second 
electron  at  the  opposite  end  of  a  diameter  should 
be  of  opposite  sign  to  the  first. 

Three  similar  electrons  at  the  corners  of  an  equi- 
lateral triangle  will  radiate  much  less  than  two ;  and 
so  with  every  addition  to  a  symmetrical  system  of 
rotating  particles,  the  radiating  power  diminishes ; 
until  when  they  form  a  continuous  ring  there  is  of 
course  no  radiation  emitted  at  all,  since  everything 
is  then  continuous. 

Professor  J.  J.  Thomson  has  calculated  the  amount 
by  which  the  radiation  is  diminished  when  the 
number  of  particles  is  increased :  and  shown  how 
greatly  it  depends  on  their  velocity.  If  they  are 
travelling  with  an  orbital  velocity  of  one-tenth  the 


182  RADIATION  FROM  ELECTRONS      [CH.  xix. 

speed  of  light,  two  electrons  at  opposite  ends  of  a 
diameter  radiate  about  one-tenth  as  much  as  either 
alone ;  four  electrons  at  the  corners  of  a  square, 
likewise  rotating  with  one -tenth  of  the  velocity  of 
light  in  its  own  plane,  will  have  a  radiating  power 
of  about  one  six-thousandth  of  that  of  one  of  them. 
But  if  the  velocity  of  the  particles  is  only  one- 
hundredth  that  of  light — as  must  often,  perhaps 
usually,  be  the  case  among  constituent  electrons 
in  an  atom, — then  a  pair  would  radiate  only 
one-thousandth  as  much  as  one.  For  three,  the 
radiating  power  is  diminished  to  about  one  two- 
millionth  ;  and  for  six,  to  something  getting  on 
for  a  trillionth, — which  practically  means  no  radiat- 
ing power  at  all. 

The  actual  numbers,  and  the  calculation,  can  be 
found  in  the  Philosophical  Magazine  for  December 
1903,  p.  681. 

All  this  depends  on  the  electrons  being  sym- 
metrically situated  round  the  centre  of  rotation ; 
but  if  by  any  cause — such  as  an  atomic  clash  or 
chemical  collision — they  are  displaced  from  sym- 
metry, then  their  centre  of  gravity  will  rotate 
round  the  original  centre,  and  will  act  as  a  single 
electron,  or  rather  as  an  electron  of  multiple  mass 
and  constitution.  The  constituent  particles  will  now 
not  compensate  each  other  at  all,  so  far  as  this 
excentric  motion  is  concerned.  Accordingly  the 
,  y  radiation  instantly  becomes  violent,  and  must  be 
regarded  as  the  source  of  the  visible  spectrum:  the 
nature  of  the  lines  depending  on  the  structure  of 
the  composite  body,  which,  by  reason  of  temporary 
displacement,  now  acts  as  a  single  radiator  of  great 
power.  In  this  way  it  is  possible  to  conceive  of  the 
particular  kind  of  radiation,  exhibited  in  the  spectrum, 


CH.  xix.]  INSTABILITY   OF   ATOM  183 

as  being  determined  by  the  character  of  the  composite 
radiator;  while  the  occurrence  of  the  radiation  itself  is 
limited  to  the  periods  during  which  the  displacement 
by  chemical  clash  or  collision  continues  effective  :  a 
period  in  each  individual  case  probably  very  short, 
but  rapidly  renewed  in  the  aggregate  by  the  com- 
bination or  collision  of  other  molecules. 

Radiation  due  to  high  temperature  may  be  caused 
in  a  somewhat  similarly  accidental  and  violent  fashion, 
not  occurring  at  all  appreciably  during  the  intervals 
of  peace  or  regular  motion. 

Instability  of  an  Atom. 

The  principle  on  which  instability  of  an  atom  is 
to  be  expected,  on  the  electrical  theory,  at  certain 
critical  points  in  its  history,  may,  according  to 
J.  J.  Thomson,  depend  upon  the  fact  that  a  rotat- 
ing ring  of  electrons  is  only  stable  so  long  as  their 
angular  velocity  exceeds  a  certain  critical  value. 
Three  electrons  indeed  are  stable  even  when  stationary, 
though  they  become  more  stable  by  rotation ;  but 
four  corpuscles  in  one  plane,  at  the  corners  of  a 

square,  are  not  stable  unless  they  are  rotating  with  an 

//          Ne2  \ 
angular  velocity  greater  than      /I  *325  — J^L   or   '57c 

as  it  is  called  in  the  next  chapter.  Whenever  their 
speed  falls  below  that  value,  they  adjust  themselves 
at  the  corners  of  a  tetrahedron  or  triangular  pyra- 
mid,— tumbling  over  into  the  new  position  with  a 
rapid  collapse,  analogous  to  the  tumbling  over  of 
a  top  when  its  rate  of  spin  has  fallen  below  a 
certain  critical  value. 

With  a  greater  rate  of  rotation,  five  corpuscles  in 
one  plane  may  be  stable ;  but  with  six  in  a  ring, 


184  RADIATION  FROM  ELECTRONS     [CH.  xix. 

stability  is  impossible  at  any  speed,  so  long  as  there 
are  only  six  present ;  but  if  one  of  the  six,  or  if  a 
seventh,  be  placed  as  a  centre  to  the  ring,  then  they 
become  stable  again  ;  and  at  a  proper  speed  there  can 
now  be  seven  or  even  eight  corpuscles  in  a  ring,  but  not 
more,  unless  more  corpuscles  be  placed  in  the  centre. 
Suppose,  for  instance,  that  three  be  put  in  the  centre  : 
they  will  there  form  a  triangle,  and  round  them  there 
may  be  a  ring  of  as  many  as  ten  others.  But  to  get 
a  stable  ring  of  twelve  corpuscles,  you  must  have 
seven  inside  altogether  ;  of  which  six  or  five  can  be  in 
another  ring,  with  one  or  two  at  the  centre  of  that. 
By  this  means  a  large  number  of  corpuscles,  all  in 
rapid  rotation,  can  be  arranged  in  a  series  of  rings ;. 
but  if  the  speed  of  any  ring  falls  below  a  certain 
critical  value  it  becomes  unstable,  and  then  there 
has  to  be  a  readjustment  of  corpuscles  into  another 
pattern,  which  must  give  rise  to  a  sudden  con- 
vulsion in  the  hypothetical  structure  of  the  atom. 
This  readjustment  involves  a  decrease  of  potential 
energy  and  consequent  increase  of  kinetic  energy, 
and  hence  might  result  in  the  expulsion  of  some 
corpuscles. 

Note  that  such  a  convulsion,  on  this  theory,  must 
undoubtedly  occur  from  time  to  time,  though  it  may 
be  a  rare  occurrence  in  the  life  of  any  one  atom ; 
because  revolving  charges  of  electricity  necessarily 
radiate  energy  to  some  extent — though  usually  to  a 
very  small  extent, — and  accordingly  their  speed  must 
gradually  be  reduced,  until  sooner  or  later  it  arrives  at 
the  critical  value  at  which  a  convulsion  must  occur. 
The  convulsion  is  followed  by  readjustment  into 
another  pattern,  and  consequent  transmutation  into 
another  element,  or  at  least  into  an  allotropic  form 
of  the  first  element  if  no  fragment  is  lost ;  and  the 


CH.  xix.]  INSTABILITY   OF   ATOM  185 

occurrence  is  accompanied,  and  indeed  demonstrated, 
by  radio-activity. 

A  list  of  the  series  of  changes  actually  observed  in 
radio-active  substances  will  be  found  above  in  Chap. 
XVIII.,  p.  170. 

Cosmic  Analogy. 

An  analogy  may  be  drawn  between  the  occasional 
disruption  of  one  of  a  large  group  of  atoms,  and  the 
phenomenon  observed  from  time  to  time  in  the  sky 
called  a  new  or  temporary  star.  Both  are  outbursts 
of  a  kind  of  radio-activity,  though  they  may  be 
excited  by  different  causes  ;  both  are  comparatively 
rare  occurrences,  when  the  whole  available  number 
of  bodies  capable  of  such  outburst  or  collision  is 
contemplated. 

Assuming  that  in  a  gramme  of  average  terrestrial 
material  there  are  a  thousand  such  eruptions  every 
second,  that  would  correspond  to  about  one  new 
star  per  century  among  a  cosmic  assemblage  of  ten 
thousand  million  bodies. 

Another  Account  of  Atomic  Instability. 

A  different  idea  of  the  nature  of  Instability  was 
suggested  by  myself.  An  electron  which  is  rotating 
outside  an  atom,  being  attracted  thereto  by  a  force 
varying  as  the  inverse  square  of  the  distance,  will,, 
as  it  tends  to  lose  energy  by  radiation,  get  drawn 
nearer  and  nearer  to  the  atom ;  and  will  increase  in 
speed  inversely  with  the  square  root  of  the  distance. 
As  the  speed  thus  increases,  the  effective  inertia  of  the 
particle  will  increase,  and  accordingly  it  will  be  more 
and  more  difficult  to  retain  it  in  an  orbit  by  the  centri- 
petal force ;  since  this  force,  being  merely  an  electrical 


186  RADIATION  FROM  ELECTRONS     [CH.  xix. 

attraction,  is  not  a  function  of  the  speed,  or,  in  so 
far  as  it  is  a  function  of  the  speed,  it  is  a  function 
which  diminishes  as  the  speed  increases.  Accordingly 
there  must  come  a  time  when  the  electrical  attraction 
is  incompetent  to  hold  in  the  revolving  mass,  which 
then  begins  to  strain  itself  a  little  further  off,  with 
the  velocity  now  acquired ;  but,  by  so  doing,  it  still 
further  diminishes  the  force  which  holds  it  in, 
without  diminishing  the  centrifugal  force  it  is  itself 
exerting ;  and  accordingly  there  is  no  longer  equi- 
librium. The  equilibrium  at  the  point  of  greatest 
proximity  is  in  fact  unstable,  and  so  the  particle  itself 
flies  off  tangentially  with  the  speed  which  it  had  then 
acquired,  thus  beginning  a  radio-activity  of  a  fresh 
kind — radio-activity  discovered  by  Becquerel — the 
emission  of  violently  flying  electrons  or  Beta-rays. 

The  whole  constitution  of  the  atom  may  be  upset 
by  losses  of  this  kind,  and  a  rearrangement  of  its 
substance  appears  occasionally  to  occur,  with  the 
flinging  away  of  some  portion  as  a  material  pro- 
jectile;  these  particles  thus  thrown  off  constituting 
the  observed  Alpha-rays.  Sometimes  electrons  are 
thrown  off  too. 

The  sudden  ejection  of  an  electron,  like  the  sudden 
stoppage  of  one,  is  well   calculated  to   excite  those 
vibrations   in   the   ether    discovered   by   Kontgen— 
known  in  the  case  of  spontaneous  radio-activity  as 
Gamma-rays. 

Electric  Theory  of  Matter. 

A  scheme  or  model  for  the  construction  of  atoms 
of  different  sorts  of  elementary  substances,  by  means 
of  groups  of  electrons  revolving  in  plane  orbits  round 
a  centre  according  to  the  law  of  direct  distance, — 
together  with  some  indication  of  the  known  spectral 


CH.  xix.]  INSTABILITY   OF   ATOM  187 

and  chemical  properties  of  such  substances,  and  the 
deduction  of  a  series  or  family  likeness  akin  to 
Mendelejeff's  series  on  this  hypothetical  constitution, 
— is  to  be  found  worked  out  in  a  masterly  manner 
by  Professor  J.  J.  Thomson  in  the  Philosophical 
Magazine  for  March,  1904. 

If  at  the  present  time  there  were  other  confirmatory 
evidence  of  this  mode  of  regarding  the  atom — if  it 
were  possible  to  understand  what  is  meant  by  positive 
electricity  existing  as  a  permeable  sphere  with  a  large 
number  of  electrons  sown  in  it — it  would  be  proper  to 
give  a  further  account  of  this  remarkable  and  attractive 
theory;    but  inasmuch  as  the  light  which  has  quite 
recently  fallen  upon  the  whole  subject  is  of  a  flicker- 
ing and  undecided  nature,  tending  somewhat  in  the 
direction  of  confusion  and  uncertainty  rather  than  con- 
firmation of  this  promising  but  still  necessarily  vague 
hypothesis — see  Chaps.  XV.  and  XVII.   and  Chap. 
XX. — I  think  it  better  to  leave  its  further  discussion 
and  development  to  a  future  time,   and  meanwhile 
await  further  theoretical  and  experimental  evidence. 
For  it  is  neither  theory  alone  nor  experiment  alone 
which  can  be  of  service   in    this  matter :    progress 
must   be   achieved    by   a   combination   of   the   two, 
welded    together    by    genius ;    and    it    is   just    this 
combination    of    theory  and    experiment — ingenious 
experiment   combined  with    advanced   mathematical 
theory — to  which  of  late  years  all  the  finest  advances 
in  physical  science  have  been  due. 


CHAPTER   XX. 

DIFFICULTIES  CONNECTED  WITH  THE  ELECTRIC 
THEORY  OF  MATTER. 

1.   Concerning  the  formation  of  Spectrum  lines. 

LORD  RAYLEIGH  has  pointed  out,  in  the  Phil.  Mag. 
for  January,  1906,  that  if  the  radiation  from  atoms  is 
due  to  shock  and  recovery,  the  series  of  vibrations 
that  would  be  obtained  would  show  a  simple  relation 
between  the  squares  of  the  frequencies,  as  is  th£  case 
with  plates  and  bells  and  other  disturbed  elastic 
vibrators,  and  not  between  the  simple  frequencies 
themselves ;  whereas  the  spectrum  observations  of 
Rydberg,  and  of  Kayser  and  Runge,  show  that 
simple  expressions  for  the  first  power  of  the 
frequency,  and  constant  differences  of  frequency 
among  a  series  of  lines,  are  really  applicable  to 
the  facts. 

Waves  of  this  observed  kind  would  be  emitted  by 
electrons  which  radiate  by  reason  of  their  unper- 
1  turbed  orbital  motion,  or  other  regular  concomitant 
of  the  constitution  of  the  atom,  but  would  not  be 
the  result  of  oscillatory  recovery  from  disturbance 
of  equilibrium. 

The  natural  frequencies  of  an  undisturbed  rotating 
ring  of  corpuscles,  for  instance,  would  be  functions  of 


€H.  xx.]    ELECTRIC  THEORY  OF  MATTER          189 

the  angular  velocity  and  of  the  number  of  corpuscles 
in  the  ring,  as  well  as  of  other  constants. 

(Thus,  for  instance — according  to  the  paper  men- 
tioned near  the  end  of  last  chapter — the  frequencies 
of  emission  possible  to  two  rotating  corpuscles- 
each  of  mass  m  and  charge  e,  rotating  with  angular 
velocity  «  inside  a  spherical  mass  of  positive  charge 
Ne  and  radius  b — will  be  the  following  six  values, 
corresponding  to  their  six  degrees  of  freedom  :— 

0,  wt  c,  c-w,  o  +  w,  ,/(3c2  +  «2), 
where  we  have  written  Ne2//cmfr3  as  c2. 

The  frequencies  c  and  o>  belong  to  vibrations 
perpendicular  to  the  plane  of  the  orbit :  the  others 
are  in  that  plane. 

It  may  be  noted  that  on  the  hypothesis  of  uniform 
distribution  of  positive  electricity  of  density  p 
throughout  the  sphere,  the  meaning  of  Ne/63  is  f  irp ; 
and  that  c2  is  the  ratio  of  this  quantity  to  the  electro- 
chemical equivalent  of  an  electron,  in  electrostatic 
measure.  The  numerical  value  of  c/J'N  is  approxi- 
mately 1016,  so  that  c  corresponds  to  high  ultra-violet 
radiation. 

For  three  corpuscles  there  should  be  nine  degrees 
of  freedom  :  six  in  the  plane,  and  three  perpendicular 
thereto.  The  corresponding  frequencies  are 

0,    ±0),  C,  «-±C,  V^  +  o,2),  0)  +  ^{^(SC2 -O)2)}. 

When  there  is  no  rotation,  in  each  of  the  two  cases 
considered,  three  of  the  frequencies  become  equal, 
and  two  vanish.) 

Ordinarily,  however,  the  constitutional  radiation  is 
excessively  weak,  barely  perceptible ;  and  it  is  known 
that  the  radiation  which  emits  light  and  produces  a 
spectrum  is  the  result  of  violence  and  chemical  clash 
— that  it  requires  something  of  the  nature  of  collision 


190  ELECTRIC  THEORY  OF  MATTER    [CH.  xx. 

to  bring  it  out.  But  then  anything  in  the  nature  of 
collision  would  give  a  series  of  vibrations  characterised 
by  the  square  of  the  frequency.  Hence  there  is  a 
difficulty. 

The  difficulty  seems  to  be  capable  of  being  over- 
come by  the  suggestion — already  made  on  page  182 
— that  during  the  chemical  collision  in  question, 
the  perturbation  is  of  the  nature  of  a  disturbance 
of  the  centre  of  gravity  of  a  revolving  system. 
Such  an  eccentricity,  or  any  other  destruction  of 
symmetry,  would  at  once  develop  strong  radiating 
power;  but  it  might  nevertheless  leave  the  harmonic 
constituents,  and  peculiarities  of  the  radiation,  to  be 
governed  by  the  simple  frequency  law  appropriate 
to  the  revolving  constituents,  rather  than  to  the 
squared  frequency  law  appropriate  to  their  elastic 
recovery  from  vibration.  In  other  words,  the  fact 
of  considerable  radiation  would  be  due  to  the 
collision,  but  the  land  of  radiation  emitted  would  be 
due  to  the  previously  existing  constitution,  upon 
which  the  disturbance  had  now  conferred  temporary 
radiating  power  of  considerable  magnitude, — tem- 
porary, because  the  radiation  itself  must  speedily 
exhaust  the  energy  of  the  disturbance  and  soon 
restore  the  pristine  condition. 

It  may  seem  an  open  question  whether  a  disturbance 
of  centre  of  gravity  would  allow  quiet  revolution  to 
continue  as  before,  or  whether  it  would  not  precipitate 
a  catastrophe.  Simple  mechanical  considerations  show, 
however  (Phil.  Mag.,  March,  1904,  p.  264),  that 
when  the  law  of  force  is  the  direct  distance,  as  it  is 
inside  the  hypothetical  sphere  of  positive  electricity, 
no  such  calamity  is  to  be  expected ;  but  that,  on  the 
contrary,  a  triangle  or  other  group  of  corpuscles,  no 
matter  how  much  displaced — provided  that  they  are 


CH.  xx.]    ELECTRIC  THEORY  OF  MATTER          191 

not  displaced  so  as  to  reach  the  boundary  of  the 
enclosing  sphere — will  continue  to  rotate  round  their 
common  centre  of  gravity  in  the  same  relative  position 
as  before;  while  this  will  revolve,  on  its  own  account, 
round  the  centre  of  the  enclosing  sphere.  Such  a 
displaced  group — being  virtually  a  solitary  though 
compound  corpuscle — will  now  be  endowed  with  great 
radiating  power. 

On  the  fairly  verified  hypothesis  that  the  mass 
of  a  corpuscle  is  wholly  electrical,  it  is  of  interest 
to  interpret  the  constant  c  further  ;  it  has  dimensions 
of  a  frequency ;  for 

Ne2 
c2  =  — ^,    while   m  = 


So 


2V 

v    I! 
or  c  = 


Taking   b   as   of  atomic   and   a   as   of  electronic 
dimensions,  this  becomes  numerically 

0     y     I    AlO 

c=     *.8    V(N  x  !0~5)  =  lO'VW  Per  second, 


where,  since  Ne  measures  the  positive  charge,  N  is 
practically  the  total  number  of  corpuscles  contained 
in  the  atom  :  not  the  number  contained  in  any  one 
ring  of  it. 

A  compound  satellite  will  rotate  round  the  centre 
of  force  with  the  same  angular  velocity  as  if  it  were 
simple,  —  for  its  mass  and  charge  are  increased  in  the 
same  proportion  ;  there  is  no  concentration  of  the 
charges  into  a  single  point,  such  as  would  be  required 
to  increase  the  mass  beyond  the  simple  multiple. 


192  ELECTRIC  THEORY  OF  MATTER     [CH.  xx. 

A  paper  by  Prof.  Jeans,  now  of  Princeton,  N.J.,  in 
-continuation  of  the  discussion  raised  by  Lord  Rayleigh, 
is  to  be  found  in  the  Philosophical  Magazine  for 
April,  1906  ;  also  another  paper  in  November,  1901. 

2.    Attempt  to  determine  the  number  of  effective 
corpuscles  in  an  Atom. 

It  is  premature  to  do  more  than  briefly  refer  to  the 
remarkable  attempt  made  by  Professor  J.  J.  Thomson, 
in  the  Philosophical  Magazine  for  June,  1906,  to 
bring  forward  three  lines  of  argument  which  tend  to 
show,  on  experimental  grounds,  that  the  number  of 
electrons  in  an  atom  is  comparable  with  its  atomic 
weight,  reckoning  hydrogen  as  unity.  It  seems  an 
improbable  result ;  but  the  only  way  to  get  round  it 
is  either  to  question  the  validity  of  the  experiments 
and  the  theory  applied  to  them,  or  else  to  realise  that 
what  is  being  measured  is,  not  the  total  number  of 
electrons,  but  the  number  of  free  or  available  or 
peculiarly  constituted  electrons.  Cf.  p.  162. 

One  of  the  arguments  may  be  simplified  as  follows  : 

If  the  atom  is  composed  of  positive  and  negative 
electricities,  these  constituent  charges  will  tend  to  be 
separated,  against  their  mutual  attraction,  when  sub- 
jected to  an  external  electric  field — such  for  instance 
as  the  field  existing  in  a  wave  of  light ;  and  since 
a  light- wave  is  large  compared  with  an  atom,  there 
will  be  time  for  a  certain  amount  of  this  separation 
to  be  effected  by  each  pulse.  Accordingly  the  wave 
will  be  as  it  were  "  loaded  "  by  the  electric  charges, 
its  velocity  of  propagation  will  be  reduced,  and 
refraction  will  occur. 

But  the  amount  of  loading,  that  is,  the  amount  of 
effective  shear  or  alternating  separation  of  the  two 


UNIVERSITY 


CH.  xx.]  DIFFICULTIES  193 

electricities,  will  depend  on  their  masses  ;  and  if  the 
mass  of  either  the  positive  or  the  negative  electricity 
were  zero  or  very  small,  it  would  be  shifted  completely, 
however  short  the  time.  Accordingly  a  short  wave 
would  then  be  retarded  just  as  much  as  a  long  one, 
—  that  is  to  say,  there  would  be  no  discrimination  of 
waves,  and  therefore  no  dispersion.  The  amount  of 
dispersion  actually  experienced  will  therefore  furnish 
a  measure  of  the  relative  inertia  of  the  two  kinds  of 
electricity  in  an  atom. 

The  only  substance  to  which  this  theory  of  refraction 
and  dispersion  can  apply,  will  be  one  whose  atoms  act 
individually  or  in  isolated  manner  ;  that  is  to  say,  they 
must  be  gases,  the  more  perfect  the  better.  Now  the 
dispersive  power  of  hydrogen  has  been  measured,  and 
is  not  zero  ;  consequently  there  must  be  some  mass 
both  in  the  positive  and  in  the  negative  electricity 
which  hypothetically  constitute  an  atom  of  hydrogen, 
and  the  measured  amount  of  dispersion  will  enable  us 
roughly  to  say  what  the  smaller  mass  may  be.  The 
result  is,  that  if  M  is  the  aggregate  mass  of  the 
carriers  of  positive  electricity,  and  nm  the  mass  of 
the  carriers  of  negative  electricity,  n  being  their 
number  —  so  that  the  mass  of  the  whole  atom  is 
M  +  mn  —  we  get,  with  the  aid  of  Ketteler's  measure- 
ments for  the  refractive  index  of  hydrogen  for  light 
of  different  wave-lengths, 

M        1 

=1  approximately. 

n 


This  shows  that  for  a  hydrogen  atom  n  is  approxi- 
mately 1  (and  it  has  to  be  a  whole  number)  ;  and  it 
also  shows  that  M  is  not  small  compared  with  nm  :  in 
fact  that  it  is  much  bigger,  —  which  is  an  unexpected 
and  puzzling  result. 


194  ELECTRIC  THEORY  OF  MATTER     [CH.  xx. 

The  other  lines  of  experimental  argument  seem  to 
be  confirmatory.  The  second  one  deduces,  from  the 
energy  of  the  Kontgen  radiation  which  is  scattered  by 
gases,  as  measured  by  Barkla  of  Liverpool,  that  mole- 
cules of  air  each  contain  approximately  25  or  28 
corpuscles ;  which  again  corresponds  to  the  molecular 
weight  of  the  chief  ingredient. 

The  third  argument  is  based  on  the  absorption  of 
beta  rays  by  metals ;  wherefrom  it  is  deduced  that 
the  number  of  corpuscles  liable  to  be  encountered  in 
each  atom  is  nearly  equal  to  the  conventional  atomic 
weight  of  the  metal  on  the  hydrogen  scale. 

This  remarkable  paper  is  the  most  serious  blow  yet 
dealt  at  the  electric  theory  of  matter,  at  least  in  its 
simpler  and  cruder  form ;  but  modes  of  getting  round 
it  are  fore- shadowed  in  Chaps.  XV.  and  XVII. 


CHAPTEK  XXL 

VALIDITY  OF  OLD  VIEWS  OF  ELECTRICAL 
PHENOMENA. 

Now  that  the  doctrine  of  electricity  (at  least  of 
negative  electricity)  as  located  in  small  charges  or 
charged  bodies  is  definitely  accepted,  and  now  that  a 
current  can  be  treated  as  the  locomotion  of  actual 
electricity,  it  may  seem  as  if  some  doubt  were  thrown 
upon  the  doctrine,  which  a  little  time  ago  was  spoken 
of  as  a  "  modern  view,"  that  the  energy  of  an  electric 
current  resides  in  the  space  round  a  conductor. 
There  is  no  inconsistency,  however.  The  whole  of  the 
fields  of  an  electron  are  outside  itself;  it  is  in  its 
fields  that  its  energy  resides,  and  it  is  in  the  space 
round  it  that  energy  is  conveyed  when  it  moves ;  for 
the  ether  in  that  space  is  subject  to  the  co-existence 
of  an  electric  and  a  magnetic  field.  So,  also,  its 
inertia  resides  in  space  round  it,  for  it  is  accounted 
for  by  the  reaction  experienced  when  its  magnetic  field 
changes,— that  is,  when  its  motion,  is  accelerated. 

In  dealing  with  the  inertia  of  matter  it  is  commonly 
supposed  that  the  inertia  resides  in  the  matter  itself : 
whereas  electrical  inertia  is  known  to  reside  in  the 
space  round  the  nucleus.  Yet  we  have  been  emphasis- 
ing and  supporting  the  view  that  material  inertia  and 
electrical  inertia  are  essentially  one  and  the  same. 


196  ELECTRICAL  PHENOMENA         [CH.  xxi. 

Is  there  no  inconsistency  here  ? 
The  appearance  of  inconsistency  vanishes  when  we 
come  to  calculate  and  realise  how  extremely  local  and 
concentrated  the  intense  part  of  the  field  of  an  electron 
is.  There  is  a  sense  in  which  it  can  be  said  that  a 
moving  body,  for  instance  a  vortex  ring,  disturbs  the 
whole  atmosphere ;  but  any  perceptible  disturbance 
resides  very  near  the  ring.  So  it  is  with  an  electron. 
The  magnetic  field  falls  off  inversely  as  the  square  of 
the  distance  from  the  moving  nucleus ;  hence  at  a 
distance  far  less  than  a  micro-millimetre,  less  even 
than  the  size  of  an  atom,  it  is  quite  inappreciable. 
The  whole  magnetic  field  on  which  its  inertia  depends 
lies  practically  very  close  to  the  electron  itself :  it  is 
just  its  extremely  small  size  that  enables  this  concen- 
tration to  be  possible,  and  even  in  a  closely  packed 
mercury  atom  there  is  practically  no  encroachment  of 
the  field  of  one  electron  on  its  neighbour's.  They  are 
all  independent,  each  with  its  own  inertia,  almost 
isolated  from  the  others  :  for  if  it  were  not  so,  the 
mass  of  a  body  in  close  chemical  combination  would 
not  continue  constant,  but  would  diminish.  Whether 
it  does  diminish,  in  the  least  degree,  is  a  question 
perhaps  worthy  of  attack.*  Minute  effects  in  this 
direction  have  been  announced,  by  Heydweiler  and  by 
Landolt ;  but  the  results  are  doubtful. 

The  momentum  of  a  moving  charge  at  ordinary 
speeds  is  simply  inversely  as  the  radius  of  the  sphere 
which  holds  it,  as  stated  in  Chap.  II. ,  but  the 
localisation  of  this  momentum,  which  is  the  point  we 
are  now  considering,  may  be  realised  approximately 
as  follows: — 

The  momentum  depends  on  the  co-existence  and 
product  of  the  electric  and  magnetic  fields.  Each 

*Cf.  Rayleigh,  British  Association  Belfast,  1902. 


CH.  xxi.]         VALIDITY   OF  OLD  VIEWS  197 

field  varies  inversely  as  the  square  of  the  distance 
from  the  moving  charge  ;  and  their  vector  product  is, 
as  regards  direction,  perpendicular  to  the  radius 
vector  at  any  point.  It  is  proportional,  at  ordinary 
speeds,  to  the  sine  of  the  angle  between  the  radius 
vector  and  the  direction  of  motion  ;  while  in  magni- 
tude it  falls  off  as  the  inverse  fourth  power  of  the 
distance.  All  this  can  be  realised  by  common  sense 
with  very  little  trouble. 

So,  then,  take  a  moving  electron,  and  consider  the 
distribution  of  its  momentum  in  the  space  round 
it.  Between  its  surface  and  a  space  of  a  hundred 
times  its  diameter,  99  per  cent,  of  its  momen- 
tum is  contained  ;  because,  to  reckon  it,  we  should 
have  to  integrate  the  factor  — 


But  a  hundred  times  the  diameter  of  an  electron 
is  only  10~n  centimetre,  that  is  to  say,  the  thousandth 
part  of  the  diameter  of  an  atom.  So,  within  the 
boundary  of  an  atom,  which  is  a  hundred-thousand 
times  an  electron's  diameter,  there  is  practically  none 
of  its  momentum  not  included. 

And  even  in  one  of  the  comparatively  closely 
packed  atoms,  e.g.  in  a  platinum  or  mercury  atom, 
the  overlapping  of  momentum  for  each  constituent  is 
extremely  small,  since  their  average  space  apart  / 
is  some  thousand  times  the  size  of  each  constituent 
electron. 

Consequently  the  assertions  that  an  electric  current 
is  a  transfer  of  electrons,  and  that  the  energy  of  a 
current  travels  in  the  space  surrounding  the  moving 
electricity,  are  statements  not  inconsistent  with  each 
other.  Nor  are  the  statements  inconsistent  that  the 


198  ELECTRICAL  PHENOMENA         [CH.  xxi. 

mass  of  a  body  resides  in  its  atoms,  and  that  inertia 
or  momentum  is  a  property  due  to  the  self-inductive 
influence  of  the  electromagnetic  field  surrounding  a 
moving  electric  nucleus. 

The  same  sort  of  thing  may  be  said  of  the  way  in 
which  a  current  is  propelled.  The  pace  of  progression 
of  electrons  through  a  solid  may  be  considerable,  see 
next  section,  but  it  is  very  far  below  the  pace  at  which 
a  telegraphic  signal  travels  along  a  wire.  They  must 
be  propelled  by  a  lateral  action,  transmitted  through 
the  ether  with  the  speed  of  light  appropriate  to  the 
surrounding  insulator,  by  some  arrangement  which 
"Modern  Views"  symbolised  in  the  form  of  cog- 
wheels :  they  cannot  be  impelled  by  end  thrust.  The 
vf  electric  current  is  a  more  material  entity,  or  has  a 
more  nearly  material  aspect,  than  was  thought 
probable  a  little  while  since  ;  but  all  that  was  taught 
about  its  mode  of  propulsion,  and  the  diffusion  of  the 
propelling  force  from  outside  to  inside,  through 
successive  layers,  as  it  were,  of  the  wire — all  that 
was  taught  about  the  paths  by  which  the  energy 
travels  and  arrives  at  point  after  point  of  the 
conductor,  there  to  be  dissipated  as  heat, — remains 
true. 

Number  of  Ions  in  Conductors. 

The  immense  number  of  electrons  that  are  necessary 
to  make  up  the  mass  of  a  piece  of  platinum,  or  of  a 
lump  of  matter  like  the  earth,  can  readily  be 
estimated ;  so,  also,  it  is  easy  to  imagine .  that  an 
enormous  number  must  be  travelling  in  order  to  give 
customary  strengths  of  current  such  as  can  readily 
pass  through  a  liquid. 

Through  a  gas,  a  limit  is  soon  found  to  the  available 
number ;  and  accordingly  the  conductivity  of  an 


CH.  XXL]    MODIFICATION   OF   OLD   VIEWS  199 

ionised  gas  falls  off'  if  we  call  upon  it  to  carry  more 
than  a  certain  current,  called  the  saturation  current. 
See  investigations  by  Town  send  and  others  briefly 
referred  to  in  Chapter  VII.  But  I  am  not  aware  of 
any  experimental  indication  of  such  a  limit  in  solids 
or  liquids,  at  present. 

In  solids  the  pace  of  travel  is  unknown,  though  it 
has  been  ingeniously  surmised,  and  is  thought  to  be 
very  great ;  considerations  of  centrifugal  force  would 
make  the  speed  of  each  electron  during  an  atomic 
encounter  equal  to  e/J(Kmr)  or  about  108  centimetres 
per  second ;  views  based  on  Maxwell's  theorem  about 
equal  distribution  of  energy  among  the  particles  of 
mixed  gases  suggest  107  for  the  average  speed  of 
electrons  at  ordinary  temperatures  in  a  solid  where 
they  are  free, — that  is,  a  hundred  kilometres  or  sixty 
miles  per  second;  though  since  each  particle  is  subject 
to  constant  changes  of  direction,  this  is  by  no  means 
the  pace  of  straightforward  progression.  But  in 
liquids  they  are  attached  to  atoms,  and  the  pace 
of  progression  is  known  both  theoretically  and 
experimentally  with  considerable  accuracy,  and  is 
comparable  to  an  inch  an  hour  for  customary 
gradients  of  potential. 

The  total  current  is  neu ;  and  to  give  a  unit  c.g.s. 
current  at  so  low  a  speed  we  can  reckon  how  many 
ions  there  must  be.  For  e=  L0~20  electromagnetic 
units;  so  if  we  take  u=W~z  centimetre  per  second, 
the  number  of  ions  engaged  in  conveying  the 
c.g.s.  unit  of  10  amperes  is  n=1023.  But,  after  all, 
that  is  nothing  very  great ;  it  is  only  about  the 
number  of  atoms  in  a  cubic  centimetre  of  liquid. 
By  applying  a  greater  gradient  of  potential  the  ions 
can  be  made  to  move  faster.  By  gradually  narrowing 
down  the  section  of  a  liquid  conductor  under  a  given 


200  ELECTRICAL  PHENOMENA         [CH.  xxi. 

gradient  of  potential,  it  might  be  possible  to  get 
evidence  of  an  approach  to  a  saturation-current- 
density  in  liquids.  The  observed  accuracy  of  Ohm's 
law*  under  such  conditions,  however,  is  against  this 
experimental  possibility. 

Conclusion. 

The  subject  is  very  far  from  exhausted,  but  I 
must  not  attempt  to  cover  more  ground.  The 
most  exciting  part  of  the  whole  is  the  explanation  of 
matter  in  terms  of  electricity,  the  view  that  electricity 
is,  after  all,  the  fundamental  substance,  and  that  what" 
we  have  been  accustomed  to  regard  as  an  indivisible 
atom  of  matter  is  built  up  out  of  it ;  that  all  atoms- 
atoms  of  all  sorts  of  substances — are  built  up  of  the 
same  thing.  In  fact  the  theoretical  and  proximate 
achievement  of  what  philosophers  have  always  sought 
after,  viz.,  a  unification  of  matter  is  offering  itself 
to  physical  enquiry.  But  it  must  be  remembered 
that  although  this  solution  is  strongly  suggested 
it  is  not  yet  a  completed  proof.  Much  more 
work  remains  to  be  done  before  we  are  certain  that 
mass  is  due  to  electric  nuclei.  If  it  is,  then 
we  encounter  another  surprising  and  suggestive 
result,  namely  that  the  spaces  inside  an  atom  are 
enormous  compared  with  the  size  of  the  electrical 
nuclei  themselves  which  compose  it ;  so  that  an  atom 
,-  <  can  be  regarded  as  a  complicated  kind  of  astronomical 
system, — like  Saturn's  ring,  or  perhaps  more  like  a 

1  nebula;  with  no  sun,  but  with  a  large  number  of  equal 
bodies    possessing    inertia    and    subject    to    mutual 

'  electric  attractive  and  repulsive  forces  of  great  mag- 
nitude,  to  replace  gravitation.     The   radiation   of  a 

*  FitzGerald  and  Trouton,  Brit.  Assoc.  Reports,  1886,  1887,  1888. 


CH.  XXL]  VIEWS   OF  ATOMS  201 

nebula  may  be  due  to  shocks  and  collisions  somewhat 
like  the  X-radiation  from  some  atoms. 

The  disproportion  between  the  size  of  an  atom  and 
the  size  of  an  electron  is  vastly  greater  than  that 
between  the  sun  and  the  earth.  If  an  electron  is 
depicted  as  a  speck  one-hundredth  of  an  inch  in 
diameter,  like  one  of  the  full-stops  on  this  page  for 
instance,  the  space  available  for  the  few  hundred  or 
thousand  of  such  constituent  dots,  to  disport  them- 
selves inside  an  atom,  is  comparable  to  a  hundred-feet 
cube ;  in  other  words,  an  atom  on  the  same  scale 
would  be  represented  by  a  church  160  feet  long,  80 
feet  broad,  and  40  feet  high, — in  which  therefore  the 
dots  would  be  almost  lost.  And  yet  on  the  electric 
theory  of  matter  they  are  all  of  the  atom  that  there 
is  ;  they  "  occupy  "  its  volume  in  the  sense  of  keeping 
other  things  out,  as  soldiers  occupy  a  country ;  they 
are  energetic  and  forceful  though  not  bulky ;  and  in 
their  mutual  relations  they  constitute  what  we  call 
the  atom  of  matter;  they  give  it  its  inertia;  they 
enable  it  to  cling  on  to  others  which  come  within 
short  range,  with  the  force  we  call  cohesion  ;  and  by 
excess  or  defect  of  one  or  more  constituents  they 
exhibit  chemical  properties  and  attach  themselves 
with  vigour  to  others  in  like  or  rather  opposite  case. 

That  such  a  hypothetical  atom,  composed  only 
of  sparse  dots,  can  move  through  the  ether  without 
resistance  is  not  surprising.  They  have  links  of 
attachment  with  each  other,  but,  so  long  as  the 
speed  is  steady,  they  have  no  links  of  attachment 
with  the  ether ;  if  they  disturb  it  at  all,  in 
steady  motion,  it  is  probably  only  by  the  simplest 
irrotational  class  of  disturbance  which  permits  of 
no  detection  by  any  optical  means.*  Nor  do 

See  Lodge,  Phil  Trans.  1893,  vol.  184,  pp.  750-754;  also  vol.  189,  p.  166. 


202  ELECTRICAL  PHENOMENA         [CH.  XXL 

they  tend  to  drag  it  about.  All  known  lines  of 
mechanical  force  reach  from  atom  to  atom,  they  never 
terminate  in  ether ;  except  indeed  at  an  advancing 
wave  front.  At  a  wave  front  is  to  be  found  one 
constituent  of  a  mechanical  pressure  of  radiation  whose 
other  constituent  acts  on  the  source.  This  is  an 
interesting  but  essentially  non-statical  case,  and  it 
leads  away  from  our  subject. 

As  to  the  nature  of  an  electron,  regarded  as  an 
ethereal  phenomenon,  it  is  too  early  to  express  any 
opinion.  At  present  it  is  not  clear  why  a  positive 
charge  should  cling  so  tenaciously  in  a  mass,  while 
an  outstanding  negative  electron  should  readily 
escape  and  travel  free.  Nor  is  the  nature  of  gravi- 
tation yet  understood.  When  the  electron  theory 
is  complete,  to. the  second  order,  or  some  higher  even 
order,  of  small  quantities — it  is  complete  now  to  the 
second  order  if  electrons  may  be  treated  as  geo- 
metrical points, — it  is  hoped  that  the  gravitative 
property  also  will  fall  into  line  and  form  part  of 
the  theory ;  at  present  it  is  an  empirical  fact  which 
we  observe  without  understanding ;  as  has  been 
our  predicament  not  only  since  the  days  of  Newton 
but  for  centuries  before  :  though  we  did  not,  before 
Newton,  know  its  importance  in  the  cosmic  scheme. 

Attention  has  hitherto  been  chiefly  concentrated 
on  the  freely  moving  active  negative  ingredient, — the 
more  sluggish  positive  charges  are  at  first  of  less 
interest, — but  the  behaviour  of  electrons  cannot  be 
fully  and  properly  understood  without  a  knowledge 
of  the  nature  and  properties  of  the  positive  con- 
stituent too.  According  to  Larmor,  positive  charge 
must  be  the  mirror-image  of  negative  charge,  in 
essential  constitution. 

The  positive  electron  has  not,  so  far  as  I  know,  been 


CH.  XXL]       ELECTRICITY   AND   MATTER  203 

as  yet  observed  free.  Some  think  it  cannot  exist  in 
a  free  state,  that  it  is  in  fact  the  rest  of  the  atom  of 
matter  from  which  a  negative  unit  charge  has  been 
removed  ;  or,  to  put  it  crudely — that  "  electricity  " 
repels  "electricity,"  and  "matter"  repels  "matter," 
but  that  Electricity  and  Matter  in  combination  form 
a  neutral  substance  which  is  the  atom  of  matter  as  we 
know  it.  Such  a  statement  is  an  extraordinary  and 
striking  return  to  the  views  expressed  by  that  great 
genius,  Benjamin  Franklin.  On  any  hypothesis  those 
views  of  his  are  of  exceeding  interest,  and  show  once 
more  the  kind  of  prophetic  insight  which  we  have 
had  occasion  to  notice  in  discoverers  before  (Appendix 
H  and  Chap.  IV.).  Undoubtedly  we  are  at  the  \ 
present  time  nearer  to  the  view  of  Benjamin 
Franklin  than  men  have  been  at  any  intervening 
period  between  his  time  and  ours. 

The  view  that  an  atom  is  composed  of  an  equal 
number  of  interleaved  or  inter-revolving  positive  and 
negative  electrons — that  view  is  not  Franklin's ;  nor 
is  it  as  yet  anything  but  a  guess.  To  make  it  more, 
work  must  be  done  upon  the  nature  and  properties  of 
the  positive  charge ;  and  the  positive  electron,  if  it 
exists,  must  be  dragged  experimentally  to  light. 

Especially  must  the  inner  ethereal  meaning  both  of 
positive  and  negative  charges  be  explained  :  whether 
on  the  notion  of  a  right-and-left-handed  self-locked 
intrinsic  wrench-strain  in  a  Kelvin  gyrostatically- 
stable  ether,  elaborated  by  Larmor,*  or  on  some 
hitherto  un imagined  plan.  And  this  will  entail  a 
quantity  of  exploring  mathematical  work  of  the 
highest  order. 

*See  Ether  and  Matter,  p.  326  ;  or  Phil.  Trans.  1894,  pp.  810,  811, 
and  1897,  pp.  209-212. 


APPENDIXES. 

APPENDIX  A. 
Calculation  of  the  Inertia  of  an  Electric  Charge. 

Let  a  spherical  conductor  of  radius  a,  carrying  a 
charge  of  electricity,  move  forward  with  moderate  speed 
u\  meaning  by  moderate  speed  anything  distinctly  less 
than  the  speed  of  light:  it  constitutes  a  current  element 
of  magnitude  eu,  and  its  circuit  is  closed  by  displace- 
ment currents  in  the  surrounding  dielectric.  For  electric 
lines  of  force  arise  in  the  medium  in  front,  and  subside 
in  the  medium  behind,  and  so  a  displacement  of  electricity 
takes  place  from  fore  to  aft,  to  compensate  the  motion 
forward ;  and  the  lines  of  displacement  are  identical  with 
the  magnetic  lines  due  to  a  short  magnet.  A  charge 
may  be  said  to  travel  carrying  its  electrostatic  lines 
with  it,  or  it  may  be  said  to  be  constantly  generating  an 
electrostatic  field  in  front  and  destroying  one  behind. 

When  an  electric  field  thus  moves,  partly  laterally,  it 
generates  a  magnetic  field — in  the  present  instance  in 
circular  lines  round  the  line  of  motion; — for  the  moving 
charge  is  an  element  of  a  linear  current.  The  generation 
of  these  magnetic  lines  acts  so  as  to  oppose  the  current 
which  produced  them ;  though  so  long  as  they  continue 
steady  they  exert  no  effect  on  it.  When  they  subside, 


APR  A.]          CALCULATION   OF   INERTIA  205 

however,  they  tend  to  prolong  the  current  which  main- 
tained them.  Consequently,  if  the  moving  charge  (or 
current)  tries  to  stop,  its  retardation  meets  with 
obstruction;  it  is  constrained  to  persist  by  the  sub- 
sidence of  the  magnetic  field  which  its  motion  excited 
and  maintains.  Its  velocity  is  not  resisted,  there  is 
nothing  equivalent  to  friction,  but  its  acceleration  +  or  — 
is  obstructed,  an  effect  precisely  analogous  to  inertia.  If 
it  is  at  rest  it  will  need  force  to  start  it,  and  if  it  is  in 
motion  its  motion  will  persist,  even  against  force,  for  a 
time. 

The  charge  acts,  therefore,  as  if  it  had  inertia,  and  we 
can  proceed  to  calculate  its  amount. 

While  moving  it  is  a  current,  and  will  be  surrounded 
by  rings  of  magnetic  force,  whose  intensity,  at  any  point 
with  polar  co-ordinates  r,  0,  referred  to  the  line  of  motion 
as  axis  and  the  moving  charge  as  origin,  will  be  the 
quite  ordinary  expression  (with  eu  for  the  current-element 

instead  of  Cds)  —  .    * 

TT     eu  sin  6 
ti  =  -  =—  . 

r2 

The  ordinary  expression  for  the  electrostatic  force  at 
the  same  point  is 


(see  note  at  end  of  Chapter  I.  with  reference  to  the  inser- 
tion of  K)  and  if  the  motion  is  slow  this  value  will  be 
preserved;  but  if  it  is  rapid  the  electric  field  gets  weaker 
along  the  axis  and  stronger  equatorially,  having  been 
shown  by  Mr.  Heaviside  (Philosophical  Magazine,  April, 
1889)  to  be  given  by  the  following  expression  — 


where  v  is  the  velocity  of  light. 


206  CALCULATION   OF   INERTIA          [APP.  A. 

The  strength  of  the  magnetic  field  will  be  similarly 
modified  in  this  case  ;  but  the  simplest  mode  of  stating  that 
is  to  express  it  in  terms  of  E,  and  to  say  that  always  — 

H  =  K^U  sin  0. 

The  rate  of  transmission  of  energy  will  be  the  vector 
product  of  E  and  H  ;  and  the  whole  magnetic  energy,  —  that 
is  the  whole  kinetic  energy  due  to  the  current,  i.e.,  due 
to  the  motion  —  will  be  obtained  by  integrating  the  ordinary 
expression  yuH2/87r,  all  over  space  outside  the  charged 
sphere,  viz.,  from  a  to  oo  all  round.  Its  charge  is  assumed 
to  be  superficial,  so  that  no  energy  is  inside.  In  the  general 
case  this  expression  is  a  little  long,  but  in  the  most  im- 
portant case,  when  the  speed  of  motion  u  is  decidedly  less 
than  the  speed  of  light  v,  it  is  quite  simple,  and  the 
working  may  as  well  be  given:  — 

Kinetic  energy 


f  fsi 
J  J  J_ 


COS20-1 


Comparing  this  with  mechanical  kinetic  energy, 
we  see  that  the  charge  on  the  sphere  confers  upon  it 
additional  kinetic  energy,  as  if  its  mass  were  increased  on 
account  of  the  charge  by  the  amount  — 


2/ze 
m=—  — 
3a 


This  may  also  be  written  — 

2 

o~2 

3t>2 


2  /UiK  g2       2          e        2 
ra  =  ^—  —  =  o~2  •  e  •  —  =  ^~9  x  charge  x  potential, 

2  2 


Q 

or,   -r  rai>2  =  the  electrostatic  energy  of  the  charge  : 

supposed  a  spherical  shell  of  electricity. 


APR  A.]          CALCULATION   OF   INERTIA  207 

In  other  words,  the  mass  equivalent  to  the  charge  is  such 
that  if  it  were  a  piece  of  matter  with  constant  inertia 
travelling  at  the  speed  of  light,  its  kinetic  energy  would 
be  half  as  great  again  as  the  potential  energy  of  the 
electric  charge  when  standing  still. 


APPENDIX  B. 
The  Electric  Field  due  to  a  Moving  Magnet. 

If  a  short  bar  magnet  or  uniformly  magnetised  sphere 
(its  moment  M  being  the  intensity  of  magnetisation  x  the 
volume  of  the  sphere)  moves  along  axially  —  that  is  in  the 
direction  of  its  magnetisation  —  with  velocity  u,  it  generates 
circular  lines  of  electric  force  all  centred  upon  its  axis, 
much  as  a  moving  charge  generates  circular  lines  of 
magnetic  force.  If  there  is  a  conducting  path  round 
any  such  circle,  then  the  motion  of  a  magnet  along  its 
axis  will  generate  a  current  in  it;  but  if  there  be  no 
conductor,  the  motion  will  only  result  in  an  electric  dis- 
placement which  subsides  when  the  magnet  stops. 

The  intensity  of  the  magnet's  field  at  any  point  along 
its  axis  is  well  known  to  be  2M/r8;  at  any  point  on  its 
equatorial  plane  it  is  —  M/r3;  and  in  any  intermediate 
direction  it  is,  as  regards  magnitude  alone  — 


All  this  holds  for  the  moving  as  for  the  stationary  magnet, 
provided  its  speed  does  not  approach  that  of  light. 
The  electric  force  at  the  same  point  is  — 


208  CALCULATION   OF   INERTIA          [APP.  B. 

The  electrostatic  energy  resulting  will  be  the  integral  of 
AcE2/87r  everywhere  outside  the  moving  magnetised  sphere 
of  radius  a,  viz. — 


Energy  =  5— 1 1 1 (  — o— )  sin20 cos2$ dr.rdO.r  sin  0 dd> 

^J      STrJJJV  r3   / 

_AcM2/&2_  M2    /'M'X2 
5<z3    ~~  Spa?  \v/  ' 

The  displacement  acts  like  an  elastic  strain  set  up  in 
the  dielectric,  storing  the  above  energy  statically;  and  so 
long  as  the  magnet  continues  moving  steadily  the  electric 
displacement  exerts  no  force  upon  it.  But  acceleration 
will  be  resisted;  for  if  the  magnet  begins  to  go  faster  it 
sets  up  more  displacement,  and  the  act  of  setting  this  up 
constitutes  a  transient  current,  which  opposes  the  motion 
as  long  as  the  acceleration  continues,  but  dies  out  the 
instant  the  motion  becomes  steady  again. 

Conversely  if  the  motion  of  the  magnet  began  to 
slacken,  the  electric  strain  would  begin  to  subside,  and 
its  subsidence  would  constitute  an  inverse  transient  current 
which  would  assist  the  motion,  i.e.,  oppose  the  slackening. 
In  other  words,  the  variations  of  the  circular  electric  strain 
in  the  surrounding  medium  confer  upon  a  moving  magnet 
a  spurious  or  apparent  momentum,  in  addition  to  its  real 
mechanical  momentum ,  and  thus  the  elastic  strain  itself 
may  be  said  to  represent  a  spurious  or  apparent  inertia 
due  to  magnetisation,  in  addition  to  any  real  mechanical 
inertia  which  the  body  holding  the  magnetism  may  itself 
possess.  And  the  amount  of  this  extra  inertia  is — 

_2*M2  =  2  M2         8 
=  5a3      5  ,uaV     15 

=  5"^~' 


APR  B.]  DIMENSIONS  209 

where  I  is  the  intensity  of  magnetisation,  and  H0  the 
intensity  of  the  field,  inside  the  substance  of  a  uniformly 
magnetised  sphere  of  radius  a  and  magnetic  moment  M. 
The  equivalent  mass  moving  with  the  velocity  of  light 
would  therefore  have  an  energy  equal  to  two-fifths  of  the 
intrinsic  energy  of  the  magnetised  sphere. 


APPENDIX  C. 
On  Electricity  and  Gravitation  and  Dimensions. 

Referring  back  to  an  article  of  mine  in  the  Philosophical 
Magazine  for  November,  1882,  page  358,  we  find  the 
fundamental  and  necessary  relation  between  constants 
stated  thus,  where  M  shall  stand  for  magnetic  pole  and  y 
for  Cavendish's  gravitation  constant  — 


F  being  force  and  I  being  length. 

If  it  is  now  going  to  turn  out  that  a  mass  is  composed 
of  electric  charges,  it  might  seem  as  if  e  and  m  were 
quantities  of  the  same  nature,  and  were  only  numerically 
connected  ;  whence  it  would  follow  that  AC  and  y  were  of 
similar  kind.  In  other  words,  Faraday's  dielectric  constant 
would  become  closely  related  to  Cavendish's  gravitation 
constant,  and  weight  as  well  as  mass  would  be  traced  to 
electricity  ;  but  such  a  deduction  is  unwarranted,  there  is 
nothing  to  prevent  essentially  different  properties  of  the 
ether  being  involved  in  the  two  kinds  of  force  —  gravitative 
and  electric. 

As  to  the  nature  of  the  gravitation  constant  itself,  we 
have  — 

_F£2_  I3        v2  _sq.  of  velocity  _  energy/mass 
^  ~~  m2  ~~  mP  ~"  mjl  ~~  linear  density  ~~  mass/length' 
L.E.  o 


210  GRAVITATION  [APR  a 

It  is  clear  that  if  gravitation  is  in  any  sense  of  electric 
origin  it  must  be  a  second  order  disturbance,  or  some 
higher  even  order,  superposed  upon  the  main  electric  effect, 
and  be  independent  of  sign.  It  would,  in  fact,  depend 
upon  e*.  For  the  gravitative  force  between  two  electrons 
at  distance  r  would  be  — 


-       _ 

ri-7  Tz- 

The  electric  force  between  the  same  two  electrons  at  the 
same  distance  is  — 

&m 

F2=—  2- 

KT2 

Therefore  the  ratio  of  the  gravitative  to  the  electric  force 
at  any  distance  is  constant  and  equal  to  — 


where    F0    is    the    electric    force    between    two    spherical 
electrons  in  contact,  and  v  is  the  velocity  of  light. 
Numerically  this  ratio  of  the  two  forces  is — 

FI  _       /m\2  _  1 /  _1_\2  _  -,  0  _  42 

F2~Kfy\eJ  ~9xl020xl-5xl07\10V  " 

so  the  electric  force  exceeds  the  gravitative  as  much  as  the 
globe  of  the  earth  exceeds  in  bulk  an  ultra-microscopic 
object. 

When  there  is  an  agglomeration  of  electrons  of  opposite 
sign,  their  electric  influence  at  a  distance  disappears,  but 
their  gravitative  potential  will  be  proportional  to  the  sum 
of  the  squares  of  the  charges.  So  with  1021  mixed  electrons 
in  each  of  two  bodies,  at  any  distance  apart,  the  gravitative 
force  between  them  will  equal  the  electric  force  between 
two  single  electrons  at  the  same  distance. 

In  my  1885  Report  to  the  British  Association  on  Electro- 
lysis, page  745,  the  following  statement  is  made : — If  the 


APR  c.]   •  DIMENSIONS  211 

opposite  electricities  were  extracted  from  a  milligramme  of 
water  and  given  to  two  spheres  one  mile  apart,  those  two 
spheres  would  attract  each  other  with  a  force  equal  to  the 
weight  of  12  tons. 


APPENDIX   D. 
Dimensions  of  e/m  Ratio. 

The  reciprocal  of  the  electrochemical  equivalent  of  a 
substance,  e/m,  may  be  expressed  as  regards  dimensions  in 
several  ways,  one  of  which  exhibits  it  as  a  certain  large 
numerical  multiple  of  >v/(«:y),  the  geometric  mean  between 
Faraday's  dielectric  constant  and  Cavendish's  gravitation 
constant.  For  hydrogen,  this  numerical  multiple  is  of 
the  order  1018;  for  silver  1016. 

Another  way  is  obtained  by  writing  — 


whence  it  follows  that  — 

m/u.e 


centimetres\ 


-,         /  -,  -.  .        //c 

and  so  em  can  be  expressed  in  A  /(  - 

\  V  grammes/ 

The  artificiality  of  these  dimensions  is  due  to  the  fact 
that  e  and  m  have  been  conventionally  measured  in 
different  ways  ;  m  is  measured  by  ratio  of  applied  external 
force  to  acceleration,  while  e,  is  measured  by  repulsive 
force  self-exerted  on  a  similar  charge  at  given  distance. 

If  we  express  //,  as  a  density  (see  "Modern  Views  of 
Electricity,"  Appendix  p),  the  electrochemical  equivalent 
comes  out  as  expressible  in  grammes  per  square  centimetre, 
that  is  to  say  a  surface  density. 


212  SATURATION  •  [APR  D. 

It  is  noteworthy  that  while  ^/(/c/x)  is  of  the  same 
dimensions  as  1/v,  ^/(K~/)  corresponds  to  1/e,  where  e  is 
an  electrochemical  equivalent. 


APPENDIX  E. 
Electric  Saturation,  etc. 

In  my  Report  on  Electrolysis  to  the  British  Association 
for  1885  (see  the  Aberdeen  volume,  pp.  762,  763),  I  call 
attention  to  the  possibility  that  an  atomic  theory  of 
electricity  would  give  rise  to  a  maximum  charge  possible 
on  a  given  area.  The  maximum  surface-density  would 
be  attained  when  every  atom  was  polarised  so  that  its 
atomic  charge  faced  outwards;  and  for  a  solid  or  liquid 
it  would  be  very  great.  For  the  charge  on  each  being 
10  ~10,  and  the  number  of  atoms  per  square  centimetre 
being  1016,  it  follows  that  the  maximum  surface  density 
possible  is  (r=106  electrostatic  units  per  square  centimetre. 
The  corresponding  gradient  of  potential  would  be  4?ro-=  107, 
or  3,000  megavolts  per  centimetre;  and  the  corresponding 
tension  would  be  27r<72  =  6  x  1()12  c.g.s.  =  40,000  tons  to  the 
square  inch.  Of  course  no  dielectric  would  stand  this 
pressure,  but  absolute  vacuum  might. 

In  practice,  therefore,  it  follows  that  when  a  surface  is 
charged  highly,  only  an  exceedingly  small  percentage  of 
the  molecules  are  polarised  with  their  charges  facing 
outwards.  For  instance,  common  air  breaks  down  when 
the  tension  rises  to  a  value  2-7n72  =  J  gramme  per  square 
centimetre  =  400  c.g.s. ;  wherefore  the  maximum  or  in 
ordinary  air  is  8  electrostatic  units  per  square  centimetre ; 
and  this  quantity  would  be  afforded  by  the  facing  outwards 
of  1011  molecules,  or  one  in  every  hundred  thousand  of  a 
solid  surface,  or  about  a  tenth  per  cent,  of  those  in  air. 


APR  E.]  ORBIT   OF  ELECTRON  213 

It  is  shown  on  p.  760  of  my  1885  B.A.  Report  on 
Electrolysis,  that  a  potential  gradient  of  the  order  1  volt 
over  molecular  distance  is  sufficient  to  overcome  atomic 
attraction  and  effect  decomposition  in  liquids.  Any  liquid 
which  is  a  conductor  throws  the  whole  applied  stress  on 
to  a  molecular  layer  contiguous  to  an  electrode,  and  accord- 
ingly something  of  the  order  of  a  volt  or  two  difference 
of  potential  between  electrodes  in  such  a  liquid  is  required, 
and  is  sufficient,  for  decomposition. 


APPENDIX  F. 
Size  of  Orbit  of  Radiating  Electron. 

Consider  two  electrons  of  opposite  sign  revolving  round 
each  other  with  luminous  frequency  n  at  any  distance  r\ 
or  better,  consider  a  free  negative  electron  revolving  round 
a  comparatively  fixed  equal  positive  charge  attached  to  an 
atom,  at  distance  r. 

The  force  between  them  is  e2//cr2,  so  the  acceleration  is  — 


But  the  acceleration  is  also  expressible  as  47rVr.     There- 
fore— 


which  is  "  Kepler's  third  law  "  for  the  case,  and  indicates 
that  the  distance  at  which  luminous  frequency  is  attain- 
able is  the  atomic  distance  10  ~8  centimetre;  in  other 
words,  that  the  electron  is  roaming  over  the  surface 
of  the  atom.  If  it  got  nearer  to  the  centre  of  force 
than  this,  without  penetrating  any  of  the  attracting  sub- 
stance, it  would  have  to  revolve  quicker  ;  and  such  rapid 


214  RADIATING   ELECTRON  [APP.  F. 

oscillations  may  be  excited  among  the  internal  paired  elec- 
trons by  shocks  and  collisions,  or  other  perturbation. 

The  most  important  aspect  of  the  above  calculation 
is  that  it  corresponds  with  the  hypothesis  that  the  whole 
of  the  mass  of  an  electron  is  electric,  and  none  of  it 
material  or  unexplained ;  for  it  shows  that  a  pure  electron 
is  able  to  revolve  at  distances  of  the  molecular  order 
with  luminous  frequency.*  The  square  of  the  wave  length 
emitted  is  proportional  to  the  cube  of  the  radius  vector  ; 
provided  the  plane  of  the  orbit  contains  the  centre  of 
force, — otherwise  there  may  be  constrained  motion  -of 
smaller  amplitude,  analogous  to  that  of  a  conical  pendulum. 


APPENDIX  G. 
The  Radiating  Power  of  a  Steadily  Revolving  Electron. 

Consider  an  electron  revolving  as  above  (Appendix  F) 
in  an  orbit  of  atomic  dimensions  b  with  luminous  frequency 
^  =  a>/27r;  and  calculate  its  radiating  power. 

By  considering  separately  the  electric  and  magnetic 
forces  due  to  such  a  particle,  at  any  point  of  space,  and 
then  applying  Poynting's  theorem  as  to  the  convection 
of  energy  wherever  the  two  fields  coexist,  we  get,  as  the 
rate  of  transmission  of  energy  past  a  point  whose  polar 
coordinates,  referred  to  centre  and  axis  of  orbit,  are  r,  0, 
the  mean  value  ^  1  +  cosse  ^v 

V  '        STT  rL 

And  integrating  this  all  over  the  sphere  of  radius  r  we 
get,  as  the  total  emission  of  energy  per  second  — 


*See  Lodge  in  The  Electrician  for  March  12th,  1897,  vol.  38,  p.  644. 


APP.  a]       CALCULATION   OF   RADIATION  215 

which  may  be  written, — with  a  as  the  radius,  m  the  mass, 
and  u  as  the  acceleration,  of  the  revolving  electron — 

man2 


where  v  is  the  velocity  of  light. 

The  fundamental  expression  for  the  amount  of  energy 
emitted  per  second  as  waves  in  the  ether,  by  a  moving 
charge  e,  was  given  by  Larmor  in  Phil.  Mag.,  December, 
1897,  page  512,  so  far  as  I  know  for  the  first  time; 
also  in  JZiher  and  Matter,  page  227,  namely  — 


This  agrees  with  the  above  calculation,  since  it  =  u2/b  =  bco2  ; 
u  being  acceleration.  Now  ju.e2  may  be  taken  as  10  ~40 
gramme-centimetre,  according  to  most  recent  measure- 
ments; and  in  a  circular  orbit  of  radius  r  the  acceler- 
ation is 


therefore   the   radiating  power   of    a   single    electron,   so 
moving,  is 

9  ..,,2          9  y  TO-*0 

w  Ai="9xio">  x  1Q46=  2  x  10~5  ergs  per  second- 

But  the  total  available  energy  possessed  by  the  revolving 
electron  of  linear  dimensions  a  is  only 


namely  its  kinetic  energy  (for  of  course  it  cannot  radiate 
away  or  dissipate  its  electrostatic  energy),  and  this 
amounts  to  — 

1  0~40 

-r,  (2-7T  x  5  x  10U  x  10-8)2  =  3  x  10-13  ergs, 


3xlO-13 


216  RADIATION   OF  ELECTRON          [APR  a 

its  velocity  being  3  x  107  centimetres  per  second,  or  one- 
thousandth  that  of  light.  So  if  the  electron  were  isolated 
from  any  supply  of  energy,  and  if  it  could  maintain  the 
pace,  it  would  at  this  rate  radiate  away  all  its  kinetic 
energy  in  10  ~8  of  a  second,  that  is  to  say  in  three  or 
four  million  revolutions.  This  may  seem  a  rapid  rate  of 
cooling,  but  it  is  not  surprising  for  an  isolated  and 
luminous  atom :  it  is  a  Hertzian  vibrator  or  emitter  of 
simple  type.  The  number  of  revolutions  which  an 
electron  must  make  in  one  second,  in  order  to  emit 
sodium  light,  is  about  8000  times  the  number  of  seconds 
which  have  passed  since  the  Christian  era. 

We  may  express  the  ratio  of  the  radiating  power  of  a 
single  electron  to  its  total  kinetic  energy,  by  the  fraction— 

2<z/'iA2     2a/0      ,„         „    a     ^n     -n- 
—  I  -  )  =  —  (27m)2  =  S7r2n  ^-  =  70  million  per  second. 
v  \u/       v  A 

In  any  large  assemblage  of  atoms  the  radiation  is  not 
free  and  unrestrained,  nor  is  it  unmaintained,  like  this ; 
but  it  must  always  be  considerable  at  anything  like 
luminous  frequency,  and  it  is  proportional  to  the  fourth 
power  of  the  frequency.  At  a  frequency  which  emits  a 
wave  ten  times  as  long  as  a  luminous  wave,  the  radiating 
power  of  a  revolving  electron  is  only  one  ten-thousandth 
of  that  above  calculated,  but  even  so  it  is  very  significant ; 
so  there  must  be  compensation  of  some  kind  or  a  substance 
could  not  permanently  exist.  The  criterion  that  a  mole- 
cule shall  not  be  destroyed  by  radiation-losses  is  given  in 
the  concluding  sentence  of  Larmor's  paper  above  quoted : 
Phil.  Mag.,  Dec.,  1897. 

The  subject  of  radiation  from  a  symmetrical  group  of 
electrons  was  pursued  above  in  Chapter  XIX. 

The  radiating  power  of  an  electron  suddenly  stopped  by 
a  collision  is  of  course  much  greater  than  the  above,  and  is 
estimated  in  Chapter  IX.  To  get  copious  Rontgen  rays 


APR  G.]  HISTORICAL   REMARK  217 

the  stopping  distance  must  be  comparable  with  the  elec- 
trons' own  diameter;  which  accordingly  accounts  for  the 
extreme  thinness  and  consequent  penetrating  character  of 
the  emitted  pulse. 


APPENDIX   H. 
Faraday's  Prophetic  Nomenclature. 

Students  of  the  life  of  Faraday  will  remember  that  when 
he  discovered  the  rotation  of  the  plane  of  polarisation  by 
a  magnetic  field  applied  to  dense  bodies  in  which  light 
travelled  along  the  lines  of  force, — wresting  the  secret  from 
nature  by  strong  and  pertinacious  experimental  research 
that  wrould  not  be  denied,  though  the  time  was  as  yet  by 
no  means  ripe  for  comprehension  of  the  fact  when  it  was 
discovered — he  labelled  his  discovery  in  a  fit  of  enthusiasm, 
"  The  Magnetisation .  of  Light  and  the  Illumination  of 
Magnetic  Lines  of  Force " :  a  label  which  puzzled  con- 
temporaries for  a  long  time. 

It  is  difficult  to  see  what  meaning  he  can  have  attached 
to,  these  phrases ;  and  for  many  years  afterwards  they 
appeared  unsuitable  misnomers,  indicating  a  foggy  concep- 
tion of  his  own  discovery. 

It  is  not  likely  that  his  state  of  mind  was  really  at  all 
clear  on  the  subject,  and  probably  he  would  at  a  later  stage 
have  been  willing  to  plead  guilty  to  a  less  than  lucid  mode 
of  conceiving  the  phenomenon ;  which  nevertheless  always 
specially  pleased  him,  though  when  it  was  reduced  to  a 
mere  rotation  of  the  plane  of  polarisation,  it  seemed  to 
many  mathematicians  and  physicists  to  have  lost  its  unique 
and  surprising  interest.  It  must  always  be  remembered, 
however,  that  interest  was  never  lost  by  either  Lord  Kelvin 
or  Clerk  Maxwell,  and  that  it  was  the  chief  fact  which 


218  HISTORICAL   REMARK  [APR  H. 

incited  Maxwell,  many  years  later,  to  begin  developing  his 
electro-magnetic  theory  of  light. 

But  how  do  the  titles  strike  us  now  ?  Do  they  not 
indicate  some  extraordinary  unconscious  insight,  such  as 
is  frequently  experienced  by  a  great  discoverer  in  the 
enthusiasm  of  discovery  ?  Remember  that  the  Hall  effect, 
the  Zeeman  effect,  the  Aurora  Borealis,  and  Faraday's 
rotation  are  all  closely  connected  with  each  other — by 
means  of  the  electron  theory. 

In  the  cathode  ray  tube  the  flying  electrons  are  deflected 
by  a  cross  magnetic  field;  or  if  they  fly  along  the  lines 
they  are  twisted  into  a  spiral  path  round  them.  In  the 
Aurora  Borealis  this  effect  is  carried  out  in  the  upper 
region  of  the  air  on  a  gigantic  scale,  and  the  earth's 
magnetic  "lines  of  force  are  illuminated"  by  flying  elec- 
trons from  the  sun  entangled  and  guided  by  them.  In  the 
Hall  effect  this  same  influence  is  felt  by  the  slowly  moving 
crowd  of  electrons  as  they  are  handed  on  from  one  atom  to 
the  next,  causing  a  curvature  of  the  current  path — in  which 
either  positive  or  negative  may  predominate.  In  the  Zeeman 
effect  the  same  cause  operates  on  the  revolving  and  vibrating 
electrons,  associated  with  a  radiating  atom  and  constituting 
a  source  of  light ;  wherefore  we  may  truly  say  that  the 
"  light  is  magnetised,"  for  the  source  of  light  is  magnetised 
directly,  and  the  effect  is  impressed  on  and  retained  by  the 
light  emitted,  and  is  made  visible  by  spectrum  analysis. 

The  first  intimation  of  that  magnetic  influence  on  light 
which  lies  at  the  base  of  all  these  at  first  sight  apparently 
diverse  phenomena  was  detected  by  Faraday  in  his  slight 
differential  rotation  of  the  plane  of  polarisation  in  one 
direction  or  the  other  by  a  magnet,  according  as  the  posi- 
tive or  the  negative  element  in  the  dense  substance  was 
most  affected. 

Hence  the  title  which  he  affixed  to  his  discovery — "  The 


APP.  H.]  RADIUM  219 

illumination  of  the  lines  of  magnetic  force  and  the  magneti- 
sation of  light "  — may  be  regarded  as  a  prophetic  flash  of 
genius. 

A  not  altogether  dissimilar  flash  has  already  been 
referred  to,  when  Crookes  hinted  prematurely  that  in  the 
cathode  rays  we  had  something  like  corpuscular  light,  and 
also  like  matter  in  a  fourth  state,  neither  solid,  liquid,  nor 
gaseous.  For,  whether  quite  right  or  not,  he  was  far 
more  right  than  the  critics  of  those  days  who  presumed 
to  deride  him. 


APPENDIX  J. 
On  the  /2-rays  from  Radium. 

Magnetic  deflexion  of  Beta-rays. 

The    following    diagram   illustrates   the   spreading   out 
into   a    sort    of    spectrum    of    the    Beta-rays    or    electric 
particles  shot  out   with  different  velocities  from  radium. 
Some  are  only  slightly  bent, — being  very  speedy. 
c          did      <** 


a  represents  the  source  of  radiation ; 

b  an  aperture  through  which  the  rays  have  to  pass; 

c  the  impression  which  would  be  produced  on  the 
photographic  plate  with  a  magnetic  field  absent,  and 

dv  d,  dz  the  impress  on  the  same  plate  due  to  the 
deflected  rays. 


220  RADIUM  [APR  j. 

In  a  uniform  magnetic  field  the  rays  will  all  be  seg- 
ments of  circles,  and  it  is  easy  to  estimate  the  radius  of 
curvature  of  the  ray  corresponding  to  any  point  in  the 
spectrum,  since  only  one  circle  can  be  drawn  through 
three  given  fixed  points  (Euclid,  IV.  5  or  III.  25),  such  points 
for  instance  as  a,  6,  and  d  ;  so,  these  three  points  being 
known,  the  circle  of  which  the  ray  forms  a  part  is  known, 
and  its  radius  of  curvature  is  therefore  determined. 

Electric  charge  carried  by  Beta-rays. 

The  fact  that  ordinary  cathode-rays  are  negatively 
electrified  was  proved  most  conclusively  by  Perrin  with 
an  apparatus  diagrammatically  represented  in  the  figure; 
where  a  represents  the  cathode, 

6  an  earthed  diaphragm  with  small  aperture,  and 
c  a  Faraday  cavity  or  hollow  vessel,  arranged  to 
catch  the  rays  in  its  interior  and  convey  the 
charge  to  an  electroscope. 


b\     c         ^ 
I  i          I       """"^e.  Electroscope 


It  is  not  so  easy  to  prove  that  the  beta  rays  emitted 
by  radium  are  electrified,  because  the  air  and  everything  in 
the  neighbourhood  is  rendered  conducting  by  their  impact, 
but  Professor  Curie  succeeded  in  establishing  the  fact  by 
enclosing  a  piece  of  metal  completely  in  solid  paraffin, 
and  showing  that  when  exposed  to  the  rays  this  metal 
became  charged. 

Strutt  exhibits  the  converse  effect  in  a  simple  and 
interesting  manner  by  hanging  up  a  radium  tube  in  a 
vacuum  and  attaching  to  it  a  pair  of  gold  leaves.  As 
the  electric  rays  are  shot  away  by  the  radium  the  leaves 
diverge  with  an  opposite  charge;  they  go  on  diverging 


APR  j.]          CHARGE   IN   RAPID   MOTION  221 

to  the  full  extent,  and  collapsing  when  they  touch  the 
boundary,  for  as  long  as  the  radium  lasts,  which  must 
be  many  centuries. 

Strutt's  apparatus  was  shown  in  figure  22,  page  177. 

For  a  good  and  clear  elementary  account  of  the  pheno- 
mena exhibited  by  radium,  especially  of  all  those  most 
important  facts  which  have  reference  to  things  other  than 
electrons, — such  as  alpha-rays,  the  emanations,  and  the 
transmutations  of  matter, — the  book  on  The  Becquerel  Rays 
and  the  Properties  of  Radium,  by  the  Hon.  R.  J.  Strutt, 
may  satisfactorily  be  referred  to,  as  an  introduction  to 
Prof.  Rutherford's  treatise. 


APPENDIX   K. 

Note  on  the  Behaviour  of  a  Charge  Moving  Nearly  at  the 
Speed  of  Light. 

According  to  investigations  by  Larmor  in  the  Phil. 
Trans.,  1897,  pp.  228-9,  and  also  according  to  the  investi- 
gations of  Mr.  Searle  (Phil.  Mag.,  Oct.  1897)  a  charge 
does  not  re-distribute  itself  on  a  moving  body  when  its 
speed  becomes  great,  but  the  lines  of  force  bend  or 
are  deflected  towards  the  equator,  without  remaining 
normal  to  the  surface  whence  they  start.  Any  un- 
certainty on  this  head  seems  to  have  been  due  to  a 
natural  confusion  between  the  electric  force  acting  on 
the  convected  charge  and  the  etherial  force  which  would 
act  on  charges  at  rest,  or  would  cause  corresponding  '  dis- 
placement' in  force  ether;  the  former  must  be  normal  to 
a  perfect  conductor,  but  the  latter  need  not :  an  assertion 
in  which  we  may  trace  some  analogy  to  the  fact  that  in 
a  moving  medium  rays  of  light  are  not  perpendicular  to 
their  wave  fronts. 


222  CHARGE   IN   RAPID   MOTION         [APR  K. 

There  is  no  question  but  that  the  lines  of  force  bend 
back  towards  the  equator,  as  stated  by  me  in  1902,  but  I 
assumed  that  this  deflexion  of  the  lines  would  entail  their 
moving  up  nearer  to  the  equator  of  the  sphere,  so  as  to 
leave  the  poles  bare  of  charge,  in  order  that  the  lines 
might  still  continue  radial.  I  admit  that  the  lines  of  force 
need  not  continue  radial  close  to  the  sphere;  but,  in  so 
far  as  the  sphere  changes  its  shape,  there  should  still  be 
some  unimportant  redistribution  of  the  charge  as  the 
speed  increases.  Mr.  Searle  calculates  that  whereas  a 
sphere  at  rest  acts  as  if  its  charge  were  at  a  central 
point,  this  equivalent  point  opens  out  into  a  uniformly 
charged  line,  forming  a  medial  and  small  portion  of  its 
diameter,  when  the  sphere  is  in  motion ;  as  the  velocity 
increases,  the  length  of  this  line  gradually  increases  also, 
until  the  speed  equals  that  of  light,  when  it  fits  the  sphere 
exactly.  But  this  leaves  out  of  account  a  distortional 
change  in  the  sphere  itself,  to  which  I  will  presently  refer. 

The  fact  is  that  the  behaviour  of  a  charged  body  moving 
at  enormous  speed  may  be  treated  exactly  in  the  manner  of 
elementary  potential  theory  for  a  charged  ellipsoid  at  rest. 

It  is  doubtful  whether  the  term  "  inertia  "  remains  useful 
under  these  conditions:  it  is  perhaps  best  to  reserve  it 
for  the  ordinary  case  when  mass  is  constant ;  for,  as 
Mr.  Searle  points  out,  three  different  estimates  of  inertia 
can  be  made: — one  the  ratio  of  force  to  acceleration, 
another  the  ratio  of  momentum  to  velocity,  and  a  third 
as  the  ratio  of  kinetic  energy  to  half  the  square  of 
velocity.  In  ordinary  matter,  as  is  well  known,  and  for 
slow  electric  motions,  these  three  estimates  are  one  and 
the  same;  but  for  violent  electric  motions  they  become 
different;  though  it  should  be  realised  how  small  the 
difference  is,  until  the  speed  of  light  is  very  closely  ap- 
proached ;  so  that  in  no  material  case  of  great  velocity  or 


APR  K.]         CHARGE    IN   RAPID    MOTION  223 

great  acceleration  that  has  ever  been  practically  dealt 
with — as,  for  instance,  the  case  of  a  cannon-ball  stopped  by 
armour  plate — is  any  sort  of  unusual  effect  to  be  expected  ; 
even  on  the  hypothesis  that  matter  is  entirely  electrically 
composed.  Nevertheless,  now  that  among  free  corpuscles 
in  a  vacuum  tube,  or  among  those  expelled  from  radium, 
it  is  becoming  practically  possible  to  attain  these  high 
speeds,  and  even  to  begin  to  base  crucial  determinations 
upon  them,  it  becomes  necessary  to  consider  the  matter 
more  carefully.  In  a  publication  at  Gottingen  in  January, 
1902,  Dr.  Abraham  has  thus  discriminated  what  he  calls 
"  longitudinal "  from  what  he  calls  "  transverse  "  inertia ; 
making  inertia  depend  not  only  on  the  speed  but  on  the 
direction  of  acceleration;  each  direction  having  a  different 
inertia  of  its  own. 

And  all  these  results  are  still  further  complicated  by  a 
consideration  of  the  effect  of  acceleration  itself,  which, 
whenever  it  is  violent,  gives  rise  to  some  perceptible 
radiation,  involving  dissipation  of  energy;  and  this  radia- 
tion loss  of  energy,  though  it  will  be  primarily  represented 
in  the  motion  as  a  resistance  or  velocity  term,  may  second- 
arily have  an  effect  on  inertia; — probably,  however,  quite 
a  small  and  subordinate  effect  in  all  practical  cases,  and 
no  effect  at  all  so  long  as  motion  occurs  with  uniform 
speed  in  a  straight  line:  for  then  there  is  no  radiation. 
But  then,  of  course,  under  those  conditions  it  is  not  possible 
to  test  or  measure  the  inertia  of  a  body ;  it  is  only  when 
the  motion  is  either  curved  or  changed  in  some  way  that 
inertia  becomes  prominent,  and  then  there  is  necessarily 
some,  though  usually  very  small,  radiation  too. 

When  magnetic  deflexion  of  a  charged  body  is  being 
observed  at  ultra-high  speeds  it  may  be  asked  whether 
it  is  possible  for  the  ordinary  expression  for  the  force 
exerted  on  a  current  by  a  moving  field  to  be  departed  from. 


224  CHARGE   IN   RAPID   MOTION         [APR  K. 

The  ordinary  expression  for  deflecting  force  is  euB.  at 
low  speeds,  for  a  charge  e  moving  at  speed  u  across  a 
magnetic  field  of  intensity  H;  but  whether  this  simple 
expression  is  departed  from  at  rhigh  speeds  must  be  a 
question  of  etherial  dynamics:  the  procedure  of  Larmor, 
based  on  the  principle  of  'Least  Action'  (see  ^Ether  and 
Matter,  p.  97),  would  give  an  answer  in  the  negative, — 
which  agrees  with  the  assumption  of  Lorentz.  It  has 
been  suggested  by  others  that  for  speeds  at  which  (u/v)2 
becomes  sensible,  we  must  use  the  more  complex  ex- 
pression for  deflecting  force  : — 

rrV2  —  U2/V,        V  +  U       ,  \ 

eH-     — (?r-l0£  — !)• 

u      \2u       v  —  u       / 

This,   however,   at  low   speeds   reduces   not  to  the  usual 

1 
simple  value,  but  to  one-third  of  that  value,  viz.  ^  Heu ; 

and  Professor  Schuster  in  the  Philosophical  Magazine 
for  January,  1897,  calls  attention  to  the  variety  of 
numerical  estimates  of  this  quantity  given  by  different 
varieties  of  the  main  theory.  But  it  appears  to  be  now 
considered  that  there  is  no  real  ambiguity  and  that 
Larmor's  view  is  correct. 

As  has  been  said  above,  at  high  speeds,  not  only  does 
effective  inertia  vary  with  speed,  but  it  has  different 
values  for  different  directions  of  acceleration  relative  to 
the  line  of  motion;  the  value  of  what  Abraham  calls 
"transverse  inertia,"  which  expresses  reaction  to  a  trans- 
verse deflecting  force,  is  quoted  by  Kaufmann  in  Comptes 
Rendus,  vol.  cxxxv,  p.  577,  writing  it  with  ra0  as  the 
equivalent  inertia  for  slow  motion,  and  with  /3  as  the 
ratio  u/v — the  ratio  of  the  velocity  of  the  particles  to 
the  velocity  of  light — thus 


APR  K.]         CHARGE   IN   RAPID   MOTION  225 

and  is  the  formula  appropriate  to  his  experiments.  All 
this  is  in  fact  deducible  at  once  by  the  usual  Lagrangian 
dynamical  method  from  Mr.  Heaviside's  expression — 
Electrical  Papers,  vol.  ii.,  p.  514 — for  kinetic  energy;  viz. 

an  expression  equivalent  to  ~  V?  multiplied  by  the  following 
quantity : — 


a 


r  being  the  squared  speed  ratio  u2/v2. 

In  Larmor's  original  treatment  of  electrical  inertia,  Phil. 
Trans.  185A  (Aug.  1894),  pp.  806-818,  there  was  no  reason 
whatever  for  anticipating  velocities  greater  than  one-tenth 
of  light,  so  a  simple  inertia  theory  seemed  amply  sufficient 
at  that  time;  the  mass  being  a  permanent  constant 
associated  with  the  electron  and  dependent  on  its 
structure. 

It  is  the  hope  of  seeing  somewhat  into  structure  that 
has  made  the  recent  experiments  on  its  modification  at 
high  speeds  so  interesting. 

Professor  J.  J.  Thomson's  corresponding  formula  for 
momentum  is  quoted  above  in  the  text,  page  133,  and 
simplified ;  and  in  simplified  form  it  may  be  re-quoted : 

It  amounts  to  this,  that  the  mass  of  an  electric  charge 
e  on  a  small  non-conducting  sphere  of  radius  a,  moving 
with  a  speed  u  =  v  sin  0,  is — 


which  we  have  tabulated  on  page  145  (see  also  page  133) 
in  the  form — 


L.E. 


226  DISTORTION  [APR  K 

and  to  a  certain  extent  it  must  be  considered  experimentally 
verified  by  Kaufmann's  results.  The  function  0(0)  has 
the  value  unity  when  u  =  0,  or  even  when  u/v  is  small. 


APPENDIX   L. 
Distortion  due  to  High-speed  Motion  through  the  Ether. 

Mr.  Searle,  in  the  Philosophical  Magazine,  October,  1897, 
points  out  that  the  simplest  charged  body  when  in  motion 
is  not  a  sphere,  but  an  oblate  spheroid,  oblate  in  the  direc- 
tion of  motion,  with  its  axes  in  the  ratio  ^(l A  1>  1  > 

and  that  this  produces  on  all  points  outside  itself  exactly 
the  same  effect  as  a  point  charge  at  its  centre:  where- 
fore such  a  spheroid  in  motion  at  the  speed  u  takes 
the  place  of  the  sphere  in  electrostatics.  He  calls  this  a 
Heaviside  ellipsoid,  because  Mr.  Heaviside  first  indicated 
its  importance  in  the  theory  of  moving  charges. 

But  it  is  well  known  that  a  spheroid  of  this  kind  is 
exactly  what  a  sphere  in  rapid  motion  would  auto- 
matically become,  on  the  FitzGerald-Lorentz  theory ;  viz., 
that  hypothesis  which  was  started  in  order  to  account 
for  the  negative  result  in  Michelson's  experiment,  by  postu- 
lating a  change  of  dimensions  in  solid  bodies  according  to 
their  direction  of  motion  through  the  ether.  This  hypo- 
thesis, shown  to  be  plausible  by  Lorentz,  became  a  definite 
theory  when  Larmor  proved  (^Jther  and  Matter,  ch.  xi.) 
that  on  the  electric  theory  of  matter — that  is,  assuming 
that  the  whole  inertia  of  matter  was  electric — not  only 
was  such  a  change  of  dimensions  reasonably  likely,  as 
FitzGerald  had  perceived,  and  likely  also  to  be  of  the 
right  amount  to  give  a  compensating  effect,  and  pre- 


APP.  L.]  DUE   TO   HIGH   SPEED  227 

cisely  zero  resultant,  in  the  Michelson  experiment,  but 
that  the  change  was  a  necessary  consequence  of  dynamical 
molecular  theory. 

The  change  of  dimensions,  thus  imagined  and  justified, 
is  gradually  coming  to  be  accepted  as  certainly  true; 
and  it  is  interesting  to  note  that  a  sphere  in  motion, 
by  reason  of  being  subject  to  this  amount  of  distortion, 
still  retains  its  property  of  being  the  simplest  geometrical 
body,  so  far  as  the  distribution  of  its  electric  field  is  con- 
cerned. True,  it  is  then  no  longer  a  sphere ;  but  no 
measuring  instrument  could  possibly  show  its  distortion, 
because  all  standards  of  measurement  would  share  it.  It 
is  a  remarkable  thing  that  this  imperceptible  and  un- 
rneasurable  uniform  distortion  of  all  matter  should  ever 
have  been  discovered :  nothing  but  an  ethereal  process 
could  have  dragged  it  to  light.  Nevertheless  dragged  to 
light  it  has  been,  by  the  combined  testimony  of  electrical 
theory  and  of  optical  experiment. 


APPENDIX  M. 
Constitution  of  Electrons. 

In  continuation  of  the  subject  treated  of  in  appendices 
K  and  L  we  may  consult  Larmor,  Phil.  Trans.  190A 
(April,  1897),  pp.  225-8.  In  ^Ether  and  Matter  (1898), 
ch.  xi.,  he  substituted  an  improved  (dynamical)  investiga- 
tion, applicable  to  a  system  of  molecules  in  the  most 
complicated  motion,  wherein  he  claims  to  cover  all 
possible  cases,  on  the  single  hypothesis  that  the  electrons 
in  an  atom  are  at  distances  apart  compared  with  which 
the  diameters  of  their  structure  are  very  small,  so  that 
they  may  be  treated  as  points.  On  that  hypothesis 


228  CONSTITUTION   OF   ELECTRONS      [APR  M. 

uniform  convection  of  a  system  at  any  speed  however 
high  should  show  no  internal  influence,  provided  the  con- 
stitution of  matter  is  wholly  electric,  i.e.  provided  atoms 
are  active  only  through  the  aether.  The  very  important 
(because  purely  electrical)  experiment  of  Trouton  and 
Noble  is  a  case  in  confirmation.  So  is  the  absence 
of  influence  on  either  of  the  two  phenomena,  magnetic 
rotation  and  double  refraction  (Rayleigh  and  Brace). 

It  is  true  that  this  way  of  explaining  the  absence 
of  any  second  order  aberration-effect  was  received  with 
scepticism  by  Poincare'  (Paris  Congress,  1900),  whose  criti- 
cism was  that  if  in  future  the  third  order  effect  also 
needed  annulment  some  new  artificial  arrangement  could 
still  be  added  on,  to  do  even  that.  The  result  of  the 
argument  has  now,  however,  gained  the  independent 
support  of  Lorentz  (1904),  whose  investigation  has  sug- 
gested, what  in  fact  is  easily  verified,  that  Larmor's 
work  proves  to  be  exact:  his  restriction  to  the  second 
order  being  unnecessary.  He  was  hardly  concerned,  how- 
ever, to  go  further,  since  the  hypothesis  of  the  infinitesimal 
effective  size  of  the  electron  already  limited  the  investi- 
gation,— nor  does  it  seem  that  Lorentz's  work  really  carries 
the  matter  further.  Larmor's  attitude  has  been  all  along 
(Phil.  Mag.,  June,  1904),  that  this  provisional  hypothesis 
holds  the  £eld  until  some  effect  of  uniform  convection 
presents  itself :  every  new  negative  result  is  a  steady 
corroboration  of  it:  but  like  any  other  physical  repre- 
sentation it  must  ultimately  reach  the  limits  of  its  appli- 
cation. 

Only  negative  electrons  are  known  in  the  free  state. 
It  remains  unsettled  whether  this  is  due  to  some  one- 
sidedness  in  the  experimental  means  hitherto  employed, 
or  whether  physical  nature  is  in  reality  intrinsically  un- 
symmetrical.  If  the  positive  electron  were  a  region  of 


APP.  M.]  LARMOR'S   THEORY  229 

singularity  (beknottedness)  of  dimension  large  compared 
with  the  negative,  it  would  be  but  a  feeble  agent  in  the 
transformation  of  energy,  and  thus  could  readily  escape 
detection.  Cf.  Jfther  and  Matter,  §  122.  But  the 
absolute  structure  of  an  electron  is  probably  very  unlike 
the  distributions  of  electric  charge  on  spheres  and  ellip- 
soids that  have  hitherto  been  taken  to  represent  it. 

The  theory  of  a  simple  molecule  appeared  for  the  first 
time  in  Phil.  Trans.,  13th  August,  1894,  pp.  806-818; 
inertia  purely  electric,  on  p.  807 ;  estimate  of  size  and 
dimensions,  and  electrodynamics  of  orbital  motions,  on 
p.  814;  Hall  effect,  etc.,  on  p.  815.  There  does  not 
appear  to  be  anything  in  Lorentz's  papers,  either  of  1892 
or  1895,  to  correspond  to  the  ideas  there  introduced. 

With  reference  to  a  theory  of  the  Zeeman  effect : .  the 
simplest  type  of  illustrative  system,  amenable  to  calcu- 
lation, would  be  a  statical  one,  in  which  the  electrons 
would  all  vibrate  round  positions  of  stable  equilibrium. 
But  this  requires  extraneous  supporting  force,  if  they  are 
in  empty  space.  A  definite  subdivision  of  the  periods 
has  been  worked  out  for  J.  J.  Thomson's  statical  illustra- 
tion, in  which  this  innate  instability  of  a  statical  system 
of  negative  electrons  (Earnshaw's  theorem)  is  obviated 
by  supposing  them  inside  a  region  of  continuous  positive 
electrification, — which  may  be  taken  to  represent  the  posi- 
tive electron.  If  the  volume  density  of  this  is  small,  the 
resulting  stability  will  be  but  slight,  and  a  small  displace- 
ment will  upset  the  system,  and  lead  to  its  break-up ; — 
which  is  unlikely,  perhaps  unreasonable. 

But  here,  as  before,  it  is  only  isotropic  configurations, 
in  the  same  sense  as  in  the  hydrokinetics  of  solids  in 
fluids, — namely,  those  with  which  an  associated  quadratic 
function  must  be  wholly  isotropic,  including  the  configura- 
tions of  the  regular  solids, — that  split  the  lines  definitely 


230  CONSTITUTION   OF  ELECTRONS     [APP.  M. 

instead  of  merely  broadening  them :  other  types  will  only 
do  so  when  they  are  all  similarly  orientated  to  the  in- 
ducing magnetic  field. 

The  experiments  of  Kaufmann  held  out  a  hope  that 
we  should  get  to  know  something  definite  about  intrinsic 
electron  structure.  They  have  proved  sufficiently  the 
fundamental  fact  that  a  free  electron  has  no  independent 
material  sub-stratum :  they  have  made  it  very  probable 
that  it  may  be  provisionally  represented  as  a  region  of 
electricity  spherically  stratified :  also  that  convection  of 
an  electron  does  not  affect  the  volume  relations  of  this 
distribution  (Bucherer);  but  unfortunately  it  has  not 
proved  possible  to  push  on  the  precision  of  the  experi- 
ment so  as  to  get  information  beyond  this. 

We  must  still  be  content  to  treat  the  electron  as  a  point, 
or  at  most  as  a  spherical  electric  aggregate  of  some  sort 
whose  volume  does  not  undergo  shrinkage.  But  the  in- 
direct evidence  afforded  by  the  entire  absence  of  convection 
effects  of  many  kinds,  such  as  the  earth's  motion  might 
be  supposed  to  excite,  is  strongly  in  favour  of  the  pro- 
visional theory  that  the  ultimate  elements  of  which 
atoms  are  constituted  are — in  their  dynamical  relations — 
purely  aethereal  structures  of  some  sort  which  probably 
we  cannot  yet  adequately  imagine. 


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